The generic Gaussian beams produced by common lasers have limited appeal in fully meeting the growing needs of modern optical systems that seek to exploit full control over all degrees of freedom of light, now referred to as structured light^1-3. Light shaping has a long history^{4, 5}, dating back thousands of years with reflective elements⁶, then refractive freeform elements⁷, and later in the 1990s based on computer generated holograms (CGHs)⁸ and diffractive optical elements (DOEs)^9-12, harnessing interference for light control. The field's recent explosion can be attributed to the on-demand rewritable solutions based on liquid crystal spatial light modulators (LC-SLMs), moving beyond display elements to sophisticated light structuring and control devices¹³. Although the underpinning technology can be traced back to the 1970s^{14, 15}, several decades of extensive material research and development, device innovation, as well as heavy investment in advanced manufacturing technology, have brought LC-SLMs to the fore as an important tool in the field of optics and photonics^16-18. This dynamic flat-panel optical device has gained increasing interest due to its attractive properties, such as phase-only modulation, photo-patternable characteristics, real-time input or output signals, high efficiency, polarization selectivity, the capability of performing dynamic switching, and its ultra-thin form factor^{19, 20}. These unique properties not only replace conventional optical devices with a digital equivalent, but also facilitate functionality beyond the textbook by modulating light beams in space^{21, 22} and time^23-25.

LC-SLMs have enabled the development of extensive compact and lightweight optical components with electronic modulation capacity, and as a result, LC-SLMs have shown great potential in widespread applications, and have been crucial in quantum optics^{26, 27}, microscopy²⁸, imaging^{29, 30}, optical trapping and tweezers^{31, 32}, materials processing³³ and holography³⁴. For instance, LC-SLMs can be used as spatial filters, deflectors, beam splitters or optical interconnects. Besides, they can lend themselves to free-space communications and high-performance computing. In computational imaging, LC-SLMs switch the ghost imaging target with different polarizations of light, lending themselves to applications in optical communication, imaging technology and security. In quantum communication, combined with the technologies of optical vortex, LC-SLMs show good performance with high capacity and large bandwidth. Moreover, LC-SLMs are ideal elements for encrypted patterns because of the high precisions and the usage of multiple controlled parameters, which can increase the security level. In microscopy, LC-SLMs allow live and real-time microscopic imaging of biological samples. In material processing, high resolutions, small pixel pitches and low cost of LC-SLMs meet the requirement of generating structures of arbitrary complexity. In light field control, LC-SLMs can work as a powerful tool in optical tweezers and optical trapping for studies of life science, and particle physics. In holographic display, LC-SLMs are dynamically programmable with high resolution and decent performance in naked-eye 3D displays. In interferometry, LC-SLMs are ideal elements for measuring the phase profile of samples at the sub-wavelength resolution.

What these many applications illustrate is the universal nature of LC-SLMs as enabling devices, and their consequent stimulating and reforming nature of research across diverse application areas. In this review, we provide our perspective on this field by reviewing the working principles of liquid crystal, diffraction optics, the recent progress of LC-SLMs, and their role in modern photonic applications. For newcomers to the field, it is inspiring to study the methods using LC-SLMs in different fields, as they often shape the trend and pave the way for modern optical technology. For those looking to improve established frameworks or develop new methods with advanced LC-SLMs, it should be fruitful to study works that are targeted at the enhancement of existing or proprietary frameworks.

