The invention of lasers has led to a boom of laser technology in various science and engineering of many interdisciplinary fields, which have been widely applied in optical manipulation, precision measurement, optical communication, laser processing, microscopy imaging, and so on. However, the simple propagation characteristics of the traditional Gaussian laser mode have hit the bottleneck in the further development of laser technology and failed to meet the ever-increasing needs in the related fields. Consequently, light field manipulation has emerged. By modulating the amplitude, phase, and polarization of the light field, many new types of spatially structured fields with novel physics effects or propagation properties have been proposed. Optical vortices and cylindrical vector beams are among the most well-known examples. To resist beam diffraction and environment disturbance, researchers have discovered a new class of spatially-structured field named “non-diffracting beam”. Theoretically, a non-diffracting beam can maintain its transverse intensity profile during propagation and can propagate over long distances with little beam spreading. Subsequently, a series of non-diffracting beams with different spatial structures, such as Mathieu beams, Weber beams, Airy beams, and Bessel beams, have been proposed, all of which exhibit the common characteristics of non-diffracting beams. As a typical non-diffracting beam, the Bessel beam quickly attracts great attention of research after being proposed as a propagation-invariant solution of the Helmholtz equation. Extensive research has been conducted on non-diffracting beams, including the applications in improving microscopy imaging quality and the performance of optical trapping. With the continuous development of light field manipulation, researchers have gradually attempted to control Bessel beams through different means by modulating or superposing the Bessel beams. Modulated Bessel beams can behave the self-accelerating propagation with nonlinear trajectories, with tunable on-axis intensities and polarizations, or even generate propagation-varied modes, which are different from traditional Bessel beams. Combining Bessel beams with other spatially structured light fields or optical elements for light field modulation would further expand the freedom degree for controlling Bessel beams. In this review, hence, we introduce the basic theory and generation methods of Bessel beams and review the research progress of the propagation control of Bessel beams, including the trajectory control, on-axis intensity management, longitudinally control of polarization, and self-similar Bessel beams.

In section 2, we introduce the basic characteristics of Bessel beams. Subsection 2.1 presents the solution of Bessel modes from the Helmholtz equation. Typical intensity and phase profiles of Bessel beams with different orders are represented (Fig. 1). The principle and several methods of generating Bessel beams are introduced in subsection 2.2. Fig. 2(a) shows the conical wave vector of Bessel beams, based on which two typical methods of generating Bessel beams with annular aperture and axicon are represented in Figs. 2(b) and 2(c), respectively. Based on the axicon-type phase, we propose a computer-generated hologram [Fig. 2(d)] and dielectric metasurface [Fig. 2(e)] to generate Bessel beams. Additionally, we introduce some other methods with the Fabry-Perot resonator [Fig. 2(f)] and optical fibers. Fig. 3 demonstrates the self-healing properties of Bessel beams. In section 3, we introduce the propagation trajectory control of Bessel beams. Subsection 3.1 presents the spiral Bessel beams, including radially self-accelerating beams (Fig. 4), accelerating rotating beams produced by the superposition of nonlinear vortex beams (Fig. 5), and spiraling zero-order Bessel beams produced by splicing the beam cone (Fig. 6). In subsection 3.2, the Bessel-like beams propagating along arbitrary trajectories based on caustic principle and pure phase modulation are shown in Figs. 7 and 8, respectively. The controllable spin Hall effect of the Bessel beam realized by geometric phase elements is introduced (Fig. 9). Subsection 3.3 represents the nonparaxial self-accelerating beams in Fig. 10, based on which tightly autofocusing beam is proposed (Fig. 11). In section 4, we introduce the axial intensity engineering of Bessel beam. In subsection 4.1, we introduce the theory of “Frozen Waves” (Fig. 12) and the modified “Frozen waves” following spiral and snake-like trajectories (Fig. 13). In subsection 4.2, the on-axis intensity modulation based on the spatial spectrum engineering [Fig. 14(a)] is introduced. By using metasurface, the on-axis intensity with rectangle and sinusoidal profiles are realized [Figs. 14(b) and 14(c)]. The on-axis intensity management is also applied to the self-accelerating Bessel beams to realize the on-demand tailored intensity along arbitrary trajectories [Fig. 14(d)]. Section 5 introduces the longitudinal control of the polarization of the Bessel beam. In subsection 5.1, the Bessel beams with propagation-varied polarization state are proposed based on the transverse- longitudinal mapping (Fig. 15). Based on the mapping, the vector Bessel-Gauss beams with propagation-variant polarization state and the corresponding self-healing are introduced (Fig. 16). In subsection 5.2, polarization oscillating beams constructed by superposing the copropagating optical frozen waves are shown in Fig. 17. In subsection 5.3, we introduce the longitudinal polarization control via the Gouy phases of beams. The self-accelerated optical activity in free space according to the Gouy phase difference between the Bessel beam and Laguerre-Gauss beam is shown in Fig. 18. We introduce the analogous optical activity in free space using a single Pancharatnam-Berry phase element, which can highly resemble the on-axis circular birefringence of beams. Fig. 19(a) shows the polarization rotator based on the theory. In addition, the off-axis circular birefringence, triggered by a tilted input Bessel beam, can generate the photonic spin Hall effect, which can be enhanced by inputting a self-accelerating Bessel-like beam [Fig. 19(b)]. In section 6, we introduce the self-similar Bessel-like beam, including self-similar beams with different scaling factors by solving the paraxial wave equation (Fig. 20), self-similar arbitrary-order Bessel-like beams based on the Fresnel integral (Fig. 21), and constructing arbitrary self-similar Bessel-like beams via transverse-longitudinal mapping (Fig. 22).

Modulated Bessel beams exhibit increased controllability during propagation while retaining the non-diffracting and self-healing properties. The trajectory, intensity, polarization state, and beam width can be flexibly controlled in the propagation direction. These characteristics have significant potential in various applications, including optical manipulation, microscopy imaging, and precision machining.

To help humans explore and understand the world, researchers have been committed to exploring diverse techniques of optical field manipulation to accomplish a variety of applications since the inception of the field of optics, including imaging, detection, sensing, communications, and so on.

With the rapid development of modern micro-nanofabrication techniques, there is increasing interest in manipulating multiple degrees of freedom of light flexibly. However, at the nanoscale, there are close couplings and interactions among classical degrees of freedom such as intensity, phase, and polarization, making it difficult to achieve flexible and independent control of these degrees of freedom. Whereas, momentum and angular momentum degrees of freedom of light, which are a fundamental dynamic physical quantity of elementary particles and class wave fields and play important roles in the light-matter interactions, offer extreme advantages in manipulating the light in the nanoscale. For example, through the spin-momentum equation, spin and orbit angular momentum can be individually controlled, allowing for more precise manipulation and utilization of the spin properties of photons individually. The numerous advantages of controlling the spin angular momentum of photons bring new opportunities for nanophotonics, particularly in the areas of optical manipulation, detection, information processing, chiral quantum optics, and quantum entanglement.

Plenty of novel and interesting optical phenomena and applications have been proposed connecting to the interactions between optical spins and matters or nanostructures, and a new research field of spin optics has been born in recent years. Previously, most of the researchers mainly focused on the optical longitudinal spin parallel to the direction of the mean wave vector. In recent years, by studying the spin-orbit couplings of confined fields, such as focused fields, guided waves, and evanescent waves, researchers have discovered a new class of optical spins that are perpendicular to the direction of the mean wave vector, which are also known as optical transverse spins. Optical transverse spin possesses the properties of spin-momentum locking, so it has been widely studied by researchers since discovered. Moreover, the discovery of optical transverse spin expands the content of optical spin-orbit interactions, and it has potential in the applications of optical manipulation, ultrahigh-precision optical detection, chiral quantum optics, and optical spin topological states. Here, we introduce the recent progress of spin optics in detail from three aspects: theory, characterizations, and applications. These theoretical concepts and frameworks of spin optics can play a critical role in further developing applications based on optical spins in optical imaging, detection, communications, and quantum technology, and they can be flexibly expanded to other classical wave fields, such as fluid waves, sound waves, and gravitational waves.

In this paper, we provide a comprehensive overview and summary of the manipulating mechanisms of spin angular momentum and discuss the underlying relationship between the Abraham-Poynting momentum density, Minkowski canonical momentum density, Belinfante's spin momentum density, spin angular momentum density, and orbital angular momentum density in classical optical theory. Subsequently, starting from the longitudinal spin in the paraxial beams, we introduce the spin angular momentum in different optical fields, including transverse spin in evanescent fields and transverse spin in interference fields. Finally, to address the difficulty in simply defining transverse and longitudinal spins in structured light fields, we present a set of spin momentum equations, analogous to Maxwell's equations, to describe the dynamical properties of spin angular momentum density and momentum density. Furthermore, these spin-momentum equations extend the properties of optical spin-momentum locking from evanescent plane waves to general evanescent fields. We also comprehensively overview the measurement techniques for spin angular momentum in confined fields and free space, including scanning near-field optical microscopy, nano-particle-film structures, photoemission electron microscopy, and nonlinear optical effects. By utilizing these techniques, it is possible to effectively extract different electromagnetic field components to obtain the information of spin angular momentum carried by the optical field. The current application scenarios of spin angular momentum are also comprehensively summarized, including weak effect measurements, optical differentials, optical lateral forces, precision sensing, and magnetic domain detection.

As a novel degree of freedom in the field of optics in addition to intensity, phase, and polarization, the spin angular momentum carried by the structured light can be applied in communication, imaging, precision detection, and other fields. In this paper, we introduce the concept, definition, classification, and physical origin of spin angular momentum and review the characterization methods of spin angular momentum developed in recent years, as well as its applications in weak effect detection, optical differentials, optical lateral forces, precision sensing, and magnetic domain detection. On the one hand, spin angular momentum is a fundamental dynamical physical quantity of basic particles such as photons and atoms, providing new perspectives for the interaction of small-scale light with matter. On the other hand, as a novel optical degree of freedom, spin angular momentum can provide new solutions for large-scale light field control, optical imaging, optical communication, and optical detection applications. In turn, it further serves to explore new mechanisms and phenomena in the interaction between light and matter, expanding the applications of spin photonics.

The two-dimensional photonic crystal slab (PhCS) is a structure characterized by the spatial periodicity of the dielectric constant within the plane. In contrast to traditional metamaterial surfaces, the two-dimensional PhCS enables light field manipulation in momentum space based on the Fourier principle, thus achieving complex and diverse functionalities. Since modes above the light cone can radiate to the far field and possess definite polarization states, polarization is matched with wave vectors, defining polarization fields in momentum space. Various polarization singularities exist within the polarization field, such as V points and C points. Previous studies generally focus on information such as frequency and momentum, while the polarization field can reflect the topological information of the bands and provide a new dimension for light field manipulation. For example, by controlling the evolution of polarization singularities, researchers have obtained bound states in the continuum (BICs) with robust characteristic and unidirectional guided resonances (UGRs). By utilizing these characteristics, researchers have designed high-performance lasers and realized complex light field manipulation and such functionalities as optical information processing. Compared to traditional structures, the two-dimensional PhCS exhibits non-local characteristics and has significant advantages in miniaturization and integration. Thus, it holds promising prospects for device applications. Studying the evolution of the polarization field helps guide the structural design of photonic crystal slabs, which expands the applications in communication, sensing, and other fields, and provides a deeper understanding of how topological photonics is manifested in optical systems.

We start by introducing the definition of the polarization field in the momentum space of the two-dimensional PhCS and introduce the concept of polarization singularities (Fig. 1). Subsequently, an analysis is conducted from the perspective of symmetry, with the relationship between the topological charge of polarization singularities and the in-plane point group symmetry examined (Fig. 2 and Table 2). Additionally, we outline the description of the polarization field using the temporal coupled mode theory (TCMT). Furthermore, the conservation law followed by the topological charges during their evolution is discussed (Fig. 3) to detail the research on the evolution of polarization singularities based on whether the band is non-degenerate or degenerate. It is observed that non-degenerate V points correspond to BICs and are split into more fundamental C points during symmetry change (Fig. 4). The evolution of these polarization singularities is controlled by structural parameters and symmetry (Fig. 5). Degenerate V points typically correspond to band degeneracy points and are also influenced by structural parameters and symmetry (Fig. 6). Based on the evolution patterns of polarization singularities, researchers have designed robust merging BICs and utilized the topological charge to generate vortex beams and beam shifts (Fig. 7), providing significant guidance for laser design. Furthermore, by altering the out-of-plane symmetry, UGR can be achieved (Fig. 8). Additionally, appropriately designed PhCS can achieve full coverage on the Poincaré sphere and perform complex image processing tasks such as edge detection (Fig. 9).

Generally, the investigation of the polarization field characteristics of PhCS guides the design of appropriate structures and can help achieve complex and rich functionalities. Despite the presence of numerous unresolved physical issues currently, the application potential of the polarization field remains largely untapped. However, these unknowns are expected to stimulate enthusiasm for exploration and boost progress in related fields.

Light is an indispensable carrier of energy and information in humans' daily life. The main information of light fields can be described by a few attributes such as amplitude, phase, frequency, and polarization. How to flexibly and effectively manipulate these light field dimensions has been a key research focus in optics and photonics. Meanwhile, with the development of technology, “Moore's Law” is gradually losing its effectiveness, and traditional electronic chips are facing increasing performance improvement challenges. Compared with electrons, photons have fast transmission velocity, high information-carrying capacity, and unique parallel processing capability. Therefore, replacing electronic components partially or completely with optical components is expected to solve many problems facing traditional electronic chips. However, traditional optical components are generally large in size and heavy. Therefore, the miniaturization and integration of multiple optical components into the same chip is an important trend in the future development of photonic chips.

Optical artificial microstructure (also called“metaatom”) is a kind of artificial structure with subwavelength size in one or more dimensions, which can resonate with light fields to achieve functions beyond traditional natural materials. A metasurface can be formed by ordering optical artificial microstructures on a two-dimensional surface. It provides not only practical and effective solutions for the miniaturization and integration of traditional optical components but also more diverse means of controlling light fields and richer light-matter interactions. However, most current metasurfaces are focused on the manipulation of free-space light fields, and a metasurface can only achieve a single or a few functions. To further achieve more compact and versatile photonic chips, researchers have begun to integrate optical artificial microstructures with on-chip optical waveguides or optical microcavities in recent years. The research on on-chip integrated artificial microstructures injects new vitality into light field manipulation and nano-photonics devices. Thanks to their subwavelength sizes and unique resonance characteristics, artificial microstructures can serve as a bridge connecting free-space light fields with on-chip waveguide modes, thus opening up new opportunities for fully manipulating light in integrated optical systems and free space. Even though various novel optical devices have been proposed based on on-chip integrated artificial microstructures in the past few years, they still face a series of challenges in large-scale ultra-compact integration and performance improvement. Therefore, a review of light field manipulation based on on-chip integrated artificial microstructures is necessary to provide helpful guidance for researchers to design novel on-chip optical devices.

Based on different types of light fields manipulated by on-chip integrated artificial microstructures, we categorize them into three classes for discussions (Fig. 1). The first category involves “meta-couplers” that can couple free-space optical modes into waveguides or microcavities and convert them into specific guided modes. The artificial microstructure-based meta-couplers can achieve more diverse and complex functions than traditional grating couplers, such as wavelength- and polarization-demultiplexing, or the excitation of specific guided modes (Fig. 2). The second category involves “in-plane modulators” that enable on-chip manipulation of confined light fields within the chip plane. Artificial microstructures can be either partially- or fully-etched aperture antennas, or they can be directly integrated onto the waveguide surface. By adopting the refractive index perturbation or phase gradient provided by the microstructures, in-plane focusing of waveguide modes, filters, mode conversions between different guided modes, and on-chip nonlinear harmonic generations can be achieved (Figs. 3 and 4). Additionally, on-chip integrated artificial microstructures can be combined with dynamic control schemes such as electro-optic modulators to further optimize the modulator's footprint and bandwidth performance. The third category involves “guided wave-driven metasurfaces” that can convert guided waves into free-space waves. By employing one-dimensional (Fig. 5) and multi-dimensional (Figs. 6 and 7) manipulation of far-field radiation, guided wave-driven metasurfaces can achieve various applications, such as holographic imaging, vortex beam generation, beam focusing, and beam deflection. Theoretically, the polarization, amplitude, phase, and orbital angular momentum of the emitted light field can be manipulated arbitrarily to provide new solutions for applications such as virtual reality, augmented reality, and information encryption and multiplexing.

We systematically introduce the research progress of on-chip integrated artificial microstructures in the areas of free-space light coupling, in-plane manipulation of guided modes, and the manipulation of off-chip radiated fields. Additionally, we provide an outlook on some emerging directions in this field. By cascading multiple optical metasurfaces on waveguides, on-chip optical components can be more compact, and multifunctional devices beyond traditional metasurfaces can be realized. Some novel physical effects such as bound states in the continuum, parity-time symmetry, and exceptional points can provide a richer range of physical processes for on-chip integrated artificial microstructures. The introduction of new materials such as two-dimensional materials and laser gain materials can provide a new platform for studying excitons, valley spin, nonlinear effects, on-chip lasing, and other phenomena. The utilization of inverse design methods such as deep learning and topological optimization can serve as powerful tools for designing on-chip integrated artificial microstructures. In summary, with the advancement of technology, the application scope of on-chip integrated artificial microstructures will become more widespread. The operating wavelength range can expand from visible and near-infrared light to terahertz, microwave, and ultraviolet wavebands. Additionally, numerous miniaturized and integrated on-chip photonic devices will continue to emerge with the help of artificial microstructures.