A liquid crystal is a phase between solid and liquid, simply defined as a liquid with molecules arranged regularly and possessing useful attributes based on the electro-optic birefringent effect, the twisted nematic effect and the hybrid field effect. The molecules are generally slender rods, shaped like cigars, with the long axis direction of each molecule roughly the same. Due to the anisotropy of liquid crystals, the dielectric constant, conductivity and refractive index are direction dependent. For liquid crystals with a positive dielectric anisotropy, the application of an electric field causes the long axis of the molecules to align along the direction of the field. This alignment induces a change in the refractive index, giving rise to the electro-optic birefringent effect. Conversely, in the case of liquid crystals with negative dielectric anisotropy, the alignment of the long axis of molecules is perpendicular to the applied electric field, resulting in an inverse refractive index change. The working principle of the electro-optic birefringent effect is shown in Fig. 1(a) and 1(b). No light is outputted when the voltage is off, while polarized light is outputted when the voltage is on. There is no birefringence effect when the polarization direction of the incident light is the same as or perpendicular to the long axis of the molecule near the incident plane. In the twisted nematic effect, the molecular orientations of the upper and lower crystal planes of the liquid crystal are different. The liquid crystal molecules can be divided into many thin layers, each with molecules of a similar orientation, changing from layer to layer. The resulting structure can make the polarization direction of linearly polarized light rotate. As shown in Fig. 1(c), for a liquid crystal with a twist angle of 90 degrees, the molecules rotate uniformly without an electric field. The twisted nematic effect appears when the electric field is introduced, since the molecules deviate from the original direction and align towards the electric field^{35, 36}, as shown in Fig. 1(d). The hybrid field effect is the combination of electro-optic birefringent effect and twisted nematic effect. In the field of optical information processing, the control of phase, amplitude and polarization of optical beams by LC-SLMs are mainly realized through the hybrid field effects³⁷.

The core of the light-controlling ability of LC-SLMs lies in the liquid crystal itself, whose properties determine the optical functionality. There are multiple liquid crystal cell structures and driving electrode configurations that can be employed for LC-SLMs. Examples include the vertical alignment liquid crystal cell (VA-LC Cell), in-plane switching liquid crystal cell (IPS-LC Cell), twisted nematic liquid crystal cell (TN-LC Cell), and super twisted nematic liquid crystal cell (STN-LC Cell). Without electric field, VA-LC cells and IPS-LC cells are uniform. In TN-LC cells, the vector of liquid crystal is twisted at approximately 90 degrees, while in STN-LC cells, the vector of liquid crystal is twisted at an angle larger than 90 degrees, such as 180 degrees, 240 degrees, or 270 degrees. Each cell comprises a 2D pixel array (M×N) that can be electrically switched on or off. Each pixel is composed of a liquid crystal cell sandwiched between transparent electrodes. In the early stage, the TN-LC cell was driven by two groups of electrodes (M+N), utilizing the multiplexing technique. The advantage of multiplexing is that M×N pixels can be addressed using only M+N electrical contacts, which significantly reduces the number of electrodes when M and N are in the order of 10³, making it suitable for high-information-content applications. However, the simplicity of multiplexing leads to a degradation of the device performance, especially in terms of contrast and limited pixel resolution. The performance of TN-LC cells is later enhanced by a different driving technique that utilizes thin film transistor (TFT) arrays. In TFT arrays, each pixel has associated transistors, which significantly improves performance but also increases production costs. These LC configurations are mainly for amplitude modulations. For phase-only modulation, homogeneous LC cells are commonly used³⁸, while TN cell can also work if the voltage is kept below the threshold³⁹. In the following section, we discuss the operating principles of various liquid crystal cells and their transmission characteristics with or without voltage.

In the VA-LC cell, as illustrated in Fig. 2(a), each liquid crystal cell consists of two glass substrates with a spacing of 3–5 μm of liquid crystal material in between. A thin alignment layer is deposited on the inner surface of the substrate to ensure that the liquid crystal molecules are aligned vertically at the same time as the surface is projected to facilitate alignment. A transparent electrode, generally made of indium tin oxide (ITO), is deposited on the inner surface of the substrate for electrical connectivity. On the two outer surfaces of the substrate, polarizers are laminated to form an orthogonal polarizer. In a basic VA-LC cell with only one domain, the absorption axis of both polarizers can be aligned at a degree angle with the horizontal direction. Meanwhile, the liquid crystal is tilted in the Y-Z plane, and the structure is symmetrical in terms of apparent brightness. For a multi-domain cell, the absorption axis is often arranged in the horizontal direction and vertical direction, respectively. This arrangement of polarizers ensures the highest contrast in both directions. Under the application of an electric field, the liquid crystal molecules tilt at 45 degrees relative to the axes of the polarizer. As a result, the liquid crystal cell behaves as a half-wave plate with high transmission to crossed polarizers. The transmittance of light through the liquid crystal cell can be modulated by controlling the voltage.

The planar conversion mode of uniform parallel arrangement nematic liquid crystal cells was introduced in the mid-1990s as a means of improving viewing angles without the use of a thin film compensator. Figure 2(b) depicts the IPS model of a nematic liquid crystal cell that is sandwiched between two crossed polarizers, with one of the polarizers having a transmission axis parallel to the liquid crystal vector in the plane of incidence. When the incident light beam passes through the liquid crystal cell, only one mode of light waves, either ordinary or extraordinary, is excited, allowing the light waves to traverse the cell without experiencing any phase delay. When the electric field is off, the crossed polarizer configuration results in zero transmission. Under the application of an electric field to the liquid crystal cell in the X-Y plane, the liquid crystal molecules align in the direction of the field, the Y-axis, resulting in a distortion denoted byβ in the X-Y plane. The distortion angleβ in an IPS-LC cell varies as a function of position Z due to the boundary conditions of the liquid crystal molecules and the direction of friction. However, unlike a TN-LC cell, the distortion of the IPS-LC cell is not a linear function of position along the Z-axis. With the exception of a small pretilt, the tilt angle relative to the Y axis can be regarded as zero provided that the electric field is maintained within the plane.

The TN-LC cell is an important type of liquid crystal cell that differs from VA-LC and IPS-LC cells. In TN-LC, the cell is composed of a liquid crystal layer that is sandwiched between a pair of polarizers, with a twist angle of 90 degrees in total. TN-LC cells are widely used in notebook computers, calculators, and other small electronic devices due to their low power consumption, fast response time, and low cost. However, they have certain limitations such as narrow viewing angles and limited color reproduction compared to other liquid crystal modes. As illustrated in Fig. 2(c), each TN-LC cell is composed of a liquid crystal layer placed between two glass plates with a gap of 5–10 μm. An ITO conductive coating is deposited on the inner surface of the glass plates, and a thin layer of polyimide with a thickness of several hundred angstroms is applied to the electrode surface. The polyimide film is wiped unidirectionally to ensure its direction is parallel to the wiping direction on the surface. In 90-degree TN, the wiping direction of the lower substrate is perpendicular to the wiping direction of the upper surface. Consequently, the liquid crystal vectors of the area between the glass plates undergo a continuous and uniform distortion of 90 degrees without voltage. A sheet polarizer is laminated on the outer surface of the glass plate, and its transmission axis is set parallel to the wiping direction of the adjacent polyimide film. When a small voltage is applied to the electrode, e.g., 3–5 V, a strong electric field is generated in the liquid crystal. The dielectric anisotropy of the liquid crystal causes it to align with the direction of the applied electric field, resulting in a vertical arrangement of liquid crystal molecules. The vector of the liquid crystal is perpendicular to the panel, which is the C-plate of the liquid crystal. When light propagates along the vertical direction of the C-plate, the polarization plane remains unchanged. When the C-plate is placed between a pair of orthogonal polarizers, it leads to zero transmittance. Thus, the transmittance of light through the liquid crystal cell can be controlled by adjusting the voltage.