The significance of optical skyrmions and the research around them cannot be overstated. Optical skyrmions which are topologically protected spin textures have attracted considerable attention due to their unique properties and potential applications in various fields. The skyrmion is a unified model of nucleons initially proposed by British particle physicist Tony Skyrme in 1962 and behaves like a nano-scale magnetic vortex with intricate textures. Meanwhile, it occupies significant positions in quantum field theory, solid-state physics, and magnetic materials. Skyrmions are widely regarded as efficient information carriers thanks to their unique topological stability, high speed, high density, and low energy consumption. However, generating optically controlled skyrmions remains a significant challenge. Breaking the limitation of topological control for skyrmions will unlock infinite possibilities for the next-generation information revolution, including applications in optical communication, information encryption, and topological phase transitions. This will present new opportunities for the expansion and practical application of advanced fundamental theories of photonics. Optical skyrmions exhibit nontrivial topological structures, robustness against external perturbations, and ultra-fast motion dynamics, serving as promising candidates for the development of novel information storage and processing technologies. Studying optical skyrmions is essential for several reasons. First, optical skyrmions provide a new paradigm for information storage with high-density and low-energy requirements. Their topological nature ensures stability against thermal fluctuations and material defects, which makes them highly reliable for long-term data retention. This property is particularly valuable in the era of big data and cloud computing, where efficient and durable information storage solutions are in high demand. Second, the unique properties of optical skyrmions make them ideal for spintronic applications. Spintronics, which utilizes the spin of electrons for information processing, has emerged as a promising field for the development of next-generation electronic devices. Optical skyrmions provide a means of manipulating and controlling spin currents, thus enabling the design of novel spin-based devices, such as spin transistors, logic gates, and memory elements, with enhanced functionality and reduced power consumption. Furthermore, the study of optical skyrmions can shed light on fundamental physics principles and contribute to our understanding of condensed matter physics. The complex interplay between spin, magnetism, and topology in optical skyrmions poses intriguing scientific challenges and opens up new avenues for exploring new phenomena. Additionally, investigating the formation, dynamics, and interactions of optical skyrmions can provide valuable insights into the fundamental laws governing quantum systems and promote the development of advanced theoretical frameworks. Meanwhile, optical skyrmions hold promise for applications in photonics and optoelectronics. The ability to control and manipulate light at the nanoscale is of significance in fields such as telecommunications, data transmission, and sensing. Optical skyrmions provide a new approach to achieving efficient light modulation, waveguiding, and information encoding, thereby enabling the development of compact and high-speed photonic devices with improved performance. In summary, the study of optical skyrmions is of paramount significance due to their potential applications in information storage, spintronics, fundamental physics research, and photonics. By unraveling the unique properties and behavior of optical skyrmions, researchers can pave the way for innovative technologies that can revolutionize various domains. Continuous exploration of this field will undoubtedly lead to exciting discoveries and transformative advancements in science and technology. In recent years, there has been a continuous emergence of optical skyrmions with different topological structures and vector configurations, including transient field skyrmions, structured medium skyrmions, free-space skyrmions, spacetime skyrmions, and momentum space skyrmions. In particular, spin skyrmions in transient fields and Stokes skyrmions in free space provide valuable references for skyrmion applications. However, the practical applications of optical skyrmions still face a series of challenges. Therefore, it is important and necessary to summarize the existing research achievements and provide more rational guidance for the future development of this field's applications.

We review the current research progress of optical skyrmions, and discuss in detail the topological structure classification of optical skyrmions, the generation and manipulation of optical skyrmions with different vector configurations, and the potential applications of optical skyrmions in micro-displacement measurement and optical communication encoding and encryption. As a result, references are provided for further development in this field. With the flourishing topological optics, the existence of optical skyrmions has been confirmed by the scientific community. In 2018, the research team led by Tsesses first realized Néel-type electric field vector optical skyrmions via surface plasmon interference excited by metal surface hexagonal grating structures [Fig. 4(a)]. Meanwhile, the research team led by Yuan realized Néel-type spin vector optical skyrmions via surface plasmon interference excited by tightly focused vector structured light fields on a metal surface [Fig. 6(a)]. Additionally, they further developed a sub-nanometer optical displacement sensing system by controlling the spin distribution of optical skyrmions on a skyrmion pair (Fig. 13), opening up the path for practical applications of optical skyrmions. In 2023, the research team led by Shen proposed a high-capacity optical communication and secure encryption scheme based on optical topological quasi-particles, with the reliance on Stokes vector optical skyrmions (Fig. 14). Currently, optical skyrmions with different topological structures and vector configurations continue to emerge, providing new ideas and methods for the study of spatio-temporal characteristics of topological structured light fields.

Optical skyrmions have become a major focus in the research on topological optics. Skyrmions can be formed and controlled within optical fields, and the development of high-dimensional structured light provides possibilities for constructing complex topological structures of high-dimensional skyrmions. In conclusion, if the topological limitations of skyrmions can be overcome to achieve freely controllable topological states, infinite possibilities will be posed to the next-generation information revolution. Applications such as optical communication, information encryption, spin-orbit interactions, and topological phase transitions will benefit from the expansion and practical applications of advanced photonics fundamentals.

Light waves will propagate without distortion in a uniform medium according to its wave equation and are widely employed for energy and information transmission. However, absolutely uniform media do not exist in the real world, and there are various defects and impurities in various media, especially in completely disordered media. Small particles within the scattering medium can make light waves deviate from their original propagation direction, which results in a disordered light field, forms speckles, and thus hinders energy and information transmission. Since in the early stages scattering was believed to be irreversible, most conventional methods relied on extracting ballistic photons from the scattering photons to address scattering-induced aberrations. As the ballistic photons decay exponentially with the increasing propagation distance, and it is difficult to extract ballistic photons from scattering photons after a certain depth, scattering correction based on ballistic photons is only applicable to weakly scattering media.

With the rapid development of spatial modulation devices such as spatial light modulators and digital micromirrors, it has become possible to realize the spatial light modulation with high accuracy. In 2007, Vellekoop and Mosk proposed a landmark new technique based on spatial light modulators that can compensate for the strong scattering effect, which is the wavefront shaping method to pre-compensate for the wavefront aberrations due to scattering by iteratively optimizing the wavefront of the input light. Meanwhile, the scattering light field manipulation has become possible. Additionally, light propagation in complex media is characterized by the transmission matrix. In just over a decade, scattering light field manipulation based on the wavefront shaping method has been widely adopted in many fields. For example, wavefront shaping methods can be employed to achieve light focusing beyond the diffraction limit by strongly scattering media and compensate for light scattering effects, further enabling high-resolution imaging at high transmission depths. In addition to the imaging field, scattering light field manipulation can transform the inherently harmful scattering medium into a variety of optical elements such as beam splitters, angular momentum generators and converters, and polarization controllers. In the field of communication, the scattering light field manipulation can increase the scattering light intensity received by an optical receiver and realize high-speed non-line-of-sight communication with lower power consumption. Additionally, mode selection of the outgoing field of a multi-mode fiber can be performed by scattering light field manipulation and the spectrum modulation of a nonlinear output field.

We focus on scattering light field manipulation, introduce the research progress in related fields and highlight the new applications of scattering light field manipulation in various research fields. Meanwhile, we first introduce the light field scattering characteristics, followed by the introduction of scattering and its light field modulation methods based on transmission matrix, feedback-based wavefront shaping, optical phase conjugation, and artificial intelligence-assisted wavefront shaping. Subsequently, the studies of the modulation methods of multiple degrees of freedom of the scattering light field, such as spatial (Figs. 1-3), polarization (Figs. 4-5), spectral (Figs. 6-8), energy (Fig. 9), and orbital angular momentum (Fig. 10) are presented. Finally, the existing applications in various fields of scattering light field manipulation are introduced. For example, the fluorescence-based transmission matrix is employed to achieve non-invasive imaging of biological tissues (Fig. 12). Orbital angular momentum communications in a complex environment are realized by exploiting the transmission matrix method (Fig. 18). Manipulation of nonlinear scattering optical field is achieved by adopting the transmission matrix method (Fig. 22). Scattering compensation of entangled photon pairs is performed by optimizing the pump wavefront (Fig. 24). Discrete Fourier transform can be achieved by utilizing the transmission matrix method (Fig. 27).

In summary, we introduce in detail the manipulation methods of each degree of freedom of the scattering light field, and the latest progress of the scattering light field manipulation in various fields, such as imaging, optical communication, nonlinear optics, quantum optics, optical sensing, integrated optics, and optical computing. Although scattering light field manipulation has made great progress, there are still some limitations to be broken through. 1) The energy utilization of scattering light is low with only part of the fully modulated scattering field. 2) The modulation speed is slow, and real-time scattering light field manipulation should be realized under dynamic scenarios. 3) It is difficult to modulate multiple physical quantities simultaneously, and most of the scattered light modulation can only realize the manipulation of a single physical quantity. With the further development of optimization algorithms, artificial intelligence, and modulation devices, scattering light field manipulation will move towards more precision, higher resolution, and deeper detection depth. The high degree of freedom brought by the combination of scattering light field manipulation and strong scattering media will also provide new solutions for the development of new optical components in the future. We believe that the further development of scattering light field manipulation will lead to many new applications.

Coherence and polarization are two intrinsic properties of optical fields. The investigation of optical coherence has boosted the development of partially coherent optics, while the study of polarization properties has led to the discovery and application of optical structured vector fields. For a long time, the coherence and polarization properties of optical fields were generally treated as independent degrees of freedom and often studied separately. Since the 1990s, researchers have gradually realized the inherent correlation between the coherence and polarization properties of optical fields. It has been recognized that coherence and polarization properties can interact during light beam propagation or in the interaction of light with complex media. The joint control of coherence and polarization has driven the study of partially coherent vector optical fields. However, previous research mainly focuses on electromagnetic Gaussian Schell-model beams, whose coherence structure follows a Gaussian distribution. Recently, with the emerging research on light field manipulation and structured light, and the development of theories and technologies for controlling the coherence structure of optical fields, the research focus on partially coherent vector beams has gradually shifted toward those with special spatial coherence structures. Due to the control of vectorial coherence structures, these beams exhibit characteristics during propagation that are completely different from traditional electromagnetic Gaussian Schell-model beams. They have potential applications in far-field polarization shaping and optical super-resolution imaging. Furthermore, with the rapid development of nano-optics, research on three-dimensional optical fields has emerged. Studies have indicated that due to the modulation of coherence, partially coherent vector fields exhibit rich three-dimensional polarization characteristics. We review the research progress on the joint control of coherence and polarization in optical fields, with a focus on the characterization and synthesis of two-dimensional partially coherent vector optical beams with special spatial coherence structures, and their robust transmission properties in complex environments. By combining developments in nanophotonics, we present the extension of two-dimensional partially coherent vector beams to three-dimensional partially coherent vector fields.

We start by reviewing the characterization, synthesis, measurement, and propagation of two-dimensional partially coherent optical beams. In the characterization of two-dimensional partially coherent vector beams, the utilization of two-dimensional coherence and polarization matrices is common. Various polarization characteristics of the beams and construction of polarization Stokes parameters and Poincaré sphere are obtained by the two-dimensional polarization matrix. Although the coherence Stokes parameters similar to the polarization Stokes parameters can be constructed using the two-dimensional coherence matrix, the lack of Hermitian symmetry in the coherence matrix prevents the direct construction of a coherence Poincaré sphere. To this end, Set?l? et al. from the University of Eastern Finland proposed a method using the Gram matrix to construct a coherence Poincaré sphere as shown in Fig. 1. This sphere can fully describe the coherence and polarization characteristics of a partially coherent vector optical beam between points r₁ and r₂ using the coherence Poincaré sphere vectors q₁₂ and q₂₁. Concerning the construction and synthesis of partially coherent vector optical beams, we primarily review methods for synthesizing partially coherent vector optical beams with novel coherence structures. This includes the scheme based on the generalized van Cittert-Zernike theorem (Fig. 2) and the method based on vector-mode superposition (Fig. 3). The former method based on the generalized van Cittert-Zernike theorem is suitable only for synthesizing vector optical beams with spatially uniform coherence structures and has low optical efficiency due to the utilization of rotating ground glass to synthesize spatially incoherent light. The latter method based on vector-mode superposition solves the low efficiency and the inability to synthesize spatially non-uniform coherence structures, providing a significant advantage in synthesizing high-power spatially non-uniform coherence structures. In terms of measuring partially coherent vector optical beams, traditional methods based on Young's double-slit interference have low spatial resolution and measurement speeds. While the Hanbury Brown-Twiss (HBT) experiment based on intensity correlation resolves the limitations of Young's double-slit interference, it only allows for the absolute value measurement of coherence structures. To this end, Chen et al. proposed a generalized Hanbury Brown-Twiss experimental scheme (Fig. 4), which introduces a vector fully coherent reference light to achieve simultaneous and rapid measurement of the real and imaginary parts of the coherence structures of partially coherent vector optical beams. Regarding the propagation of partially coherent vector optical beams, studies indicate that due to the modulation of vectorial coherence structures, these beams exhibit completely different propagation characteristics compared to traditional electromagnetic Gaussian Schell-model beams. The former shows a gradual increase in polarization degree during propagation, while the latter exhibits a gradual decrease in polarization degree during propagation (Fig. 5). Meanwhile, it is demonstrated that vector optical beams with special coherence structures exhibit robust propagation characteristics in complex media (Fig. 6) to present potential applications in far-field polarization shaping. Additionally, we review the research on three-dimensional partially coherent vector optical fields. In the characterization of three-dimensional partially coherent vector fields, three-dimensional coherence and polarization matrices are employed. Unlike fully coherent vector optical fields, partially coherent vector fields exhibit rich three-dimensional polarization characteristics due to the coherence modulation, with polarization dimensions exceeding 2 (Fig. 7). In contrast, fully coherent vector optical fields localized in a plane at a determined spatial position only exhibit two-dimensional polarization characteristics. Furthermore, for clearer presentation of three-dimensional polarization structures in partially coherent vector optical fields, characteristic decomposition is utilized to decompose the three-dimensional polarization matrix into fully polarized state, middle-component polarization state, and three-dimensional unpolarized state (Fig. 8). The middle-component state is generally considered as the two-dimensional unpolarized state, but under complex polarization matrix of the middle-component state, it exhibits three-dimensional polarization properties, which can be characterized by the concept of the degree of nonregularity.

It is shown that rich three-dimensional polarization structures are presented in partially coherent tightly focused fields. In studying the three-dimensional polarization characteristics of partially coherent tightly focused fields, the first challenge is the rapid calculation of the tightly focused fields. Traditional methods using the Richard-Wolf vector diffraction integral formula for direct integration typically take hundreds of hours. To enhance computational efficiency, Tong et al. proposed a method based on random-mode expansion in 2020 to achieve rapid computation of partially coherent tightly focused fields. Subsequently, researchers from Spain (Carnicer et al.) and China (Chen et al.) separately put forward convolution algorithms to fast calculate the tight focusing properties of partially coherent vector optical beams with a Schell-model correlation function. Compared to random mode expansion algorithms, the advantage of convolution algorithms is that the computation time is independent of the coherence length of the incident partially coherent vector beams, providing a significant advantage in computing the tightly focused characteristics of low-coherence optical fields. However, the four-dimensional convolution algorithm can only compute the tightly focused characteristics of partially coherent optical fields with Schell-model correlations. The random mode expansion algorithm is still required to improve computational efficiency and thus compute the tightly focused characteristics of partially coherent fields with spatially non-uniform correlations. Additionally, the four-dimensional convolution algorithm can only rapidly compute the polarization characteristics of tightly focused fields. The mode superposition algorithm is still required to compute the coherence characteristics between two or more points in the tightly focused field. By adopting fast algorithms, it is discovered that coherence structures play a critical role in shaping tightly focused fields. Research indicates that the transverse and longitudinal intensities of the tightly focused field can be controlled by the coherence structure of the incident light (Fig. 9). Furthermore, fast algorithms help discovered that in the tightly focused field of a radially polarized Gaussian Schell-model beam, three-dimensional polarization states with polarization dimension greater than 2 and three-dimensional degree of polarization less than 0.5 can be observed. By controlling the coherence length of the incident beam, the polarization dimension and three-dimensional degree of polarization of the focused field can be controlled (Fig. 10). Additionally, by introducing coherence structure control, three-dimensional unpolarized lattice and channels with specific spatial distributions can be designed near the focus (Fig. 11). Due to the rich three-dimensional polarization structures in partially coherent tightly focused fields, the spin angular momentum vector of the field can be decomposed into contributions from the fully polarized state and middle-component state. Under the nonregular middle-component state, the spin angular momentum will be carried. Research indicates that for the classical Gaussian Schell-model beams, the focused field exhibits three-dimensional nonregular polarization characteristics under moderate coherence length. Therefore, the spin angular momentum is contributed by both the fully polarized state and the nonregular middle-component state. Since the coherence structures and radial polarization of the optical field exhibit rotational symmetry, the generated spin angular momentum in the focused field has a vortex distribution with rotational symmetry as well. When the coherence structure or polarization state exhibits spatial asymmetry, it is found that the directions for spin vectors of the fully polarized state and middle-component state can be completely different (Fig. 12).

We review partially coherent vector optical fields, including two-dimensional partially coherent vector beams and three-dimensional partially coherent vector fields. Meanwhile, we emphasize the basic principles and experimental techniques for controlling and measuring the two-dimensional coherence structure of partially coherent vector beams and analyze the propagation characteristics of beams with novel vectorial coherence structures. Results show that partially coherent vector optical beams controlled by coherence structures can maintain robust propagation characteristics in complex environments and have potential applications in far-field optical polarization shaping. Additionally, in conjunction with the development of nanophotonics, we discuss the extension of two-dimensional partially coherent beams to three-dimensional partially coherent fields. Specifically, we introduce the three-dimensional polarization structure, three-dimensional nonregular polarization state, and spin angular momentum structure caused by optical coherence in vector optical fields. Genuine three-dimensional polarization structures are discovered in partially coherent tightly focused fields, with the influence of coherence on polarization dimensions, three-dimensional degree of polarization, degree of nonregularity, and spin angular momentum structure analyzed. Optical coherence as a novel degree of freedom plays a crucial role in the control and application expansion of vector optical fields. With the development of temporal and spatio-temporal joint control techniques in the optical field, temporal or spatio-temporal structured optical fields play a significant role in fields such as ultra-fast optics, quantum optics, and nonlinear optics. Currently, the spatial coherence structure control of vector optical fields has been widely studied, but research on their temporal or even spatio-temporal joint control is limited. Optical coherence as an intrinsic property of the optical field is expected to provide a novel degree of freedom for spatio-temporal structured optical fields and thus expand the application range of such fields. Additionally, we specifically review the joint control of coherence and polarization parameters. Optical coherence plays a crucial role in the joint control of more parameters. Research suggests that coherence plays an important role in the spin (polarization)-orbital angular momentum (phase) coupling of light. In the case of three-dimensional partially coherent vector optical fields, coherence not only induces three-dimensional polarization structures in tightly focused fields but also plays a significant role in controlling the evanescent waves and surface plasmon polaritons. Finally, this has led to the research on physical properties and potential applications of partially coherent surface waves.

Multifunctional integrated devices have become the mainstream of nanophononics research in recent years as optical devices continue to evolve towards high capacity, multichannel, low loss and integration. Additionally, the arbitrary manipulation of circularly polarized (CP) electromagnetic (EM) waves is significant for a wide range of applications such as chiral molecule manipulation, imaging, and optical communication. However, conventional optical devices composed of natural materials cannot realize multiplexing with only one optical device because they rely on the body properties to change the propagation phase so as to modulate electromagnetic waves. As a result, conventional optical devices are not conducive to the diversification, integration, miniaturization, and efficiency improvement of optical devices due to the single function, system complexity, large size, and low efficiency.

In recent years, metasurfaces consisting of a series of ultra-thin subwavelength artificial atoms arranged in a specific manner in the plane have demonstrated powerful modulation of electromagnetic waves, providing a good platform for realizing multifunctional integration. Researchers have discovered a series of exotic physical phenomena and powerful planar optical devices by exploiting the advantages of metasurfaces, such as lightness and thinness, large degree of modulation freedom, low loss, and easy conformality and integration. The mechanisms for modulating the phase of EM waves based on metasurfaces can be classified into three main types including resonant phase, geometric phase, and propagation phase. The resonant phase modulation mechanism is usually achieved by changing the geometry of the constituent artificial atoms to shift their resonant frequencies under arbitrarily polarized incident light. The propagation phase is realized by accumulating the phase of an EM wave as it propagates within the artificial atoms of the medium. The geometric phase is achieved by rotating the artificial atoms to change the phase of the outgoing light, while the polarization state of the outgoing light is opposite to the circular polarization state of the incident light. Among them, the resonance phase and the propagation phase do not depend on the polarization state of the incident light, while the geometric phase relies on the CP light. Typically, the three types of metasurfaces realize a single function, and it is vital to extend the integration of device functions as the application and device integration requirements continue to increase. By changing the geometry of the two orthogonal directions of the artificial atoms and employing the resonance phase or propagation phase to design the resonance frequency of the artificial atoms, researchers can realize multifunctional integration of different lines of polarized incident light under irradiation from the device, which can be completely different in free space. This type of device is complicated by the fact that the two main axes of artificial atoms are not completely independent, resulting in crosstalk and complex design. Due to the strong controllability of CP waves, geometric phase metasurfaces have caught enormous research interest. However, these meta-devices exhibit locked functionalities under illuminations of CP light with different chirality. Meanwhile, such metasurfaces for modulating CP light are also employed to achieve multifunctional integration. This is yielded by combining several sets of geometric phases with different functions in the same device, and thus several different functions are formed in free space under irradiation from the same CP light, which is referred to as a “merge phase metasurface”. However, as it does not fully decouple different chirality of light, there is still function binding and low efficiency. More recently, researchers have found that the combination of the spin-dependent geometric phase with the resonance or propagation phase can unlock the fixed function. Such metasurfaces often referred to as composite phase metasurfaces have been adopted to further improve device performance and integration in response to the growing demand for integrated optics applications. Starting from the three different phase mechanisms for electromagnetic wave manipulation by metasurfaces, we present a brief overview of resonant phase metasurfaces, geometric phase metasurfaces, propagation phase metasurfaces, and composite phase metasurfaces, with their operating principles, design strategies, and experimental implementations included, and recent research advances in this field briefly discussed.

Finally, we study spin-decoupled composite phase metasurfaces. Today’s multifunctional devices are still at the laboratory stage, but in the future, they can be integrated with research in other fields to solve some bottlenecks, such as directing incident light of different chirality to different regions on a chip for biomonitoring. Additionally, most polarization multiplexing devices to date can only perform passive and static functions. Therefore, the study of multifunctional devices with active tunable operation of incident waves of different polarization states will play a vital role in future practical applications. We hope that this brief review will help readers deepen their understanding of geometric phase metasurfaces and composite phase metasurfaces, and provide guidance for designing their components in the future.

Photons have several important degrees-of-freedom available for control belonging to the spatial domain, such as the path and orbital angular momentum (OAM) degrees-of-freedom. These available multiple spatial degrees-of-freedom and the high dimensionality of each degree-of-freedom provide for us diverse spatial methods, which can achieve spatial control of photonic quantum states in multiple degrees-of-freedom, high dimensionality, and multi-photons. Specifically, the preparation of spatially entangled photon states and their applications in optical quantum information have attracted extensive attention. Both path and OAM degrees-of-freedom can theoretically construct infinite-dimensional Hilbert spaces. Therefore, path and OAM degrees-of-freedom have inherent advantages in realizing the field of high-dimensional coding, which has attracted more extensive attention from researchers. The high-dimensional coding and high-dimensional entanglement of the path and OAM degrees-of-freedom themselves continue to break records. The multi-degree-of-freedom entangled photonic modulation schemes in which two or more degrees-of-freedom are jointly involved have likewise made progress. It is important to summarize the existing research on spatial control of photonic quantum state to promote the future development of the field.

The encoding of quantum information in single photons has evolved from a single degree-of-freedom to multiple degrees-of-freedom encoded together. On-demand conversion of quantum information among different degree-of-freedom through linear optical elements and such active modulation has built a series of quantum optical platforms such as weak measurements and quantum walks. Two-photon entangled states also emerge from the two-dimensional space of a single degree-of-freedom and are realized in multi-degree-of-freedom and high-dimensional systems. For two-photon spatial-domain entanglement, the original polarization-entangled photons are converted into OAM-entangled photons by SLM. Different polarizations can be loaded with different OAMs by a Sagnac interferometer, and two-photon entanglement of two photons with different OAMs has been reported. Subsequent work increases the OAM quantum number of entangled photons to 10010. In addition to the above preparation of OAM entangled photons using entanglement conversion, two-photon entanglement in Hilbert space higher than 100 dimensions has been realized by preparing a high-dimensional OAM entangled source through spontaneous parametric down-conversion and further combining it with the modulation of the radial modes of photons. At the same time, measurements of high-dimensional entangled sources develop in parallel. The successful realization of HOM interference based on multi-degree-of-freedom optical quantum states paves the way for the expansion of optical quantum technology in higher dimensions. Although the quantum modulation of the space domain of multi-photons is complex and difficult, researchers continue to make important progress in the preparation of high-dimensional entangled states and optical quantum information processing. The study of space-domain modulation of optical quantum states not only allows for selecting photons generated by transitions under spontaneous down conversion in free space but also considers using a variety of microstructures for the generation and modulation of photons. These microstructured devices allow for efficient beam modulation, localized control of polarization, and a significant enhancement of the efficiency of the emitted and detected photons. In the field of quantum photo generation, the generation of down converted photon pairs with spontaneous parametrization over 100 paths has already been achieved by integrating metal lens arrays with nonlinear crystals on a two-dimensional hypersurface. This holds the promise of generating high-dimensional hyperentangled and multiphoton states in an integrated and efficient manner.

In this review, starting from the linear control of a single photon in the spatial domain, we successively describe the spatial coding and transformation of a single photon, the preparation and measurement of two-photon entangled states, as well as the preparation of multi-photon high-dimensional spatial entangled states and their applications in quantum information. We mainly focus on the control in multi-degree-of-freedom and high-dimensional quantum information transformation. In addition, we discuss the recent progress on the spatial photonic quantum states in preparation, coding, measurement, and application. Meanwhile, possible solutions to some key issues are also explored. However, the study on the spatial control of photonic quantum states is still in its infancy and flourishing. There are many challenging important scientific issues and key technologies that need to be solved and broken through: how to achieve high-quality high-dimensional hyperentangled sources based on the spontaneous parametric down-conversion process, how to realize high-dimensional entanglement of multi-photon and multi-degree-of-freedom, and how to construct a feasible way to characterize the high-dimensional spatially entangled states. The interaction of photons with matter has always been a fascinating topic in optical research, and this is also true in the study of optical quantum information. Many studies of the interaction of vector light with matter have been reported, especially concerning the interaction with atomic gases. Most of the experimental studies in this research area belong to the semi-classical regime. We are looking forward to the continuous flow of research results on the interaction of single photons with atoms encoded in the spatial domain.

The light-matter interaction at the nanoscale is crucial for the development of miniaturized optoelectronic devices. These devices often encounter energy leakage and loss, stimulating researchers to explore non-Hermitian photonics. An exceptional point, a specific optical degenerate state with identical momentum and energy has emerged as a research hotspot in this field. In recent years, the research on physical mechanisms of phenomena like parity-time symmetry, geometric phase, asymmetric scattering, and bound states in the continuum (BICs) has all revolved around exceptional points. These unique physical mechanisms are expected to inject new energy into the advancement of fields such as quantum computing, advanced materials, and low-power optoelectronic devices. We primarily focus on the chiral phenomena associated with the BIC mode, a concept originating from quantum mechanics and first proposed by von Neumann and Wigner in 1929. They identified a unique solution to the Schr?dinger equation: a spatially localized electronic state with zero linewidth and positive energy, despite existing within the continuum spectrum of the radiation. Theoretically, BICs are non-radiating solutions to the wave equation and can manifest in various systems such as acoustics and fluids. However, it was not until 2008 that this concept was introduced into optics by Borisov et al. Subsequently, Plotnik et al. utilized a single-mode optical waveguide array to achieve an initial experimental observation of BICs. In 2013, researchers from MIT detected optical BICs in periodic photonic crystal slabs, boosting further exploration of BIC modes in planar artificial nanostructures. Optical BICs not only squeeze light fields and enhance resonance Q-factors in real space but also exhibit diverse polarization topological properties in momentum space. By adjusting the interaction between BIC modes, individuals can precisely manipulate the distribution, polarization, and emission of the light fields. Over the past decade, owing to the easily fabricated metasurface platform with numerous degrees of freedom, optical BICs have rapidly evolved as a novel approach for controlling light fields in nanophotonics. Additionally, artificial nanostructures can offer chiroptical responses surpassing those of natural materials, with the involved intricate physical mechanisms catching significant attention. The momentum space characteristics of optical BICs provide fresh theoretical insights and design strategies for enhancing the chiroptical response of chiral metasurfaces. The ideal BIC mode is completely decoupled from the free space. By breaking the symmetry of the system, the topology charge of the ideal BIC in momentum space splits into two circularly polarized states, which enables precise control of the radiation process to maximize the chiroptical response. In approximately 2020, research teams from the Russian Academy of Science and the City University of New York independently verified that high-Q quasi-BIC resonances can manipulate the wavefront of circularly polarized light and optimize the chiroptical response of metasurfaces. Both studies utilized periodic chiral metasurfaces with dual tuning parameters, and it was easy to break the symmetry within and out of the structural plane by simultaneously controlling the two parameters. This transformation converted the ideal BIC (with an infinite Q-factor) into chiral quasi-BIC. This highlights that the often-disregarded longitudinal dimension of metasurfaces, particularly symmetry, plays a crucial role in their interaction with circularly polarized light. However, the experimental validation was hindered until 2022 due to constraints in fabricating multi-layer metasurfaces. Our team overcame this obstacle by employing a tilted etching scheme to break the out-of-plane symmetry and observe chiral quasi-BIC in the visible spectrum. Over the last decade, BICs have been identified in different photonic structures, particularly in the metasurfaces platform, which leads to numerous fascinating phenomena. By thoroughly investigating the properties of BICs in both real and momentum spaces, it is possible to reveal clearer physical mechanisms behind various intricate chiroptical phenomena.

The concept of BIC has been around for almost a century, with well-established basic theories and various property studies. We begin by briefly outlining the concept and characteristics of BIC (Fig. 1), and then discuss the topic of chiral quasi-BIC (Fig. 2). Subsequently, we explore the applications of chiral BIC and other chiroptical phenomena related to BIC. In Fig. 3, we summarize the methods for creating chiral BIC by breaking the structural symmetry. Figure. 4 illustrates instances of chiral BIC resulting from the disruption of the individual dimension symmetry of nanostructures (including the breaking of in-plane or out-of-plane symmetry), while Fig. 5 presents research on intrinsic chirality induced by slant-perturbation metasurfaces that completely break both in-plane and out-of-plane symmetries. In addition to the tilted etching method, out-of-plane symmetry can also be disrupted by grayscale electron beam lithography and multi-step nanofabrication methods (Fig. 6). We have included Table 1 to compare the specific features of chiral BIC nanodevices currently yielded in the laboratory. Furthermore, we present examples of other chiroptical phenomena related to BICs in Figs. 7-9, corresponding to nonlinear circular dichroism, vortex beam generation, superchiral field enhancement, and the optical spin Hall effect, respectively. Finally, we address the current challenges and potential applications in this field.

In photonics, BIC initially caught attention for its exceptional high-Q resonance and later was extensively studied due to its unique momentum space polarization characteristics. The high-Q BIC can significantly enhance the performance of applications that rely on strong light-matter interaction, with lowered laser thresholds and improved nonlinear conversion efficiency. Meanwhile, the polarization characteristics of BICs in momentum space have greatly expanded the application fields, thus achieving polarization conversion and enhancing chiral light-matter interaction. Furthermore, more attention is paid to exploring new applications and mechanisms of BIC in combination with novel materials or special photonic structural systems. Although research on BICs in nanostructures has rapidly developed from theory to experimental stages, it still faces many challenges. In terms of sample design, there is an urgent need to explore rapid design schemes using artificial intelligence or inverse design methods. In sample fabrication, tasks such as improving the fabrication precision, implementing double-layer metasurfaces, and incorporating active semiconductor materials are very difficult. In terms of sample characterization, the extreme high-Q resonances make it difficult to measure the physical properties of BICs. Generally, although the biggest challenge in this field is from sample fabrication, combining sophisticated fabrication steps with reasonable sample design can accelerate the development of BIC-assisted photonic devices.

Ultrashort pulses lay the foundation of ultra-fast optics. The ability to control all the fundamental degrees of freedom of ultrashort pulses in both space and time domains has the potential to unlock a manifold of exotic light-matter interactions, unveil new physics, and enable new applications. The unique characteristics of ultrashort pulses, including short pulse duration, wide spectral bandwidth, and high peak power, make spatio-temporal ultrashort pulse tailoring face quite challenging. As ultra-thin planar optical elements composed of an array of deep sub-wavelength nanostructures, metasurfaces enable multifunctional optical field control at the nanoscale. This controllability, combined with merits including easy fabrication, integrability, and high damage threshold, makes metasurfaces ideal candidates in sculpting ultra-fast optical fields. We review the latest developments in metasurface-enabled spatio-temporal control of ultrashort pulses, especially by leveraging the Fourier synthesis approach to achieve complete four-dimensional pulse shaping in space and time. Then, brief discussions are carried out on free-space spatio-temporal pulse shaping via metasurfaces.

Ultrashort pulse shaping is usually realized by employing the Fourier synthesis approach, where a grating and lens pair disperse and then focus different wavelength components of the pulse at the Fourier plane to spatially separate different wavelengths. A modulator, which traditionally can be a liquid-crystal-based spatial light modulator, a digital micromirror device or an acousto-optic modulator, is placed at the Fourier plane to provide the pulse-shaping masking function. Recently, finely tailored ultrashort pulse shaping operations have been realized by adopting an ingeniously designed single-layer dielectric metasurface as the modulator. Temporal phase modulation, independent temporal phase and amplitude modulation, and temporal polarization modulation of the ultrashort pulses are theoretically and experimentally demonstrated. We discuss metasurface-enabled temporal pulse shaping in Section 2, where the metasurface device is divided into hundreds of independently designed units termed as "superpixels", with each superpixel composed of a two-dimensional array of identical nanopillars. For phase-only modulation, nanopillars with square cross-sections are sufficient. Meanwhile, pulse compression and pulse distortion are demonstrated as examples of the temporal phase modulation capability. For independent phase and amplitude modulation, nanopillars with rectangular cross-sections are selected, with phase modulations along the two birefringent axes following the half-wave plate condition. As a result, the transmitted phase is controlled by the lateral size of the nanopillar, while the transmitted amplitude is engineered by the rotation angle of the nanopillar. To demonstrate the versatility of this approach, we split an input ultrashort pulse with a temporal duration of 10 fs into two replicas, separated by 30 fs. Meanwhile, the temporal polarization state of the ultrashort pulse can also be controlled with rectangular nanopillars. For a nanopillar with a rotation angle θ, the phase retardation between the transmitted phase along the two birefringent axes determines the transmitted polarization change. This approach allows the conversion of any arbitrary input temporal polarization states into desired output temporal polarization states. A variety of polarization-shaped ultrashort pulses with rich instantaneous time-varying polarization states are synthesized. Additionally, by further engineering the masking function at both the superpixel and the individual nanopillar level, complete four-dimensional properties (phase, amplitude, polarization, and spatial wavefront) of an ultrashort pulse can also be manipulated via a single-layer dielectric metasurface, which is discussed in detail in Section 3. Complex spatio-temporal wave packets that previously either have only been theoretically proposed or require complicated high-harmonic nonlinear generation processes are experimentally synthesized. The packets include a light coil exhibiting a helical intensity distribution evolution and another pulse with coherently multiplexed time-varying orbital angular momentum (OAM) orders. This approach provides a universal way for controlling the complete four-dimensional properties of light, and can be easily extended to synthesize other forms of spatio-temporal wave packets by metasurface design engineering, or wavelength regimes by nonlinear response. In addition to shaping ultrashort pulses via a metasurface-enabled Fourier synthesizer, free-space spatio-temporal pulse shaping using metasurfaces is also discussed in Section 4. Compared to the Fourier approach, free-space pulse shaping greatly lowers the complexity of the shaping apparatus but puts forward more requirements for the frequency interval of the input pulse and nanopillar geometry. Thus, metasurface-enabled free-space spatio-temporal pulse shaping is still an ongoing and active research field. Till now, several spatio-temporal wave packets such as pulses carrying transverse OAMs have been yielded by free-space metasurfaces.

We have witnessed significant developments in spatio-temporal control of ultrashort pulses in the past few years, and the advancements have already shown great potential in numerous fields. With the current trajectory of ultrashort pulse shaping moving toward more extreme high brightness sources and more complex functionalities, spatio-temporal optical field control approaches with higher resolution, wider spectral coverage, higher damage threshold, more compact footprint, and higher active tunability are highly desirable. We review the outstanding performance of the metasurface-based approaches and their potential to overcome some of these challenges. It is expected that continuous studies on metasurface design, simulation, and fabrication can have more general and complete control over the spatio-temporal wave packet synthesis.

Electromagnetic (EM) wave front modulation has significance for both scientific studies and industrial applications. However, traditional components for wave field manipulations are often bulky and heavy, which restricts their utilization in miniaturized optical devices and compact detection systems. Metasurfaces are usually composed of arrays of artificial microstructures, also known as meta-atoms, and arranged in a uniform or non-uniform spatial pattern. They can arbitrarily manipulate the amplitude, phase, and polarization of light with sub-wavelength resolution. As a result, metasurfaces have caught much attention in the research on next-generation optical systems. The metasurface design and fabrication has dramatically boosted the employment of optical field modification in compact optical equipment. Metasurfaces are anticipated to break through the bottleneck of conventional optical components and systems, paving the way for miniaturization, integration, and multifunctional processes. While traditional optical elements primarily regulate the optical field by phase accumulation of light along propagation, metasurfaces provide a novel method for controlling the optical field at subwavelength ranges via the interaction between light and meta-atoms. As a two-dimensional planar material with a thin depth profile, a metasurface can generate non-classical phase distributions for transmitted and reflected electromagnetic waves at its interface. Therefore, more flexible control over the wavefront can be realized. Polarization is an inherent property of light waves and electromagnetic waves. It comprises abundant information on substances, which is essential for target detection and identification. The efficient polarization state control is the core content of electromagnetic wave manipulation, which is vital for imaging, communication, display, optical encryption, and optical force manipulation. Due to its ability to manipulate the polarization state on the subwavelength scale, the metasurface serves as a powerful tool for polarization regulation and vector beam generation. Conventional polarization regulators such as those found in natural materials and three-dimensional superstructural materials typically control the global polarization of light by manipulating the amplitude and phase delay of the electric field in the orthogonal polarization components. In contrast, polarization and wavefront modulation by metasurface are the results of“abrupt phase changes”in anisotropic reflection/transmission at the interface.“Abrupt phase changes”mean a surface effect that depending on the mechanism can originate from the geometric (Pancharatnam Berry) phase, propagation phase, and generalized geometric phase. Artificially created meta-atoms can overcome the limitations of natural materials, like limited birefringence and polarization sensitivity. Acting as birefringent elements, the meta-atoms with specific designs can significantly enhance the polarization modulation capability, and be adopted to realize subwavelength pixelated polarization control for polarization conversion, polarization-dependent multiplexing and even generating complex vector beams. In recent years, polarization-modulated metasurfaces have drawn a lot of attention both in theory and applications, with continuously evolving new principles and applications. Thus, it is important to outline present research and emerging applications and thus better guide future development.

We describe the basic principle and typical structure of metasurface design for polarization control, and then introduce and discuss the representative applications of metasurfaces, including polarization conversion along the propagation direction, vector vortex beam generation, vector holography and encryption, polarimeter, and dynamic control. In classic optics, the light polarization is commonly expressed mathematically by the Jones vector. Thus, the polarization control mechanism of metasurfaces is explained by solving Jones matrix. The roadmap of electromagnetic polarization manipulations with metasurfaces is summarized in Fig. 1. The two important mechanisms for metasurfaces to control polarization are the geometric phase and the propagation phase. The geometric phase for anisotropic materials is solely determined by the rotation angle θ as it results from the photonic spin-orbit interaction (PSOI). The propagation phase is related to the shape and size of the structure. Recently, our research group has proposed a novel principle of metasurfaces to break the PSOI symmetry by merging the geometric phase and propagation phase. We also summarize some emerging applications of polarization modulation by metasurfaces, involving polarization conversion along propagation direction, vector vortex beam generation, vector holography and encryption, polarimeter, and dynamic control. Meanwhile, we elaborate on the ideas of each study, analyze their advantages and limitations, and discuss their prospective implementations. For example, in addition to controlling polarization in the transverse plane, a new class of metasurfaces achieves parallel polarization transformations along the optical path. In this case, a single metasurface can mimic an arrangement of multiple polarization optics cascaded in series. By employing the polarization-dependent phase optimization concept, our group has reported a crosstalk-free broadband achromatic full Stokes imaging polarimeter composed of polarization-sensitive dielectric metalenses. The average crosstalk under incident light with arbitrary polarization has been largely reduced to ensure a more precise measurement of the polarization state. Finally, the challenges and future development direction of polarization-modulated metasurfaces and the areas are also prospected.

In summary, we highlight the promising polarization-related applications for metasurfaces and serve as up-to-date references for researchers in metasurface and metamaterial fields. As a new generation of transformative optical devices, polarization-modulated metasurfaces will provide a broad platform for polarization conversion, vector vortex beam generation, vector holography and encryption, polarimeter, etc.

Scattering medium is a substance commonly found in nature such as turbid atmosphere, smoke, and biological tissues. Coherent light beams propagating through scattering media will be disrupted due to random scattering effects. The wavefront will be destroyed, and the transmission direction will deviate from the original input direction and becomes chaotic. Random scattered light interference will form a particle-like intensity pattern, known as an “optical speckle”. In multi-mode fibers, due to mode dispersion and inter-modal interference, a similar scattering distribution will be formed. Thus, multi-mode fibers are also regarded as a special class of scattering medium.

Due to the scattering phenomenon, it is difficult to maintain the original spatial distribution of the light beam, and the energy is exponentially attenuated with the increasing penetration depth, which greatly limits the applications of advanced technologies such as optical tweezers, optical communications, and biomedicine in a strong scattering environment. However, in 1990, Freund proposed that light scattering in static scattering media is a deterministic linear process, a property that reveals the possibility of reutilizing the energy of the scattered light field. Due to the existence of a deterministic response relationship between incident and scattered lights, suitable input conditions can lead to the formation of the desired distribution of the output light field after passing through the scattering medium. In 2007, Vellekoop and Mosk put forward the concept of optical wavefront shaping whereby optimizing the distribution of the incident light wavefront leads to an in-phase coherent superposition of the light field at the target point, which thus achieves a focused light field that reaches the diffraction limit after the scattering medium. The focusing spot that reaches the diffraction limit is realized after the scattering medium. The emergence of wavefront shaping technology makes it possible to effectively employ the scattered light, thereby overcoming the limitations of the scattering problem for the above optical applications.

With the development of modulation devices and computer technology in recent years, increasingly more wavefront shaping methods have been applied to scattering medium focusing, mainly including iterative optimization methods, transmission matrix methods, and phase conjugate methods. The focusing quality and speed have been continuously improved, and exciting progress has been made in the applications based on this. By adopting wavefront shaping techniques, precise light manipulation through strong scattering media has become possible. The intensity of fluorescence excitation in deep biological tissues can be greatly enhanced to expand the penetration depth of fluorescence imaging. Additionally, even the scattering media can be adopted to improve the numerical aperture of the focusing objective lens and thus achieve focusing beyond the diffraction limit. Thanks to the wavefront shaping technology, the scattering medium has become a new type of optical device with the ultra-high degree of freedom of operation, which can realize some special applications that cannot be accomplished by ballistic light, such as functional modules in optical computing, super-resolution imaging, and directional energy delivery. Therefore, it is necessary to sort out the representative studies of wavefront shaping-based optical focusing technology for scattering media in recent years and the outlook on the future development direction.

Focusing through turbid medium based on wavefront shaping technique is mainly divided into three technical routes of the iterative optimization method, transmission matrix method, and phase conjugate method, with the basic principles shown in Fig. 1. Among them, the iterative optimization method relies on the set feedback physical quantities, improves the evaluation value by changing the input conditions, and finally realizes the light focusing at the target position. Meanwhile, this method plays an important role in complex optimization scenarios and dynamic scattering media. Currently, the most employed ones are intelligent optimization algorithms (Fig. 3) and neural network algorithms (Fig. 4). Diverse feedback signals further broaden the applications of this method (Fig. 7). On the other hand, the transmission matrix method relies on the measurement of the transmission matrix to establish a correlation between the input optimized wavefront and the scattered light field on the target focusing plane. Additionally, it employs the operation of time inversion to calculate the optimized wavefront for achieving focusing, which provides a powerful theoretical research tool for studying the mechanism of light transmission and focusing in scattering media (Fig. 8). By depending on the physical quantities of interest, various types of transport matrices have been developed (Figs. 9-11) and adopted in a variety of fields such as energy transport, optical communication, and particle manipulation (Figs. 12-13). The phase conjugate method relies on the light source placed at the target focusing position and utilizes the reversibility principle of the optical path to solve the phase of the received scattering light field. The utilization of the conjugate phase as the input condition can achieve focusing, which requires the fewest number of calculations and is currently applied to internal focusing of dynamic scattering media (Figs. 15-16).

Till now, scattering medium focusing based on wavefront shaping has successfully realized dynamic focusing inside or through the scattering medium, providing powerful technical support for applications including optical manipulation, long-distance communication, and deep biological tissue imaging. In future development, researchers should further improve the optical field transport mechanism inside the scattering medium, build a more refined physical model, and explore more dimensions of controllable physical quantities. Finally, broader scattering focusing and optical field modulation can be achieved, with the application scope of wavefront shaping technology in optics expanded. Additionally, combined with emerging optical computing, artificial intelligence, and other technologies, it is expected to achieve more compact optical path structure and faster and more efficient optimization. In conclusion, under the traction of cutting-edge exploration and the impetus of technological innovation, the scattering medium focusing technology based on wavefront shaping will continue to break through the limitations of traditional optical scattering and provide brand-new possibilities for optical applications in strong scattering environments.

The continuous progress in modern materials science, information technology, and biotechnology has greatly boosted societal advancement. As human understanding of the microcosm deepens, the capability to better describe and characterize the interactions between atomic-scale light and matter, and to achieve the simultaneous participation, coordinated regulation, and multi-modal coupling of multiple physical fields can significantly provide diverse methods and approaches for artificially controlling these matters. Scanning near-field optical microscopy (SNOM) with 40 years’ history can serve as a promising tool for these fundamental purposes by hoping to carry out measurement and characterization of light fields and light-matter interactions at deep-subwavelength and even nanometer scales. The essential elements for in-depth exploration of multi-physical field interaction systems in experiments are listed. They include the measurement, characterization, and analysis methods for light-matter interactions at the micro and nanoscales, interactions between photons and various quasi-particles, coupling between quasi-particles, and coupling and regulation between multiple physical fields. Meanwhile, a systematic and precise experimental study on the spatio-temporal details of the interaction among light and molecules, two-dimensional materials, quantum dots, metal nanoparticles, and nonlinear structures at the micro and nanoscales can reveal deep physics and a series of new phenomena and laws. Additionally, it is imperative to develop new methods, technologies, tools, and instrumentation of SNOM for microscopic imaging and spectral analysis with higher spatial resolution (approximately 10 nm), higher temporal resolution (about 50-100 fs), and higher brightness (transmission efficiency of 1%-10%). Thus, it is vital to deeply, completely, and compactly introduce and describe the history of SNOM and its applications, with the route towards building such a fundamental high-performance SNOM machine presented.

Due to the limitations of traditional optical imaging methods, researchers have turned their attention to near-field imaging. Owing to its exceptional optical resolution down to 10 nm and spectral analysis capabilities, SNOM provides a powerful near-field optical characterization tool with high spatio-temporal resolution for studying many crucial frontier scientific problems in physics, chemistry, materials science, and life sciences. In 1928, Synge first proposed the concept of near-field microscopy (Fig. 2) to improve the resolution of traditional microscopes. Until the 1980s, with the successful invention of lasers and scanning tunneling microscopes, Pohl, Lewis, and Betzig respectively made outstanding contributions to SNOM systems and nanoscanning tips, realized Synge’s vision, and increased the optical diffraction limit by one to two orders of magnitude, thus catching great attention from both academia and the industry. However, due to the fundamental limitations that resolution and transmittance cannot be achieved simultaneously, the typical a-SNOM is difficult to apply to biology and medicine that require both advantages. Therefore, as a pioneer of a-SNOM technology, Betzig abandoned this technological route after 1993 and sought alternative methods. Then, he quickly yielded success in fluorescence microscopy imaging technology and was awarded the Nobel Prize in Chemistry in 2014. To solve this problem, many researchers have subsequently made many improvements on the s-SNOM with better performance (Fig. 3). Despite decent progress in certain aspects, there is still significant room for improvement in the overall performance optimization, including resolution, throughput, and signal-to-noise ratio. Meanwhile, many studies adopt s-SNOM imaging technology to study the spatio-temporal details of light-matter interactions at the micro and nanoscales, including atoms, molecules, two-dimensional materials, quantum dots, biomolecules, and nonlinear structures. Finally, a series of new phenomena and laws in deep physics, chemistry, and biology are revealed. In recent years, we have carried out a project to build a novel SNOM tip based on the innovative concept and mechanism of SPP energy transfer (Fig. 5). This tip features a metal spiral cone-shaped structure, constant high resolution (10 nm), high transmission efficiency (10%), and high signal-to-noise ratio (20 dB). Employing the nano spot of the SNOM probe as an illumination light source is expected to measure and analyze the physical, chemical, and biological properties of micro and nano substances such as single molecules.

Generally, SNOM technology has become an important tool for studying near-field optics. Further improvement in the spatio-temporal resolution of SNOM technology will promote fundamental and applied research on the light-matter interactions at the nanoscale and even single-molecule scale.

Chirality is a property of an object that cannot be superimposed on its mirror image by translation or rotation operations. The two enantiomers of chiral molecules have the same physical properties but completely different chemical properties. Therefore, effective detection and characterization of chiral molecules are crucial for such fields as pharmaceuticals and biochemistry. Chiral objects exhibit optical activity, and the optical chirality response generated during the interaction with other chiral objects provides a basic strategy for effective enantiomer identification. The light field plays a vital role in the detection of chiral molecules, and according to Curie's asymmetry principle, the chiral response often requires a chiral light field. The light field chirality greatly affects the optical response intensity of chiral media. Therefore, how to enhance the chirality of ordinary light fields is a core issue in chirality research. The circularly polarized light field is the most common type of chiral light, playing an important part in chiral responses such as optical rotation, circular dichroism, and Raman optical activity. However, the chiral response generated by circularly polarized light fields is often weak, which greatly affects the ability of these methods to detect molecular chirality. Therefore, many other optical fields have been proposed, such as superchiral field, optical field with orbital angular momentum, and synthetic chiral light.

Currently, extensive theoretical and experimental research has been conducted on the regulation of chiral light fields and their ultra-sensitive detection with the assistance of artificial nanostructures. After the concept of optical chirality (C) was proposed, its physical meaning was improved by Tang and Cohen. By employing the expression of optical chirality, when the optical chirality of a certain light field is greater than that of circularly polarized light, it is called superchiral field. When chiral structures are adopted for chiral detection, the chiral signals of molecules are often influenced by the chiral signal of the structure itself (Fig. 1). To this end, it is proposed that non-chiral structures should be utilized to generate superchiral fields for enhanced spectral detection, such as the study of nanostructure superchiral hotspots, and the construction of vector exceptional points (EPs) and Bound states in the continuum (BICs) to generate strong and uniform superchiral field over a large area, which has been experimentally validated (Fig. 2). In molecular chirality ultra-sensitive detection based on superchiral field, the initial research mostly focuses on enhancing the circular dichroism signal of molecules by obtaining superchiral hotspots with enhanced chirality density (Fig. 3). Initially, it was believed that the significant enhancement of chiral signals by placing molecules in hotspots was due to the enhanced field strength at the hotspots. Later, it was theoretically proven that the peak/valley intensity of plasma-induced circular dichroism enhancement directly corresponds to a larger optical chirality in the near-field, rather than a larger enhanced electromagnetic field intensity at the hotspots (Fig. 4). Additionally, the interaction between orbital angular momentum beams and chiral molecules has been extensively discussed. Placing chiral molecules in the hotspots of dimers can observe a significant enhancement effect of chiral signals (Fig. 3). The study of employing dielectric nanoparticles to enhance molecular Raman optical activity (ROA) signals can provide more comprehensive information on molecular chirality structures, and also investigate the thermal effects of dielectric and metal structures under light irradiation (Fig. 4). Meanwhile, the strength of chiral optical gradient force is related to the gradient of optical field chirality. The utilization of a superchiral field can increase the total optical force difference of enantiomers, achieving the separation of enantiomers and nanoparticles (Fig. 5). Research based on circularly polarized light or superchiral light fields requires consideration of both electric dipole interactions and magnetic dipole interactions (or electric quadrupole interactions) between light and matter. However, the interaction between magnetic dipoles and electric quadrupoles is usually weak, with often small detection signal strength. The interaction between synthetic chiral light and chiral substances can generate significant and freely adjustable enantioselectivity in pure electric dipole effects. Synthetic chiral light is a light field composed of multiple light frequencies, which requires that the polarization of the total light field should not be coplanar, and its chirality is only related to the light field itself at a certain point (Fig. 6). The synthesis of dual color chiral light mainly employs strong field physics to recognize chiral molecules, such as photoexcited circular dichroism (PXCD) and high harmonic generation (HHG) spectroscopy. The research on the tricolor synthesis of chiral light is mainly based on the cyclic three-level model, and researchers have discussed enantiomer specific state transfer (ESST) and enantiomer spatial separation. For chiral detection, different types of optical responses that can be adopted to distinguish left and right hands have been discussed, such as enantioselective light absorption, enantioselective three-wave mixing, enantioselective ac Stark effect, and enantioselective response of cavity molecule mixing systems (Fig. 7).

We introduce chiral light fields and their applications in molecular chirality detection. Firstly, we present the enhancement of superchiral fields based on nanostructures and review their applications in two aspects, including chiral molecule ultra-sensitive detection based on superchiral hotspots and chiral optical force enhancement based on vector exceptional points. Then the relevant research on synthetic chiral light is discussed. Currently, the main focus is on the detection of chiral molecules using bicolor and tricolor synthetic chiral light. Meanwhile, we have developed methods such as photoexcited circular dichroism, high harmonic generation spectroscopy, and enantioselective ac Stark effect. In addition, research on ESST has also been conducted based on synthetic chiral light. The research on the chiral light field and its applications in molecular chirality detection is still in the development stage. Thus, designing reasonable nanostructures to achieve uniformity and higher optical chirality C in the development of superchiral fields is a challenge and key. A clearer understanding of the interaction mechanism between the superchiral field and the near chiral field of nanostructures can potentially boost the development of higher-precision chiral spectroscopy methods. In addition, the utilization of chiral optical forces is a rapidly developing field where there have been many theoretical studies so far, demonstrating enormous potential in chiral separation. The research on synthetic chiral light is still in its early stage. In the future, we hope to combine synthetic chiral light with nanostructures to develop a new generation of surface-enhanced chiral light.

In biomedical imaging applications, optical scattering disrupts the predictability of the light path, challenging the achievement of high-resolution optical imaging in deep tissue. Even state-of-the-art microscopy is limited to operating at roughly one millimeter in depth using visible light. Overcoming the scattering effect for deep tissue imaging remains a significant challenge. Wavefront shaping methods present a promising solution, allowing researchers to achieve high-resolution imaging through scattering media. By modulating the phase of incident light and compensating for wavefront distortion due to scattering, these methods effectively refocus scattered light, enabling high-resolution imaging in deep tissue.

Wavefront shaping methods can be categorized into three types: feedback-based, transmission matrix-based, and optical phase conjugation-based. These methods differ in system complexity and time effectiveness for obtaining the phase map. Feedback-based wavefront shaping, the first successful method for focusing light through scattering media, has a simple setup and low algorithm complexity. Research in this area has focused on improving optimization algorithms to find the optimal phase distribution, enhancing robustness and convergence speed. Transmission matrix-based wavefront shaping models light propagation in a scattering medium by using a linear transmission matrix, enabling wide-field imaging of hidden objects after obtaining the optical transmission matrix. Neural networks excel in manipulating nonlinear scattering and assist in wavefront shaping, particularly in scenarios involving multimode gain fibers and strongly absorbing tissue. Optical phase conjugation-based wavefront shaping is the most efficient method, requiring only a one-time measurement to determine a row vector of the transmission matrix. It efficiently acquires and controls information about the scattered light field, demonstrating advantages in dynamic scattering processes. In applications such as imaging living tissue, where optical scattering is dynamic on a millisecond to microsecond timescale due to physiological processes, optical phase conjugation-based wavefront shaping stands out as a promising method for high-resolution imaging.

To achieve internal focusing and imaging within scattering media, wavefront shaping methods need to be combined with guiding stars. Guiding stars within the scattering medium result from local interactions with scattered light, causing observable changes in intensity, phase, and frequency. Wavefront shaping locates guiding stars by perceiving these changes, guiding scattered light to achieve focus at the guiding star's location. Focused ultrasound serves as a “virtual guiding star”, freely adjustable within biological tissue. This allows researchers, under the influence of optical scattering, to achieve a bright optical focus guided by focused ultrasound. Scanning this focus and measuring the intensity of frequency-shifted light enable the reconstruction of absorption distribution images of objects within the scattering medium.

In summary, wavefront shaping methods offer new possibilities for achieving high-resolution imaging through scattering media. By modulating the incident light phase and compensating for wavefront distortion, these methods efficiently refocus scattered light for high-resolution imaging in deep tissue. Combining wavefront shaping with guiding stars holds promise for internal focusing and imaging within scattering media, particularly in biomedical imaging applications.

For the first time, a research group at the University of Twente introduced the wavefront shaping method (Fig. 2). They utilized feedback-based wavefront shaping to refocus scattered light by adjusting the target function, successfully achieving simultaneous focusing of scattered light at multiple target positions (Fig. 4). Another research group then employed a coaxial interference method to obtain the optical transmission matrix of scattering media. With the acquired transmission matrix, they could focus light to arbitrary positions on the output plane (Fig. 7). To mitigate coherent noise caused by the external reference beam, direct intensity detection approaches for retrieving the transmission matrix were proposed and validated. The optical phase conjugation-based wavefront shaping method stood out as the most efficient approach for focusing light through scattering media, relying on the time-reversal symmetry of the optical wave propagation equation.

In 2008, researchers used a phase conjugate mirror based on photorefractive crystals to focus scattered light through biological tissue. Although phase conjugate mirrors based on photorefractive crystals have advantages in processing speed and controlling mode count, their limited efficiency in generating conjugate wavefronts restricts their applicability. Consequently, the combination of high-performance cameras and spatial light modulators (SLMs) has gradually become the mainstream solution (Fig. 10). Digital optical phase conjugate mirrors have an advantage in modulation efficiency and wavelength insensitivity, establishing their dominance in optical imaging, control, and therapeutic applications.

In 2011, ultrasonic guided stars were first proposed and applied in optical phase conjugation-based wavefront shaping, successfully achieving optical focusing and imaging within scattering media. Two independent research groups in the United States demonstrated focusing light deep inside scattering media with ultrasonic guided stars (Fig. 12). In summary, the development of small-sized, high-contrast, non-invasive, and easily controllable guiding stars has become a current focus in wavefront shaping research.

Wavefront shaping offers an effective approach for comprehensive exploration and precise control of scattered light. This capability allows for the alleviation of information disorder caused by scattering, facilitating high-resolution optical imaging within scattering media. This review delves into the historical development of wavefront shaping, discusses various wavefront shaping methods, highlights their applications in overcoming optical scattering for deep tissue imaging, and provides insights into future trends in the advancement of wavefront shaping techniques.

Traditional high-resolution microscopy techniques are limited in imaging within confined and narrow spaces, such as the cavities of animals or the inner chambers of precision instruments, due to their bulky and complex systems. Microscopic endoscopy technology allows for high-resolution observations within cavities by inserting miniature probes. Common types of endoscopes include rigid endoscopes composed of purely optical lenses and electronic endoscopes using image sensors, with diameters typically ranging from millimeters to centimeters. To achieve imaging systems with even smaller diameters, researchers have begun to explore the use of fiber bundles or single fibers for miniature endoscopic imaging. However, these systems typically require gradient refractive index lenses or scanning devices, resulting in diameters much larger than the imaging field and encountering issues such as edge aberrations and honeycomb noise. In recent years, ultrathin lensless multimode fiber (MMF) endoscopes have emerged as a new research hotspot, achieving numerous breakthroughs in imaging modes such as real sample imaging and image transmission.

MMFs, as a type of multimode linear system, have historically been regarded as unpredictable due to their rich spatiotemporal modes (phase, amplitude, polarization, wavelength, and pulse delay) and the sensitive and complex mode coupling characteristics. With recent advancements in optical wavefront shaping and optical field measurement technologies, significant strides have been achieved in controlling optical fields within MMFs. This progress positions them as promising candidates for a new generation of minimally invasive super-resolution endoscopic imaging tools. In comparison to traditional endoscopes, MMF endoscopy technology presents several notable advantages. Firstly, it fully exploits the spatial multiplexing capability of fibers, resulting in ultra-high mode density. Moreover, its spatial bandwidth product exceeds that of fiber bundle endoscopes by an order of magnitude under identical probe diameters. Secondly, no additional lens system is required at the fiber probe end, reducing probe size and encapsulation requirements substantially. Thirdly, leveraging MMFs as the transmission medium enables the creation of complex three-dimensional light field distributions at the fiber exit end through encoded wavefront modulation techniques and mode calculations. This facilitates three-dimensional scanning imaging of samples, yielding more comprehensive and detailed sample information than traditional methods. Furthermore, MMFs fabricated from inert and biocompatible hydrogel materials can be directly integrated into disposable medical endoscopic systems. Overall, MMF-based endoscopic detection systems have made significant advancements and are poised to complement traditional endoscopic techniques in achieving high-precision detection in confined spaces. Nonetheless, the feasibility and performance enhancement of this technology in medical and industrial detection applications encounter various challenges. Consequently, summarizing existing research to inform the future rational development of this field is deemed important and necessary.

We initially introduced the mechanism of measuring the spatiotemporal optical field transmission matrix in MMFs and then delineated the evolution of MMFs in real sample imaging, encompassing fluorescence imaging, reflection imaging, unlabeled specific imaging, and multimode imaging, along with image transmission imaging methods, and their imaging performance was summarized (Table 1). We also discussed the application of deep learning, metamaterials, adaptive beacons, and other strategies in disturbance-resistant imaging with MMFs. Finally, we looked ahead to the future of MMFs for fast perturbation-resistant, high-pixel, and multifunctional imaging.

MMF imaging is one of the representative achievements with significant influence and wide application in the field of scattering medium imaging, playing an increasingly important role in biomedical, material science, industrial testing, and other fields. Studying the theoretical and technical issues of measuring and imaging the spatiotemporal optical field of MMFs is of great significance for improving imaging spatial resolution, suppressing noise, and obtaining multidimensional imaging information.

The optical orbital angular momentum (OAM) can exist either as longitudinal OAM in the spatial vortex beam or transverse OAM in the spatiotemporal optical vortices. In contrast to the amount of research focused on longitudinal OAM, very few pay attention to optical fields with transverse OAM. Unlike longitudinal OAM which is only affected by diffraction, transverse OAM can be affected by both diffractive effect and dispersive effect. One of the biggest challenges in utilizing optical fields carrying transverse OAM is to overcome diffraction and dispersion as the optical field propagates. Diffraction and dispersion will cause the fields to spread in space and time, which limits the applications of the optical field with OAM. We introduce a class of three-dimensional (3D) spatiotemporal localized wave packets with transverse optical OAM. The combination of the transverse OAM and the localized waves enables it to be immune to both dispersion and diffraction as the wave packet propagates. 3D spatiotemporal localized wave packets carrying transverse OAM provide a new opportunity for the utilization of transverse OAM and are expected to be applied in optical communication, quantum optics, and other fields in the future.

In previous studies, the vortex phase is placed in the spatial x-y plane and the resulting localized wave packet carries longitudinal OAM. In this study, we rotate the polar axis by 90°, so that it is now aligned in the y-direction. Therefore, the vortex phase term eim? locates in the x-t plane. Two spatiotemporal localized wave packets carrying two types of OAM: longitudinal OAM and transverse OAM are plotted (Fig. 1). Then, the theoretical derivation [Eqs. (4)-(6)] proves that the transverse OAM possessed by each photon is m?. In Fig. 2, 3D spatiotemporal localized wave packets described by Eq. (7) with different orders are presented. From the basic-order to higher-order 3D spatiotemporal localized wave packets with transverse OAM, a kind of 3D spatiotemporal localized wave packets in abnormal medium is proposed.

To investigate the localized property, we choose one of the family of 3D localized wave packets and simulate its propagation in a virtual medium BK7 with negative material dispersion (β2=-25.26 fs² mm^-1) at the central wavelength of 1550 nm. As a comparison, we filter out the central lobe of the wave packet and propagate it in the same medium. Due to the condition that the effects of diffraction and dispersion are equalized, a proper pulse duration and beam size of the filtered wave packet is 112.25 fs and 0.30 mm at L=0 mm, respectively. Hence, we have diffractive length and dispersive length around Ldiff=Ldis=180 mm. As shown in Figs. 3 and 4, the spatiotemporal localized wave packet keeps its intensity shape without any distorts during propagation. It is noted that the central lobe wave packet experiences dramatic change and is magnified proportionally in intensity profile compared with the spatiotemporal localized wave packet. The propagation invariability of spatiotemporal localized wave packets has been presented. The ability of the wave packet to propagate free of diffraction/dispersion is only valid when the diffraction effect and the dispersion effect are balanced with each other. In other words, the wave packets propagate unstably in the unbalanced diffraction and dispersion. In addition, the localized capacity cannot be continued permanently due to finite energy in practice. However, the limited invariantly propagated length is longer than the length of the filtered wave packets. On the other side, self-healing is also often used to characterize non-spreading wave packets, leading to a wavefront reconstruction after an electromagnetic absorption obstacle. To verify the self-healing of the spatiotemporal localized waves, we numerically simulate that a rectangular plate (around widths of 600 μm) perfectly absorbing electromagnetic fields is placed in the central part of the spatiotemporal localized wave packet and propagate the blocked wave in BK7 (β2=-25.26 fs² mm^-1). 3D iso-intensity profile of the blocked wave packet in anomalous medium at different propagated lengths (0, 230, 320, and 500 mm) is shown in Fig. 5. We can see that the up blocked area and the down area are split into two rings and move towards to the central part in Fig. 5(d). In the end, the wave packets can be recovered to their original spatiotemporal localized wave packets. The linear momentum density and intensity distribution of the blocked wave packet at different propagated distances in y-t plane are shown in Figs. 5(e)-5(h). The direction of linear momentum density is labelled by arrows and points to the blocked areas visually indicating the reason why self-healing can happen in the spatiotemporal localized wave packets.

In summary, we present a new class of 3D spatiotemporal localized wave packets carrying transverse optical OAM. These wave packets exist in abnormal dispersion and can propagate invariantly when the diffractive effect and the dispersive effect are equal. To investigate the non-spreading nature of these wave packets, we simulate a wave packet (l,m)=(2,1) propagating in a proper and real medium BK7 glass. The results show that the wave packet propagates over several Rayleigh lengths while keeping its structure invariant. The wave packet can be recovered to its origin even when passing through a blocked obstacle. This kind of wave packets may provide new applications related to transverse OAM in the fields such as quantum optics and optical communications.

Due to the strong light-matter interactions, coupled plasmonic systems have broad applications in such areas as light manipulation, optical sensing, optical imaging, and optoelectronic devices. However, the inherent dissipation of materials and radiation dissipation of resonant structures limit the strength, service life, and propagation distance of coupled plasmonics, weakening the coupling signals and reducing the sensitivity and other performance of coupled plasmon devices. One possible solution is to add optical gain materials into the systems to compensate for the dissipation, but the utilization of gain materials is still limited because of the introduction of noise and instability. Another possibility is to employ complex frequency waves as light sources. It has been theoretically demonstrated that complex frequency waves with temporal attenuation can restore information losses. Unfortunately, producing complex frequency waves in real optical systems still faces significant challenges and has not been yielded experimentally. Currently, a novel method for synthesizing complex frequency waves has been proposed to be successfully applied to super-resolution imaging and highly sensitive biosensing. Therefore, we adopt this method to compensate for the dissipation of coupled plasmonic systems, thereby enhancing their resonance signals and avoiding experimental challenges. We hope that our study can benefit the development of coupled plasmonic systems for various potential applications.

We employ a periodic plasmonic structure composed of two perpendicular silver rods as an example to investigate the mechanism behind the attenuation of coupled resonance in coupled plasmonic systems. The structure is simulated by the finite-difference time-domain (FDTD) method using CST Studio Suite software. In the simulation, a plane wave with different polarization angles (45°, 90°, and 135°) is normally incident onto the structure with the periodic boundary to obtain the transmission coefficients, with the permittivity of silver described by the Drude model. Furthermore, we combine the Lorentz polarization model with temporal coupled-mode theory to analyze the interaction of plasmonic modes.

The simulation results (Fig. 1) show that under an incident wave whose polarization angle equals 45° (135°) , the eigenmode of the plasmonic structure appears at 290 THz (310 THz) with no conversion of orthogonal polarization. Subsequently, a wave with 90° polarization can simultaneously excite the two eigenmodes and generate the coupled signal of the structure. Theoretical analysis shows that the strength of the coupled plasmonic signals depends on the frequency difference and the dissipation of the eigenmodes. Under the relatively small frequency difference and large dissipation, the two coupled new modes will have a large broadening and high overlap in the spectra, causing the coupled valley in the center to be weakened and shallowed. The Lorentz polarization model shows that complex frequency waves with temporal attenuation can enhance the weakened signals by reducing the dissipation of the eigenmodes. Based on Fourier transform analysis, the linear responses excited by complex frequency waves can be synthesized by the coherent combination of multiple real frequency responses. The calculation results (Fig. 3) show that synthesized complex frequency waves with different virtual gains can gradually enhance the coupled signals, where the coupled valley in the spectral line becomes increasingly deeper. Additionally, the synthesized complex frequency wave method is also effective for different coupling strengths (distance adjustment between silver rods). Even if the original signal is difficult to distinguish, this method can also restore it to the split state.

We study the dissipation in coupled plasmonic systems based on numerical simulations using CST Studio Suite software and theoretical analysis that incorporates the Lorentz polarization model and temporal coupled modes theory. Meanwhile, we explain the formation mechanism of coupled plasmonic signals and identify their limiting factors. Our findings suggest that under small coupling strength, larger dissipation of plasmonic systems will significantly hamper their coupled resonance. Then, we analyze the influence of complex frequency wave excitation on coupled plasmonic systems, and the results indicate that complex frequency waves with temporal attenuation can compensate for the dissipation of the system and restore the weak signal. To avoid the experimental difficulties of complex frequency waves in real optical systems, we employ a new method for synthesizing complex frequency responses via real frequency waves to calculate the transmission spectrum of the coupled plasmonic structure excited by complex frequency waves. Our results demonstrate that the proposed method can compensate for the dissipation of the coupled plasmonic structure in different conditions, significantly enhancing the coupled signals with almost no additional cost. The findings provide a practical and general method for solving the long-standing dissipation of coupled plasmonic systems, facilitating further applications of coupled plasmonic systems such as optical imaging, spectroscopy technology, and optical sensing.

Vortex beams with orbital angular momentum (OAM) have many unique properties compared to other beams, and their spiral wavefront structure and phase changes open up new dimensions for applications such as lithography, optical communication, optical trapping, and quantum entanglement. In recent decades, researchers have been exploring the linear and nonlinear transmission of the Laguerre-Gaussian (LG) vortex beam in media, and the coverage has been continuously expanded, which lays a solid foundation for developing the optical vortex. Most relevant research focuses on analyzing the properties of vortex beams and their linear transmission and evolution. However, the ultrashort pulse vortex laser has become a research hotspot with extensive studies. Since the inclusion of nonlinear processes will greatly increase the complexity of vortex beam analysis, the study on transmission and evolution of ultrashort pulse vortex lasers in nonlinear media is still rare. Thus, we experimentally investigate the propagation of mid-infrared LG beams in organic crystal DSTMS due to the cubic-quintic nonlinear effect and analyze the differences in the effect of polarization of the incident vortex beam on the transverse light field distribution.

High power mid-infrared optical parametric amplifier (OPA) pulses with 1450 nm center wavelength, 60 fs pulse duration, and 1 kHz repetition rate serve as the pump of the system. After passing through a customized spiral phase plate (SPP), the mid-infrared laser light is modulated into vortex beams and incident perpendicularly onto the surface of an organic crystal with a 640 μm thickness. A 4f imaging system is constructed using two lenses to conduct imaging on the spot in either plane perpendicular to the light propagation direction within the crystal. The CCD camera moves back and forth in the horizontal direction to observe and record the spot evolution of the vortex beam during propagation, starting from the rear surface of the crystal.

In the experiment, the spot changes of mid-infrared vortex light before and after passing through the DSTMS crystal are found and compared with those of the BBO crystal to analyze the spot characteristics of the vortex beam after passing through different crystals. After passing through the BBO crystal, there is still only one bright ring in the spot, with the spot radius almost unchanged. However, after passing through the DSTMS crystal, the spot changes significantly from the original doughnut structure to three thin bright rings, and the number of rings increases. This is due to the nonlinear process of three-photon absorption of pump light by the DSTMS crystal. When the pump light polarization fulfills the optimal THz generation conditions, the nonlinear refractive index of DSTMS mainly originates from the quasi-χ(3) effect due to a combination of the cascaded 2^nd-order OR process and the linear EO effect. The contribution from the intrinsic χ(3) nonlinearity of DSTMS should be negligible. Its additional nonlinear refractive index causes the refractive index of the pump light to vary with light intensity, which in turn leads to spectrum broadening. For each spectral component generated after the spectrum broadening of the incident LG beam in the Kerr medium, its respective corresponding LG mode has the same topological charge and radial index. As the frequency value of each spectral component is different, the respective corresponding Rayleigh length and beam waist position are different to bring various light field expressions for the LG vortex beam corresponding to each spectral component. Therefore, the corresponding brightest rings have different radii, and each bright ring generally does not coincide with each other in the observation plane, resulting in a weak spot intensity in most regions of the observation plane. To verify the above optical spot evolution process, we can simulate the light field distribution of the LG beam before and after passing through the DSTMS medium with a Kerr-like effect by MATLAB simulation analysis based on the generalized Gaussian beam decomposition method, with the simulation results shown in Fig. 3. Fig. 3(c) reveals that the effect of the Kerr medium on the incident LG beam is to produce LG beams with different radial modes. Meanwhile, the effect of the polarization of the incident vortex light on the spot of the outgoing light from the rear surface of the crystal is further investigated experimentally, and the experimental results illustrate that the incident light with different polarization produces vortex beams with different light intensity distributions.

We research the evolutionary mechanism of vortex beams in nonlinear organic crystal DSTMS initially, showing that the nonlinear transmission effect can change the light intensity distribution of vortex beams to a large extent. The generalized Gaussian beam decomposition method is utilized to simulate and analyze the light intensity distribution of the LG beam before and after passing through the medium with a Kerr-like effect, which indicates that the Kerr medium affects the incident LG beam by producing LG beams with different radial modes. Additionally, the effect of different polarization of the incident vortex light on vortex mid-infrared laser transmission in DSTMS is studied to demonstrate the effect of nonlinear transmission on the LG beam.

Optical and electronic computing systems attempt to understand large amounts of visual data originating from scenarios such as autonomous driving, machine vision, medical diagnostics, remote sensing, defense, and the Internet of Everything. These data are interpreted by artificial intelligence (AI) algorithms, where electronic deep neural networks swiftly emerge as the standard algorithm for visual data processing. Optical neural networks that utilize photons as computational carriers feature high speed, low power, high throughput, and massive parallelism. With the deep integration of optics, optoelectronics, and electronics, the optoelectronic hybrid network model combines the bandwidth of optical computation with the flexibility of electronic computation, providing an order of magnitude increase in the density, speed, and energy of computational systems. However, existing architectures are usually designed for a single task and lack the ability to process multiple tasks in parallel. Therefore, we propose a novel optoelectronic hybrid neural network computational model for multidimensional modulation of linear and nonlinear light waves via nonlinear metasurfaces to simultaneously process information from multiple channels.

The nonlinear metasurface structure employs a one-fold symmetric U-shaped resonant unit to realize the nonlinear multiplexing function of the network and high second harmonic efficiency. Based on the geometrical phase, continuous phase modulation is realized by rotating its spatial angle. The transmission spectrum of the structure at circular polarization is simulated using FDTD. Its resonance wavelength is identified and selected as 1160 nm. Meanwhile, an optoelectronic hybrid network architecture for nonlinear metasurfaces is constructed to realize item classification and reconstruction of coding by phase multiplexing of fundamental and two-fold frequencies. The front-end optical network and the two back-end electronic networks are trained as a package, and the co-objective loss function for recognition and reconstruction is optimized using the gradient descent algorithm and the error back-propagation algorithm. After the networks are trained, unique metasurface structures are identified by extracting the multiplexed phases.

The results after network training are shown in Fig. 1, and the classification part achieves a blind test accuracy of 95.53% on the MNIST test dataset, with the normalized loss function of the reconstruction of the coding converging to 0.031. The design results and simulated transmission spectra of the nonlinear metasurface are shown in Fig. 2, where its fundamental mid-wave resonates most intensely near 1160 nm and a second-order resonance exists near 704 nm. The simulation results of the network classification performance at fundamental frequency are shown in Fig. 3. The distribution of the fundamental frequency output behind the nonlinear metasurface is irregular, but the back-end electronic network can efficiently learn these differences and classify them. Figure 4 reveals the reconstruction results of the network, where the more random optical output is more favorable for encrypting the information. The PSNR of the reconstructed digit “1” reaches a maximum of 30.12 dB, and the average PSNR of the whole test set is 26.13 dB, which indicates that the model yields high reconstruction performance.

We demonstrate an optoelectronic hybrid network model based on a nonlinear metasurface that achieves the dual tasks of performing handwritten digit classification and reconstruction in both fundamental and twofold channels. High accuracy (95.53%) and high image quality (average PSNR >26 dB) are obtained by joint training optimization. The proposed method combines the advantages of optical and electronic computations and simultaneously achieves high parallelism, high accuracy, and low power consumption. Since the nonlinear high-frequency channels can be increased, the machine vision concept can also be extended to perform other learning tasks in parallel, such as edge extraction, image segmentation, and super-resolution imaging. In future work, we will experimentally prepare the device using processes such as electron beam lithography and deposition. The proposed methodology is important for massively parallel optoelectronic computing and will find new applications in machine vision, smart driving, bio-imaging, and smart medicine.

Edge detection technology based on optical analog differentiation is widely employed in fields such as microscopic imaging, data processing, and machine vision. In recent years, with the development of nanofabrication technology, various optical analog differentiators utilizing metasurfaces and metamaterials have been invented, which highly reduces the space required for optical imaging systems. We plan to propose a topological differentiator with a topological charge of 2 based on an all-dielectric one-dimensional photonic crystal (1DPC). By properly designing the bandgap structure of the 1DPC and the polarization state of input and output light fields, this topological device can perform isotropic two-dimensional second-order differential operations on the input optical field, leading to edge enhancement imaging and highly efficient edge information extraction.

The photonic chip is fabricated via PECVD (Oxford System 100, UK) of SiO₂ and Si₃N₄ layers on a standard microscope cover slip. All experiments are performed using a modified upright optical microscope (Ti2-U, Nikon, Japan), and the illumination beam with a central wavelength of 643 nm and a bandwidth of 2 nm is emitted from a supercontinuum fiber laser (SuperK EXU-6, NKT Photonics, Denmark). Left-handed circularly polarized input light incident on the objects of interest is placed on the photonic chip, and the right-handed circularly polarized component of output light passing through the photonic chip is filtered out with imaging conducted onto the detector. We introduce a spherical reference light to interfere with the output field to measure the winding number of topological charge.

According to the intensity profile in every direction of the back focal plane of the fabricated photonic chip, the optical transfer function of the chip satisfies the form required for second-order differentiation, which means this photonic chip can implement isotropic second-order differentiation. The interference result between reference light and output light represents that there is a second-order topological charge in the expression of optical transfer functions, which leads to isotropic differentiation. The USAF resolution test chart is adopted to demonstrate the performance of this photonic chip. Two peaks at the location of the chart's edge mean second-order differentiation is implemented. Additionally, the edge detection on biological objects indicates that this photonic chip can also be applied to the biological field.

We design a two-dimensional second-order topological differential optical chip operating in the transmission mode. The optical chip is composed of all-dielectric one-dimensional photonic crystals. By adjusting the structural parameters of photonic crystals, the optical transfer function required for second-order differential operation can be achieved. When the polarization states of the incident light and the output light are left-handed circularly polarized and right-handed circularly polarized respectively, a second-order topological charge is generated in the optical transfer function to achieve isotropic two-dimensional differential operation. We demonstrate the differential operation effect of the prepared optical chip on the incident light field by employing the USAF resolution test chart and biological sample. This topological differential device characterized by high throughput, high speed, and easy fabrication will have potential applications in optical computing, imaging, and sensing.

Nickel-based superalloys have already been extensively used in aviation manufacturing, particularly in the production of jet engine components such as turbine blades, airframe parts, and nuclear power plant components. The mechanical properties of these alloys make them highly desirable for these applications. To ensure the successful application of single crystal nickel-based superalloys, it is crucial to have a comprehensive understanding of their anisotropic properties. This includes knowledge of the elastic coefficients, thermal expansivity, and thermal conductivity. For these purposes, acoustic wave velocity is often employed as a primary quantity to access the parameters of these alloys since it is influenced by the module of elasticity and density. Any variation in material properties like porosity, residual stress, or even coating thickness in the case of surface waves can lead to changes in acoustic wave velocity. Monitoring the acoustic wave velocity can provide valuable information about the ongoing processes and their effects on material properties. Measuring the changes in acoustic wave velocity makes it possible to assess and track the progress of these processes. This information is important in evaluating the quality and integrity of manufactured components, as it helps in identifying deviations or abnormalities that may affect the final product.

Nondestructive testing (NDT) has offered a powerful approach for safety critical material inspections such as those in aerospace and nuclear industries by minimizing the risk of failure, thereby reducing costs and maximizing safety. Laser ultrasound technology (LUT) uses a pulsed laser source to locally heat the sample, and acoustic waves are then generated due to thermal elastic processes. A second laser is used to probe the generated acoustic wave. As thermal elastic constants are highly related to samples' density, stress, as well as crystallographic structures, one can then access the macroscopic or microscopic information of the sample and thus find the defects at both scales. As a consequence, LUT is receiving growing attention thanks to its great potential in the evaluation of defects, crystallographic orientation, and residual stress. Moreover, as LUT uses lasers to excite and detect the signals, the entire process is contactless, and it thus shows great advantages when inspecting samples with complex geometric structures and brings great convenience when used in environments with elevated temperatures or toxicity. In addition, LUT can inspect small specimens with high spatial revolution by using lenticular systems that allow the pump and probe lasers to focus on the surface of the sample. In recent years, laser ultrasound systems combined with wavefront modulation techniques have shown the capability of generating and detecting surface acoustic wave (SAW) with a specific frequency, which makes the mathematical modeling much simpler during data processing and in turn leads to an easier approach to access critical material properties such as crystallographic structures.

We discuss a new LUT that utilizes wavefront control to investigate the relationship between SAW velocity and crystal orientation in nickel-based superalloys. Nickel-based superalloys are widely used in aerospace turbofan blades due to their thermal resistance. Understanding the mechanical anisotropy of these materials is crucial for ensuring the mechanical performance and flight safety of turbofan blades. The technology combines numerical simulation and experiments to accurately measure the propagation velocity of SAWs and analyze the material's mechanical properties. A laser ultrasonic finite element numerical simulation model based on wavefront control is proposed. The simulation results reveal that the anisotropy ratios of SAW velocity in single crystal nickel-based superalloys in the (100) and (001) planes are 0.073 and 0.18, respectively (Fig. 4 & Fig. 6). To further investigate the relationship between crystal orientation and acoustic velocity in nickel-based superalloys, a laser ultrasonic microscopy system is employed (Fig. 7). This system enables the scanning and imaging of the surface acoustic velocity in both single crystal and polycrystalline nickel-based superalloys, facilitating the visualization analysis of surface defects and grain distribution (Fig. 10).

The simulation and experiment results indicate that the SAW velocity is sensitive to the orientation of the crystalline axis, which proves the capability of laser ultrasound systems combined with wavefront modulation techniques in the field of crystalline orientation determination and defect detection in an NDT manner

Photons can carry spin angular momentum (SAM) related to their polarization state and orbital angular momentum (OAM) related to their spiral phase. In recent years, spatiotemporal optical vortices (STOVs) that carry transverse OAM have gained rapidly growing interest in the field of optics due to their capacity to introduce new degrees of freedom for regulating the optical field. Current research is primarily concentrated on low-order STOVs, with limited attention given to the generation and propagation characteristics of high-order STOVs. We mainly investigate the generation of high-order strongly focused STOVs based on incident wavepacket preconditioning using mode conversion theory. Additionally, we also study the propagation characteristics of highly localized STOVs both before and after the focal plane.

Research has shown that when STOVs are focused by a high numerical aperture (NA) objective lens, they will experience the so-called “spatiotemporal astigmatism” effect similar to the focusing effect of a cylindrical lens on the Laguerre-Gaussian (LG) light field. Thus, STOVs will collapse and lose their spatiotemporal spiral phase on the focal plane of the high NA objective lens. With the understanding of such a spatiotemporal astigmatism, we preconditioned the incident wavepacket by a linear superposition of LG spatiotemporal wavepackets and then employed a high NA objective lens to focus the preconditioned incident wavepacket. The high-order STOVs on the focal plane or propagating away from the focal plane were calculated based on the Richards Wolf diffraction theory. In the simulations, it was assumed that the NA of the objective lens was 0.9, and the waist radius was set to be 0.5. Meanwhile, spatiotemporal coupling was ignored, and thus each temporal slice of the incident wavepacket was focused onto its corresponding temporal slice within the focal volume. The spatial sizes of the incident wavepackets were normalized to the pupil of the objective lens.

Although the third-order STOV exhibits transverse OAM (Fig. 1), its helical phase disappears when strongly focused by a high NA objective lens (Fig. 3). Based on mode conversion theory, we construct a third-order diagonal Hermitian-Gaussian (HG) wavepacket as the incident wavepacket by linearly superimposing third-order LG wavepackets. The preconditioned incident wavepacket is split, but the corresponding tightly focused wavepacket returns to a doughnut shape and regains the spatiotemporal spiral phase (Fig. 4). The phase of the focused wavepacket undergoes three continuous changes from -π to π in the clockwise direction, indicating that the strongly focused wavepacket is a high-order STOV with a purely transverse OAM with a topological charge of +3. Tightly focused STOVs with purely transverse OAM with a higher topological charge can also be generated based on mode conversion theory. For example, the fourth-order preconditioned incident wavepacket is strongly focused on realizing a fourth-order highly confined STOV (Fig. 5). We can find that the intensity distribution of the focused wavepacket exhibits a doughnut shape in the x-t plane. Additionally, the phase distribution changes continuously four times in the clockwise direction from -π to π in the x-tplane. The results once again demonstrate the feasibility of the presented method.

To study the propagation characteristics of highly localized STOVs both before and after the focal plane, we calculate the focused wavepackets at zf=λ and zf=-λ, respectively (Fig. 6). λ is the center wavelength of the wavepacket. From them, we can learn that the propagated focused three-order STOV degrades into three first-order vortices distributed diagonally in the x-tplane, and each vortex carries a transverse OAM of topological charge of +1. However, when the focused wavepacket propagates from zf=-λ to zf=λ, the intensity distribution of the focused wavepacket will rotate 90°. The total topological charge of the focused wavepacket in each case is 3. The results show that the total topological charge remains unchanged. The intensity distribution rotates, and the third-order phase singularity degrades into three first-order phase singularities for the propagated highly confined STOVs.

In the paper, we study the generation of high-order STOVs and their propagation characteristics. Due to the spatiotemporal astigmatism effect of the objective lens, the LG STOV will collapse after being strongly focused by a high NA objective lens, which will lead to the disappearance of the spatiotemporal spiral phase. To solve the problem, we linearly superimpose the LG wavepackets into diagonal HG wavepackets based on the mode conversion theory. Using the preconditioned wavepackets as the incident wavepackets of the focusing system, we successfully generate STOVs with topological charges of +3 and +4 on the focal plane of a high NA objective lens. When highly confined STOV propagates in the vicinity of the focal plane, the topological charge remains unchanged, and the intensity distribution rotates. The high-order spatiotemporal phase singularity will degrade into several first-order spatiotemporal phase singularities, which can be employed to generate spatiotemporal vortex arrays.

The traditional focusing device is restricted by the Abbe diffraction limit. This means that the spatial resolution cannot exceed its theoretical minimum value of 0.5λ/NA, where λ is the working wavelength and NA is the numerical aperture. Existing methods to break the diffraction limit require a near-field environment, which is insufficient for far-field super-resolution imaging in the optical sense. The principle of optical super-oscillation states that it is theoretically possible to produce a super-resolution spot of arbitrary smallness by rationally modulating the wavefront of incident light. Optical super-oscillation has been extensively studied by researchers in super-resolution optical lenses, and this principle enables the experimental realization of far-field super-resolution focusing. However, the optical field regulation of the super-oscillation lens depends on precise nano-processing technology. Additionally, the fabrication cost and complexity limit the device to a small size. Thus, we propose a method to generate the far-field super-resolution optical field based on the spatial light modulator. The design of the far-field super-resolution focusing device is based on the super-oscillation principle, with the binary particle swarm optimization algorithm and the angular spectrum diffraction theory combined. The generated focal spot full width at half maximum (FWHM) is smaller than the diffraction limit, which can be employed to construct the far-field super-resolution optical field.

The device is designed based on the super-oscillation principle and adopts eight-value phase control for circularly polarized light with a wavelength of 632.8 nm. The two-dimensional phase distribution of the device is optimized using the binary particle swarm optimization algorithm and angular spectrum diffraction theory. This optimization helps obtain the optimal phase of the mask and its corresponding characteristic parameters. The device is composed of a series of concentric ring belts, each with 8 μm width, which is equal to the size of spatial light modulator (SLM) pixels adopted in subsequent experiments. To obtain an optimized phase mask, we calculate the phase of each ring belt and generate a grayscale image based on the SLM phase control characteristics. Additionally, to verify the focusing performance of the designed device, we design and build a construction and measurement system for the far-field super-resolution optical field. We measure the characteristic parameters of the super-resolution optical field using an objective lens combined with a complementary metal oxide semiconductor (CMOS) camera. The motorized linear translation stage is moved to obtain the two-dimensional optical field distribution at different positions. Finally, an image processing algorithm is then utilized to extract the key focusing parameters of the focal spot, leading to a three-dimensional intensity distribution of the optical field.

First, the corresponding grayscale images are generated based on the phase of each ring belt of the super-oscillatory mask obtained from the optimized design (Fig. 3). Next, the design results of the optical field are calculated by adopting the angular spectrum diffraction theory (Fig. 4). An experimental platform is then set up, and the super-oscillatory mask is loaded onto the liquid crystal screen of the spatial light modulator. Finally, the optical field is scanned and tested within the range of Z=185.00 mm to Z=195.00 mm. The scanning step ΔZ is 0.05 mm, and the intensity distribution of the optical field is obtained. Experiment and theoretical results demonstrate excellent agreement, and the transverse FWHM at the focal length of the focal spot is 22.384 μm, which is below the diffraction limit (0.5λ/NA, 23.732 μm), with far-field super-resolution focusing achieved (Fig. 6). Along the propagation direction, the vertical FWHM is 6.029 mm, creating an optical needle (Fig. 7). The device is easy to operate and does not require complex processing.

To solve the problem of traditional focusing devices are constrained by the diffraction limit, we propose a method for constructing a far-field super-resolution optical field with eight-value phase control based on the optical super-oscillation principle. By adopting particle swarm optimization and angular spectrum diffraction theory, we design a far-field super-resolution focusing device for circularly polarized light with a wavelength of 632.8 nm. This is achieved by loading a super-oscillation phase mask onto the liquid crystal screen of a spatial optical modulator. By adjusting the phase of the incident optical field, the device generates an optical needle with the vertical FWHM of 6.029 mm. The FWHM at the focal length of the focal spot is lower than the diffraction limit, thus achieving far-field super-resolution focusing. This method can be applied to the visible bands and extended to other optical bands, providing core focusing devices for optical microscopy, optical imaging, and other optical applications.

Traditional imaging systems, due to their focal plane structure, exhibit significant optical gain but have a limited depth of focus. This creates a paradoxical scenario: achieving high image quality comes at the expense of weak laser protection capabilities. Established methods for laser protection in optoelectronic imaging systems encounter challenges including reliance on prior knowledge, bandwidth limitations, and degraded image quality. To address the conflict between image quality and laser protection, researchers utilize wavefront coding technology, leveraging its deep focus characteristics and light field regulation. This enables defocusing the image plane to enhance the system's laser protection capacity without compromising image quality. While wavefront coding can achieve a balance, previous studies have placed excessive focus on how defocus affects laser protection, overlooking its consequential impact on image quality and essentially ignoring how image quality can restrict laser protection. Therefore, investigating the balance between laser protection capability and image quality in wavefront coded imaging systems, as well as understanding the limits of the system's laser protection, is of utmost importance. We aim to examine this balance within the context of the arcsine wavefront coded imaging system and discern the limits of its laser protection capabilities.

Using the arcsine phase mask (ASPM) as an exemplar, we build imaging and laser transmission models for a defocused wavefront coding system. The trends are investigated in image quality and laser protection as the defocus parameters shift. By employing a decoupling approach, we take the system's image quality as a fundamental constraint. To ascertain the system's maximum permissible defocus parameters, we introduce quantitative evaluation metrics. Furthermore, our study assesses the system's laser protection capability based on these parameters, providing insights into the protection limits of wavefront coded imaging system.

Numerical simulations of the imaging model demonstrate that in conventional imaging system, increasing defocus parameters gradually blur the resulting image, leading to a significant deterioration in image quality. In the case of the ASPM wavefront coded imaging system, the coded image, modulated by the ASPM, also becomes blurred. However, by selecting an exploratory parameter K=4.25×10^-4, the decoded image closely resembles the imaging effect of the conventional imaging system in its non-defocused state. This indicates that the ASPM wavefront coded imaging system achieves superior depth-of-focus extensions through joint hardware and software optimization (Fig. 5). To quantitatively evaluate the changes in image quality with defocus parameters, we employ peak signal-to-noise ratio and structural similarity metrics. Based on the Rayleigh criterion and using the peak signal-to-noise ratio and structural similarity values of the conventional imaging system as a threshold, we compute the defocus limit for the wavefront coded imaging system to be 9.70λ. The numerical simulation results of the laser propagation model reveal that as defocus parameters increase, the size of the light spot at the imaging plane of the conventional system grows rapidly. This leads to a sharp decline in light intensity and a significant reduction in the maximum single-pixel receiving power. However, the wavefront coded imaging system, with its defocus invariance, exhibits a more gradual decline in its maximum single-pixel receiving power (Fig. 6). Furthermore, both the conventional and wavefront coded systems show a decreasing trend in echo-detection receiving power (Fig. 7 and Fig. 8). At the same defocus parameters, the echo spot size of the wavefront coded imaging system is similar to that of the conventional imaging system, and their echo-detection receiving power are essentially the same. Therefore, the defocus limit of the imaging system determines the boundary of its laser protection capability.

By considering the image quality of the ASPM wavefront coded imaging system as a fundamental constraint, we establish that the maximum permissible defocus parameter for the wavefront coded imaging system is determined to be 9.70λ. When compared to the non-defocused state of the conventional imaging system, at this specific defocus parameter, the ASPM wavefront coded imaging system experiences a significant decline in the maximum single-pixel receiving power, reaching 96.37%. Additionally, the echo-detection receiving power drops to 0.217‰. These findings highlight the enhanced capabilities of the wavefront coded imaging system, with an improvement over one order of magnitude in anti-laser damage and three orders of magnitude in anti-laser active detection.

3D display technology is the entrance to the realistic-feeling metaverse for tabletop, portable, and near-eye electronic devices. True 3D displays are mainly divided into light field displays and holographic displays, among which light field displays can be further subdivided into integral-imaging displays, directional light field displays, and compressive light field displays. Compressive light field displays utilize the scattering characteristic of display panels and the correlation between viewpoint images of the 3D scene. The compressive light field display is a candidate for portable 3D display owing to its compact structure, moderate viewing angle, and high spatial resolution. However, computational resources of portable electronic devices are restricted to satisfy their duration demand. Meanwhile, iterative algorithms to solve the compressive light field display patterns have the problem of heavy computation, preventing compressive light field displays from being a practical solution to portable dynamic 3D displays. With the development of artificial intelligence technology, image generation algorithms based on deep learning are gradually applied to 3D displays. Deep neural networks can be trained to fit the iterative process. Additionally, fast display image synthesis could be realized with rapid forward propagation of artificial neural networks. Previously, researchers proposed a stacked CNN-based method to generate images for compressive light field displays. However, the stacked CNN-based method suffers from convergence and over-fitting problems. U-Net is initially employed for image segmentation in computed tomography to handle slicing data and output the organ’s cancer probability. The skip connection added in the U-Net architecture significantly improves its convergence compared with the stacked CNN model. Light field data are pretty similar to slicing data in computed tomography. Thus, we introduce U-Net as the network model for optimizing compressive light field display patterns for better convergence and generalization. Given a specific viewing angle, several augmented target light field datasets are generated as the training sets of U-Net. After the U-Net converges, the trained U-Net synthesizes the display patterns that reconstruct the target light field for testing. The training and testing results prove that compared to the stacked CNN-based method and iterative algorithms, the proposed U-Net-based pattern generation method for compressive light field displays features higher reconstruction quality and fewer computing resources.

An artificial neural network’s training procedure can be split into forward and backward propagation. The forward propagation includes the following steps. Firstly, the target light field for training is input into the network, display images are output, and then the light field is reconstructed by simulated perspective projection. The backward propagation is to update the network’s parameters with the loss function and regular terms. Meanwhile, the above procedure is repeated during every epoch and batch. When the training is finished, the target light field for testing is input into the network, and display images are synthesized. This is called the inference procedure. The datasets, network architecture, and hyper-parameters are carefully designed to fit the features of compressive light field displays. The datasets contain 1260 pairs of image blocks cropped from seven scenes. The ReLU function is set as the activation function of the U-Net model initialized uniformly with Kaiming Initialization. The loss function is the mean square error between the target and reconstructed light field and the regular term is the effective range of image pixel values.

Performances of the proposed U-Net-based method, the stacked CNN-based method, and iterative algorithms are compared fairly for multiplicative (Fig. 8), additive (Fig. 9), polarized (Fig. 10), and hybrid (Fig. 11) types of compressive light field displays. The training and testing results (Figs. 17-20) prove that the proposed method’s light field reconstruction quality is always 2 dB higher than that of stacked CNN-based method. The reason is that the U-Net-based method utilizes the value range of image pixels more effectively than the stacked CNN-based method. Additionally, for additive-type compressive light field displays, the proposed method takes less time to reach the same reconstruction quality than iterative algorithms (Fig. 21).

To improve the image quality, uniformity, and computation performance of compressive light field displays, we apply an elaborate U-Net model to synthesize display images. The proposed method is compared with the stacked CNN method and iterative algorithms by simulating the perspective projection of display images with the same target light field as input. For the additive-type compressive light field display, the trained U-Net’s inference speed is much faster than the speed of iterative algorithm under the same reconstruction quality. However, the trained U-Net’s generalization performance still needs promotion for multiplicative and polarized-type compressive light field displays. Possible improvements are changing activation functions and increasing the network’s depth.

Thermal effects in optical microcavities have an important influence on field evolution. Currently, the study on thermal effects in microcavities focuses on thermal oscillations. The thermal oscillations are caused by thermal expansion, thermo-optic effect, and Kerr effect, which lead to strong mode oscillations in microcavities. Self-stabilization of optical microcavities can be achieved by exploiting the resonance shift induced by the dynamic thermal effect. Through the thermo-optic (TO) effect, optical microcavities can be employed as temperature sensors with sensitivities up to 0.016% (RH) or higher. In addition, some studies on the thermal effect of microcavities focus on the influence of the optical field variation and thermal effect during the scanning process of the pump wavelength. However, there is a lack of discussion on the influence of thermal effects on the optical field in the microcavity, and existing studies fail to analyze how to maintain the solitons generated during the thermal effects. Therefore, in this paper, the effect of thermal response on the optical field in the enclosure is analyzed by taking the silica optical microcavity as an example, and a multi-soliton holding method is proposed.

In general, the variation of the optical field in the microcavity with time was described by the Lugiato-Lefever equation (LLE). On the basis of LLE, the thermal effect in the microcavity was taken into account, which consisted of the TO effect and the thermo-expansion (TE) effect. For the optical microcavity of SiO₂ material discussed in this paper, since both the TO and TE effects were positive, and the coefficient of the TO effect was much larger than that of the TE effect, only the TO effect in the thermal effect was considered for the SiO₂ optical microcavity. Generally speaking, during the microcavity operation, the thermal effect caused by the absorption of the optical field could change the resonant wavelength of the microcavity, which further led to the change of the detuning parameter. Therefore, the thermal effect would eventually cause a change in the microcavity operating state. In this paper, we combined the thermal effect with the LLE, and the field in SiO₂ optical microcavities with thermal effects was investigated.

It is found that when the initial state is zero detuning, the resonant wavelength of the microcavity drifts in the positive direction under the thermal effect, and the resulting thermal detuning can excite the optical field in the form of multiple solitons inside the microcavity. However, with the accumulation of thermal effects, the thermal shift of the resonant wavelength increases, causing excessive detuning in the cavity, which leads to the gradual disappearance of the multi-soliton. In other words, under the influence of the thermal effect, the multi-soliton optical field can only exist briefly in the SiO₂ optical microcavity. On this basis, we propose to utilize the regulating of the pump wavelength and power to maintain the multi-soliton in the microcavity. When the multi-soliton is generated in the microcavity, the pump wavelength is scanned at a suitable speed to compensate for the detuning caused by the thermal effect so that the total detuning in the microcavity remains constant. In this case, the multi-soliton state in the cavity can be maintained stably even if thermal effects exist.

Since the tuning power and wavelength scanning speed of the pump lead to different results in the evolution of the original multi-soliton optical field, the effect of the pump tuning parameters on the multi-soliton optical field is also investigated. It is found that the number of regulated multi-soliton pulses is related to the regulating power of the pump. Higher regulating power of the pump indicates a more pronounced thermal effect in the microcavity and a larger resulting thermal shift of the resonant wavelength. When the pump wavelength is scanned at the same rate, a highly regulated pump power induces a larger detuning parameter, and the regulated multi-soliton optical field contains a larger number of pulses. Moreover, by keeping the regulated pump power constant, only a proper tuning speed of the pump wavelength can maintain the multi-soliton optical field in the microcavity. A small tuning speed of the pump wavelength leads to a gradual disappearance of the multi-soliton optical field. If the pump wavelength scanning is too fast, it will make the drift of the pump wavelength exceed that of the resonant wavelength, which makes the microcavity in a positive detuned state and ultimately leads to the evolution of the original multi-soliton optical field into a chaotic optical field. The results are of great significance for the generation of stable multi-soliton optical fields in SiO₂ optical microcavities in practice.

The regulating process of SiO₂ microcavity optical field under thermal effect is investigated. When the initial condition of the microcavity is zero detuning, the optical field in the form of multiple solitons can be generated inside the microcavity under the thermal effect. However, due to the increasing thermal detuning caused by the thermal effect, the multi-soliton will eventually disappear. In order to maintain the multi-soliton optical field in the microcavity, we propose to utilize the tuning of the pump wavelength and power to maintain the multi-soliton in the microcavity. After the generation of multi-soliton in the microcavity, the pump wavelength is scanned at a suitable speed to compensate for the detuning caused by thermal effects so that the total detuning in the microcavity remains constant. In this case, even if there is a thermal effect, the multi-soliton state in the cavity can be maintained stably. We also investigate the effect of the pump tuning parameters on the multi-soliton optical field. Higher tuning power of the pump indicates more obvious thermal effects in the cavity and larger thermal drift of the resonant wavelength, and the tuned multi-soliton light field contains more pulses. The small tuning speed of the pump wavelength will lead to the gradual disappearance of the multi-soliton optical field. The fast pump wavelength scanning will make the drift of the pump wavelength exceed the shift of the resonant wavelength, thus making the microcavity in a positive detuned state and ultimately leading to the evolution of the original multi-soliton optical field into a chaotic optical field. The study on the thermal effect of optical microcavities has important practical significance for the real application of optical microcavities.

In the context of multifunctional operation and diversified application requirements, how to expand the controllable degrees of freedom of vortex beams has become an urgent scientific problem to be solved. Compared to traditional vortex beams with one phase singularity, multi-singularity vortex beams generated by vortex coherent superposition can achieve precise control on phase singularities, significantly enriching the control methods of phases in structured light fields. Light sources are crucial for the application of structured beams. Compared to highly coherent structured beams, partially coherent structured beams are proven to have the ability of anti-turbulence scintillation and speckle suppression, which demonstrate significant advantages in atmospheric transmission and imaging. As a common partially coherent fiber laser, random fiber lasers (RFLs) which employ Rayleigh scattering in passive fibers to provide random distributed feedback are widely adopted as illumination sources for structured light fields. Currently, various typical structured beams such as LP₁₁ mode, vortex beam, and cylindrical vector beam have been generated and controlled based on RFLs. However, there are no reports on RFL-based multi-singularity vortex beams. The combination of the partial coherence of RFLs and singularity control of structured beams can expand the multidimensional manipulation of structured light fields, and the application scope in many fields such as optical tweezers, free-space communication, and speckle correlation imaging. Here, multi-singularity vortex beams generated by an RFL are firstly proposed and demonstrated. The RFL with a central wavelength of 1081.3 nm is constructed and employed as the illumination. By coherent superposition between Laguerre-Gaussian (LG) beams with different topological charges, multi-singularity vortex beams with controllable singularity numbers are achieved.

Coherent superposition of two zero-order LG beams is simulated and analyzed. The distribution of superimposed light field is given by Eq. (4), and intensity and phase distributions of superposition states with different topological charges are obtained. The RFL is experimentally built with a backward-pumped half-opened cavity, as shown in Fig. 5(a). The pump light is provided by a 1030 nm ytterbium-doped fiber oscillator, and the output end is connected with a cladding power stripper (CPS) to filter out the cladding light. A circulator (Cir) is mounted after the CPS to protect the pump source from backward light. Subsequently, by employing a 1030 nm/1080 nm wavelength division multiplexer (WDM), the 1030 nm pump light is injected into a 5 km single-mode fiber (SMF) with a core/cladding diameter of 8 μm/125 μm. The generated 1081.3 nm signal light is reflected by a highly reflective fiber Bragg grating (HR FBG, the center wavelength of 1081.3 nm and reflective bandwidth of 0.07 nm), and then it is emitted via the WDM. The laser gain of the RFL is provided by stimulated Raman scattering in the SMF, and the feedback is offered by both random distributed scattering in the SMF and point feedback of the HR FBG. By utilizing the RFL as the illumination, a spatially optical path is constructed to generate a multi-singularity structured light field [Fig. 5(b)]. The Gaussian beam from the RFL is firstly collimated and expanded, and then transmitted into horizontally polarized beam with high polarization degree and adjustable intensity by two polarization beam splitters (PBS1, PBS2) and a half wave plate (HWP). After a 50∶50 non-polarization beam splitter (BS), the horizontally polarized beam is divided into a transmitted beam and a reflected beam, which are incident at different positions of the spatial light modulator (SLM) after being reflected. By loading different phase maps on the SLM, two vortex beams with different topological charges can be obtained. Meanwhile, interference is conducted on the two vortex beams by the BS to form a vortex superposition state with multiple singularities. The intensity of the superimposed beam is focused via a lens and collected by a CCD camera.

The superimposed intensity distributions of zero-order LG beams with different topological charges perform petal patterns, and the number of petals is l1-l2. Meanwhile, the phase distributions of the superimposed beams vary according to different topological charges. The phase distributions obtained by superimposing two zero-order LG beams with equal absolute value and opposite signs of topological charges are shown in Fig. 1, with no spiral phase wavefront. Superposition states generated by zero-order LG beams with unequal absolute values of topological charges are described in Figs. 2, 3, and 4, and have the characteristic of spiral phase wavefront with newborn phase singularities due to phase coupling. The newborn singularity number is l1-l2, and the total singularity number is l1-l2+1. The topological charge of the central singularity corresponds to the topological charge of the LG beam with a smaller diameter. The absolute values of topological charges of the newborn singularities are 1, which are uniformly distributed around the central singularity.

The output characteristics of the RFL are demonstrated in Fig. 6. The central wavelength of the random laser is located at 1081.3 nm with a generation threshold of 2.36 W and a maximum power of 2.26 W, corresponding to a slope efficiency of 58.91%. Further power enhancement is limited by the stimulated Raman scattering effect. The 3 dB bandwidth of the RFL gradually widens with the increasing pump power, reaching a maximum of 0.23 nm. The vortex superposition states using the RFL as the illumination are plotted in Figs. 7 and 8. The experimental beam spots are consistent with the simulation results. By changing the topological charge of the LG beam, the singularity number of the generated multi-singularity vortex beam can be flexibly switched.

Partially coherent multi-singularity vortex beams generated by an RFL are firstly proposed and demonstrated. The superposition state of two zero-order LG beams is simulated. The results indicate that vortex superposition states with equally absolute values and opposite signs of topological charges show no spiral phase distribution, while the states with unequal absolute values of topological charges generate new phase singularities due to phase coupling between the two LG beams. Additionally, a random distributed feedback fiber laser with a central wavelength of 1081.3 nm is constructed, with a maximum output power of 2.26 W. By employing the RFL as the illumination, a spatially triangular interference path is built to achieve coherent superposition of vortex beams. Multi-singularity vortex beams with various intensity distributions are generated, and newborn singularities are uniformly distributed around the central singularity. The total singularity number is l1-l2+1, which can be flexibly tuned by adjusting the topological charges of the two LG beams. This work may expand the application scope of RFLs, and provide light sources for many fields such as particle trapping, vortex optical multiplexing communication, and imaging.

High-power mid-infrared lasers extensively apply in explosive monitoring, medical diagnosis, environmental monitoring, infrared countermeasures, and industrial control. However, limited by the upper-level electron injection efficiency and the energy level structure, the output power of the mid-infrared laser quantum cascade operating under fundamental transverse mode cannot exceed 3 W. Beam combining technology has been proven to be an effective way to further expand output power and brightness. Taking full advantage of good linear polarization characteristics of semiconductor lasers, polarization beam combining offers simple structure and high efficiency. Moreover, it can be synergistically combined with other beam combining technologies to further enhance output power and laser brightness. Traditional polarization beam combiners are Brewster plate, metal grating polarizer, and birefringent prism. For the Brewster plate, broadband (approximate 100 nm), high transmission coating for P-polarization is required. It is a big challenge to mid-infrared. Due to the presence of metal lines, the transmission of the metal grating polarizer is usually lower than 80%, which results in a low beam combing efficiency. Commonly used birefringent MgF₂ prism in mid-infrared has a small separation angle of 1.2°, which makes the optical path arrangement difficult. Metasurfaces offer a high degree of freedom in optical wave amplitude, phase, and polarization state regulations. It has already been applied in polarization beam splitters, which inspires the design of a beam combiner. By anomalous reflection, two light beams with orthogonal polarizations and different incident angles can be reflected in the same direction. We propose a polarization beam combiner based on anomalous reflection metasurface, which shows a high efficiency and broad working spectral band.

The proposed metasurface consists of periodic supercells. Each supercell contains 10 discrete single cells, which comprise a metal substrate, a dielectric middle layer, and a top rectangular column. By changing the two side lengths of the rectangular column of single cells, desired phase responses can be achieved for two orthogonal polarized incident beams. When ten optimized single cells are arranged spatially, the X-direction linear polarization (X-LP) incident beams experience a positive linear phase response. Meanwhile, the Y-direction linear polarization (Y-LP) incident beam experiences a negative linear phase response. Therefore, both beams are reflected perpendicularly to the metasurface when the incident angles of X-LP and Y-LP beams are 11.54° and -11.54° respectively.

According to the purpose and methodology of this study, we design a metasurface polarization beam splitter optical path operating in the middle-wave infrared range [Fig. 1(a)] and a three-layer metasurface structure [Fig. 1(b)]. By modeling the individual unit cell of the metasurface [Fig. 1(c)], we calculate the phase and amplitude responses of X-LP and Y-LP incident beams as we vary the length and width of the rectangular antenna column from 0.2 to 1.6 μm [Fig. 2(a)-(b)]. The particle swarm optimization algorithm is employed to determine the dimensions of the rectangular antenna that satisfy our desired phase requirements (Table 1). The phase introduced by the designed single cell aligns well with expectations for both incident polarizations while maintaining consistently high reflectivity levels throughout [Fig. 2(c)]. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface [Fig. 3(a)-(b)]. Reversely, when the collimated X-LP and Y-LP beams incident perpendicularly on the metasurface beam combiner, the X-LP beam is reflected in 11.54° direction and the Y-LP beam is reflected in -11.54° direction [Fig. 3(c)-(d)]. When the incident beam has a divergence angle of 50 mrad, the reflected beam has a divergence angle of 48 mrad [Fig. 3(e)]. To study the anomalous reflection of the metasurface for a light source with broad spectral bandwidth, we scan the incident light central wavelength from 3.9 to 4.1 μm. The resulting combined beam exhibits a divergent angle of 10 mrad while the reflectivity is maintained as high as 95% (Fig. 4). Based on the above theoretical simulation results, the reflected beam propagation properties in the free space are investigated by Zemax’s physical optical propagation (POP) tool. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the reflected X-LP beam is 1.11, and that of the reflected Y-LP beam is 1.12 (Fig. 5). Therefore, when X-LP and Y-LP beams are combined to propagate in the same direction, the beam quality factor of the combined beam is 1.12 [Fig. 6(a)]. The spectrum of the combined beam coincides well with the overlap of the two individual incident laser spectra [Fig. 6(b)]. Consequently, this study demonstrates that a polarization beam combiner based on the anomalous reflective metasurface has not only high combination efficiency but also broad operation bandwidth. It is suitable to be used for the mid-infrared QCL power combining.

We study a polarization beam combiner based on anomalous reflective metasurface, which is utilized to combine two incident beams with orthogonal linear polarizations. The beam combiner consists of periodic supercells with a dimension of 2 μm×20 μm. Each supercell contains 10 single cells of 2 μm×2 μm. The single cell comprises a metal substrate, a dielectric middle layer, and a top rectangular column. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface. The polarization beam combination is realized. Within a broad spectral band of 3.9 to 4.1 μm, high average anomalous reflectivity of 96.6% and 97.7% are obtained for X-LP and Y-LP incident beams, respectively. Based on the near field reflective intensity and phase distribution, the propagation of the combined beam in free space is simulated by the periodic field splicing method and Gaussian beam propagation law. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the combined beam is 1.12. The metasurface beam combiner shows high design flexibility and can be prepared by mature MEMS technology. It has a good potential to solve the problems in mid- and long-infrared power beam combinations.

In recent years, vortex beams carrying orbital angular momentum (OAM) have caught much attention due to their research significance and application prospects. With the applications of vortex beams in sensing, measurement, and high-capacity optical communication, the output bandwidth and wavelength tunability of vortex beams have become a research focus. Breaking through the emission wavelength limitation of rare-earth doped fiber, and the device of broadband mode conversion is the basis for realizing the output of special band/broadband vortex light. Currently, many devices can realize vortex beam output in a fiber laser. However, most devices are designed and manufactured according to the target wavelength. The acoustically-induced fiber grating (AIFG) achieves mode conversion by acousto-optic coupling in passive fibers. When the operating wavelength changes, it only needs to change the frequency of the loaded electric signal, without re-designing and replacing the parameters of the mode conversion device. Theoretically, it has an extremely wide operating bandwidth. Considering the above requirements, the structure of random Raman fiber laser (RRFL) based on distributed Rayleigh backscattering is adopted to realize broadband vortex beams by combining the AIFG.

By combining the AIFG and RRFL, when the output wavelength is converted by Raman frequency shift, there is no need to redesign and replace the mode conversion device. The transmission spectrum of the LP₀₁ mode is tested in Fig. 1(b), which indicates that there is a high efficiency of mode conversion from 1000 to 1700 nm. The RRFL is built as shown in Fig. 2. An amplified spontaneous emission (ASE) source including two amplification stages is utilized as the pump source which is then coupled into the half-open cavity of RRFL by wavelength division multiplexing (WDM). The half-open cavity is formed by a high-reflective (HR) optical fiber mirror which is attached to the WDM, a piece of gain fiber, and a homemade fiber endcap. The reflectance of the HR mirror is more than 99.5% at 1-2 μm, and anti-reflection coating is conducted on the endcap to evade unwanted end feedback. The gain fiber is the commercial CS980 fiber with a length of 500 m. Once the suitable electrical signal is loaded on the AIFG, the output mode is converted to LP₁₁ mode, and the ring-shaped radially polarized light and vortex beam with topological charge l=±1 output can be realized by precise polarization control.

When the pump power reaches the Raman threshold, the pump energy begins to transfer to the Raman Stokes. By integrating the output spectrum, the variation curves of the Raman optical power of each order are calculated, as shown in Fig. 3(a). When the pump power reaches 76 W, the output wavelength reaches 1513.7 nm by the six-stage Raman shift, with a power of 23.6 W and a total efficiency of 31.1%. With the cascaded wavelength conversion, the purity and efficiency of high-order Raman light decrease, which is shown in Figs. 3(c) and 3(d). With the increasing output wavelength, the loss of gain fiber rises with the incomplete conversion of each stage, which results in a gradual efficiency decrease. Once there is a π/2 phase difference between the eigenmodes by controlling the polarization controller (PC), the vortex beam can be realized via the superposition of the two modes, and the “Y-shaped” interference fringe can be detected by the self-interference experiment (Fig. 5), which proves that the vortex beam with topological charge l=±1 is generated.

We propose an all-fiber high-power RRFL with vortex beam output in the 1.1-1.5 μm band. Based on the cascaded Raman shift and broadband AIFG, the output of vortex beams with topological charges l=±1 at 1133.9, 1197.6, 1260.5, 1331.8, 1414.5, and 1513.7 nm wavelengths is realized, and the topological charge is verified by self-interference experiments. After the six-stage conversion, the power at 1513.7 nm wavelength is 23.6 W, with an efficiency of 31.1%. The ultra-wide wavelength tuning capability of the AIFG is expected to make it a key device to fill the spectral gap of vortex beams and can provide a reliable light source for the application of special wavelength vortex beams. By replacing the pump source, gain fiber, and related devices, the wavelength coverage of the vortex beam can be further expanded in other wavebands, and the application of vortex light in multi-dimensional optical communication and interaction between light field and matter can be further expanded.

The problem of low optical efficiency commonly exists on metasurfaces, which restricts their application and development. Although the efficiency of metasurfaces designed based on dielectric nanobricks structures is greatly improved compared to metal metasurfaces, the scattering and reflection losses of the unit structure are still relatively large. Metasurfaces are generally composed of high refractive index nanobricks to reduce their thickness and preparation process difficulty. Due to the high refractive index of the equivalent film layer on a high refractive index metasurfaces, it leads to significant interface reflection loss. In terms of improving the efficiency of metasurface devices, current research mainly focuses on improving the diffraction efficiency of metasurfaces and reducing scattering losses. However, there is no research focus on the reflection loss of metasurfaces currently, so it is necessary to study reducing the reflection loss of metasurfaces.

We propose an efficient design scheme for metasurfaces based on optical thin film theory to solve the problem of interface reflection loss caused by the mismatch between the equivalent refractive index of the metasurfaces and the substrate, as well as the mismatch between the equivalent optical thickness of the metasurfaces and the wavelength. First, we design the metasurface lens. Then, based on the equivalent medium theory, the metasurfaces are equivalent to a layer of dielectric thin films and serve as the outermost layer of the multi-layer antireflection coating system, with the equivalent layer thickness being the height of the metasurfaces. Finally, the optical thin film theory is adopted to design the antireflection coating that matches the substrate and incident medium.

We simulate the near-infrared broadband silicon nanobrick metasurface lens on the quartz substrate and compare it with the metasurfaces designed with optical thin films. The transmittance of the antireflection coating designed by the equivalent medium theory is much higher than that of the equivalent film layer on the metasurfaces, with an average transmittance of 12.4% higher (Fig. 4). Comparison is made between the light field distribution patterns of a metasurface lens without optical thin films and with optical thin films (the antireflection coating structure of optical thin films combined with a metasurface) at different wavelengths (1460, 1530, 1600 nm). It can be seen that the focal spot size and focal length of the two types of structured metasurfaces at the same wavelength are basically the same. In the case of optical thin films, the light intensity at the focal point is significantly higher than that without optical thin films, whereas the focal point position is not affected by the antireflection coating and remains unchanged. This indicates that optical thin films only increase the transmittance of the metasurfaces and have little effect on their focusing performance (Figs. 5-7). The transmittance curves in the 1450-1600 nm wavelength range and the focusing efficiency at 1450, 1490, 1530, 1565, 1600 nm wavelengths are simulated and calculated. From the transmittance curves, it can be seen that in the 1450-1600 nm wavelength range, the transmittance of the metasurface lens designed with optical thin films remains around 94.0%, with the highest peak reaching 95.5%, which is much higher than that of metasurface without optical thin films, with an average increase of more than 10.5% (Fig. 8 and Fig. 9). The results of simulation calculations indicate that our proposed idea of combining optical thin films with metasurfaces is reasonable and has the potential to be applied to the actual production of metasurfaces.

We propose the concept of using optical thin films to improve the efficiency of metasurfaces. The characteristics of metasurface lens are studied in the near-infrared, and based on the properties of additional functional optical thin films on metasurfaces, the influence of the antireflection coating on the transmittance and focusing performance of metasurfaces are studied. Research has shown that combining the structure of optical thin films with the metasurfaces can significantly improve the optical efficiency of metasurfaces without affecting their optical properties. The idea of combining metasurfaces with the proposed optical thin films is expected to solve the problem of low efficiency of metasurfaces, bringing new ideas for the design of metasurface devices.

To solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent three-dimensional spatial resolution have important applications in optical microscopy and metal particle capture. In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions. To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.

We present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by de-focusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.

Firstly, the number of generated spatial spherical focused spots is related to odd or even multiple of half wavelength (Fig. 2). When the length of the dipole antenna L is an odd multiple of half wavelength, two same intensity spherical spots symmetrical at the center of the focus are formed in the set spatial direction. When L is an even multiple of half wavelength, three spherical focused spots with the equal size are formed, with one high-intensity spot at the focus and two lower-intensity spots symmetrically arranged. Since the distance between spatial spherical focused spots is calculated to be equal to L, the distance of spatial spherical focused spots can be easily adjusted by changing the parameter L. Meanwhile, arbitrary spatial directions of spherical focused spots are created to demonstrate the flexibility of the proposed method (Figs. 4 and 5). It is observed that the direction of the spherical focused spots is consistent with the polarization direction of the dipole antenna. Finally, we investigate the normalized input field Eiρ,φ required to create the spatial spherical focused spots (Figs. 6 and 7). It is evident that the polarization direction of the input field is determined by the dipole antenna parameter φ0, and the dipole antenna parameter θ0 determines the spatial rotation angle of the input field.

We present a simple and flexible method for generating spherical focused spots of prescribed length and controllable spatial orientation. By focusing the electromagnetic field radiated by a virtual dipole antenna in reverse at the focal point of a 4Pi focusing system, spherical focused spots with specified characteristics can be conveniently obtained. The simulation results show that the number of spherical focused spots is related to odd or even multiple of half a wavelength, and the distance between spherical focused spots is adjustable and only depends on the antenna length L, while the spatial direction of spherical focused spots is controllable and depends on the antenna parameters θ0,φ0. Furthermore, all spherical focused spots generated by the optical antennas are of the same size, with a full width at half maximum (FWHM) of 0.459λ. The generated spatial spherical focused spots have potential applications in precise multi-point trapping of spatial nanoparticles with full degrees of freedom, showing broad prospect in optical micro-manipulation.

Light absorption and scattering pose great challenges to applications such as atmospheric optical communication and biological optical manipulation. Exploring special beams with minimal influence has been a research hotspot in light field manipulation. Currently, a mainstream method is to shape the beam by wavefront shaping to restore its light field. However, this method is quite complex and requires pre-calibration of the scattering process and restoration via complex algorithms, which increases the difficulty. Therefore, we directly look for a more robust beam that can reduce the light field distortion in complex environments. Meanwhile, we investigate the propagation characteristics of circular swallowtail beams with autofocusing properties in atmospheric turbulence. By analyzing the distortion and intensity fluctuations of the beam in complex environments, we study circular swallowtail beams' propagation in resisting turbulence scattering. Finally, theoretical support is provided for selecting beams that are stable and have high focal intensity and effective propagation in complex environments.

We utilize the Kolmogorov turbulence theory to model turbulence strength, and employ a modified power spectral density and the multi-phase screen method to simulate turbulence. The turbulence magnitude indicates the level of turbulent disturbance. Initially, we adopt the multi-phase screen method to simulate the propagation of beams in turbulence. Then, we observe the propagation process and perform statistical analysis of instantaneous intensity at the focal point. In experiments, an alcohol lamp and tin foil are leveraged to mimic turbulence conditions. The beam passes above the tin foil during monitoring beam disturbance via a CCD camera. Additionally, we calculate the scintillation index (SI) of the circular swallowtail beam using simulations to observe intensity fluctuations. Finally, we analyze variations in SI and autofocusing factor with parameters of the circular swallowtail beam, providing a quantitative analysis for selecting appropriate parameters.

As turbulence increases, the propagation quality of the swallowtail beam decreases, leading to beam drift and scintillation. By optimizing the beam scale factor and initial transverse position, the autofocusing stability can be improved. Theoretical studies have shown that circular swallowtail beams with strong autofocusing ability perform better in turbulence. This characteristic is attributed to the self-healing ability of swallowtail beams, which allows the beams to quickly restore their intensity distribution to a state close to the original after encountering obstacles. Specifically, based on catastrophe diffraction theory, the self-accelerating propagation properties of swallowtail and Airy beams arise from catastrophe caustics. Catastrophe caustics are regions where light intensity reaches the maximum, and are closely associated with stable“singularities”, also known as caustics. The structural stability of caustics is an inherent feature of catastrophe beams. The results demonstrate that circular swallowtail beams have advantages in resisting turbulence scattering, providing important options for optical communication, optical trapping, and light field manipulation in complex environments.

We analyze the propagation of beams after passing through turbulence, the longitudinal offset at the focal point, and the statistical distribution of the focal intensity position. The results indicate that circular swallowtail beams with strong self-healing abilities exhibit excellent robustness, with relatively small intensity distortion and fluctuations. Furthermore, by studying the SI variation with propagation distance, it is observed that circular swallowtail beams with strong autofocusing abilities are less disturbed, with lighter scintillation and advantages in intensity stability. Finally, by parameter scanning, a series of circular swallowtail beams with the same focal length but different size factors w and control radius parameters r₀ are identified. The autofocusing factor and SI are calculated for these beams. It is observed that the SI initially decreases and then increases with w and r₀, while the autofocusing factor (K) simultaneously increases and then decreases. The research results not only provide a solid basis for regulating the propagation characteristics of circular swallowtail beams in turbulence but also theoretical support for selecting stable, high focal intensity, thus effectively propagating beams in complex environments.

Quantum teleportation can transfer arbitrary unknown quantum states between two distant users with the help of quantum entanglement, thereby facilitating the construction of quantum networks, implementation of quantum logic operations, and advancement in quantum computing. Continuous variable (CV) polarized light field is an important quantum resource, with advantages such as high efficiency in preparation, transmission, and measurement. It is suitable for long-distance quantum state transmission and can directly interact with atomic nodes. Therefore, it is desired to implement a quantum teleportation network of the CV polarized light field. However, the precise control and transformation of the polarization state of the light field are key to the quantum teleportation of an arbitrary CV polarization state. Quantum teleportation of the CV polarization state requires reversible control, enabling transformation from any arbitrary polarization state to a predetermined state for quantum teleportation, followed by restoration to the initial polarization state. Nevertheless, existing studies on polarization control primarily focus on unidirectional control, which fails to meet these requirements. This scheme intends to realize reversible precise regulation of any polarization state of the light field and achieve effective conversion between the initial polarization state and the predetermined polarization state.

The amplitude-division polarization measurement method and the wave plate polarization controller are employed in this paper to achieve polarization measurement and reversible control. The field-programmable gate array (FPGA) and host computer are utilized for control optimization and information display. First, a combination of half wave plate (HWP) and quarter wave plate (QWP) is used to generate incident field polarization states uniformly distributed on the Poincare sphere. Second, an amplitude-division polarization measurement system consisting of the partial polarization beam splitter, polarization beam splitter, HWP, and QWP is employed to spatially modulate the incident polarization state of the light field. Full Stokes parameters are measured in real time through inversion, which are then converted into azimuth and elliptic frequency. Additionally, based on the obtained polarization measurement information, a wave plate polarization controller comprising of HWP and QWP is used to convert arbitrary polarizations into preset polarizations and restore the initial polarizations, thereby enabling reversible control over the polarization state of the light field. Finally, communication between the systems for both polarization measurement and control is realized by combining FPGA with the host computer, while an optimization algorithm designed specifically for controlling errors caused by optical systems enhances control accuracy.

The reversible control system for the polarization state of the light field exhibits precise measurement and effective manipulation of polarization. The azimuth is measured by rotating HWP to generate linearly polarized light. The average error between the measured result and the theoretical value is 0.543°. The ellipticity is measured by rotating the QWP to produce different degrees of ellipticity polarization. The average error between the measured results and the theoretical value is 0.432°. The aforementioned results of the polarization azimuth and elliptic ratio measurements demonstrate the precise effectiveness of the polarization measurement system, thereby providing valuable test outcomes for the polarization control component. Through the forward polarization control of the incident polarized light field by QWP 1 and HWP 1, the azimuth of the converted linearly polarized light is close to 90°, and the average error is 0.474°. The forward polarization control successfully achieves precise and efficient conversion from the arbitrary polarization state to the predetermined target polarization state, with the measured value closely approximating the set value. The average error of the azimuth is 0.636°, and the average error of the ellipticity is 0.479° for the inverse polarization control of the incident polarized state by HWP 2 and QWP 2. The reverse polarization control successfully achieves accurate and efficient conversion from the preset polarization state to the initial incident polarization state, resulting in a restored polarization state that closely approximates the initial polarization state.

The measurement and reversible control of the polarization state of the optical field are realized by using the amplitude split polarization measurement method and the wave plate polarization control method. Algorithm optimization and semi-open-loop structure design have been employed to achieve an average measurement error of less than 0.543° for any polarization state. Furthermore, the average preset conversion error is less than 0.474° and the average reduced conversion error is less than 0.636° for any polarization control conversion. The system can realize the effective conversion between the initial and the preset polarization states, which provides key technical support for the efficient quantum teleportation of the CV polarization state. Using an optical fiber system and free space is the main way to realize the long-distance transmission of quantum states. A quantum key distribution of 200 km can be achieved by maintaining a polarization offset in the optical fiber. Free space is not sensitive to polarization, so the polarization state can be easily and directly realized for long-distance quantum communication. This scheme can realize the efficient conversion between the initial and preset polarization state of the light field, so it is of great research significance for the long-distance state transmission in free space or long-distance optical fiber quantum state transmission combined with the bias-preserving controller.