When a voltage is applied to the liquid crystal cell, the orientation of liquid crystal molecules changes in response to the electric field. The orientations of these molecules in the liquid crystal cell are determined by the balance between elastic energy and electrostatic energy. The change in orientation results in a change in the transmittance of the liquid crystal cell. Typically, the display panel is composed of a 2D array of liquid crystal pixels, which is M × N, with each pixel being a small liquid crystal cell that can be electrically turned on or off. To achieve this, it is necessary to electrically position each individual liquid crystal cell, which can be achieved using multi-channel circuit technology requiring only M + N electrodes. However, due to crosstalk, the voltage difference between on and off in each liquid crystal cell cannot be too large, limiting the contrast of the display. To address this issue, the STN-LC cell is developed. By applying an appropriate voltage, the liquid crystal vector in the STN-LC cell is effectively distorted or redistributed, resulting in high contrast. Figure 2(d) depicts the molecular orientations of the STN-LC cell with a twist angle of 180 degrees in total. The high contrast is achieved by distorting or redistributing the liquid crystal vectors in the liquid crystal cell under an appropriate external voltage.

When the aforementioned cells are arranged together on a one-dimensional or two-dimensional plane, they form an LC-SLM device. By designing the shape, size, position and orientation of the unit structures, LC-SLMs can modulate the optical parameters, e.g., amplitude, phase and polarization of the incident light wave in an arbitrary manner. This unique ability of modulation with multi-degree of freedom allows for the replacement of traditional optical elements with bulky structures and single functionality, making the LC-SLMs lightweight, ultrathin, and multifunctional devices^{40, 41}. In addition, LC-SLMs are compatible with semiconductor manufacturing techniques, enabling mass production and manufacturing. LC-SLMs have obvious advantages in the lightweight and integration of photoelectric systems, and they show great potential in the fields of high-end equipment, aerospace and electronics. With the continuous advancements in material research and significant investments in advanced manufacturing technologies, the performances of LC-SLMs have significantly improved, as shown in Fig. 3. These improvements have led to a decrease in the pixel pitch to the micron level and an increase in the number of pixels to tens of millions. Compound Photonics and Himax have demonstrated SLMs with a pixel pitch of about 3 μm and 4.25 μm⁴². Today, high-performance LC-SLM devices are available commercially, and Table 1 provides a summary of the state-of-the-art LC-SLMs that are currently available in the market.

Large-aperture liquid crystal devices have emerged as a significant area of research and technological innovation within the field of optics^{43, 44}. These devices leverage the unique properties of liquid crystals, such as the tunable refractive index and responsiveness to external electric fields, to create versatile and dynamically controllable optical components. The potential of large aperture liquid crystal devices lies in the ability to manipulate light across a broad spectral range. This makes them particularly valuable for various applications, ranging from beam shaping to adaptive optics. Their dynamic tunability allows for real-time adjustments in response to changing environmental conditions or specific operational requirements.

While research devices are capable of controlling light by geometric phase^{45, 46}, they are not yet commercially available, and thus, most commercial LC-SLMs available today modulate only the dynamic (or propagation) phase of the light. This phase-only functionality can be exploited for control of many degrees of freedom, extending to amplitude modulation and polarization modulation. As the liquid crystals in each cell are rotated, the local refractive index n(x,y) changes, resulting in a phase change across the device given by Φ_SLM(x,y) = kn(x,y)d, where k is the wavenumber of the light and d is the thickness of LC cell. The question is how to use this phase change as a means to control and shape light. The answer lies in the notion of diffraction. Diffraction is a fundamental optical phenomenon that accounts for many phenomena that cannot be explained by geometrical optics, such as the bending and spreading of the light. Early optical elements were designed based on refraction and reflection, where diffraction was considered a hindrance. However, the advent of fast computers and modern lithography meant that optical elements could be designed and fabricated to exploit diffraction and interference. Such diffractive optical elements (DOEs), either as smooth kinoforms or binary equivalents, have given birth to a myriad of new optical functionalities, such as pattern generators, beam shapers, and gratings, all utilizing a surface relief profile with a depth on the order of the wavelength of the light. As a consequence, DOEs are typically much thinner and lighter than conventional refractive elements, making them an attractive replacement in a number of applications. In the context of this review, we can treat the LC-SLM as a pixelated DOE that is rewritable, so that all the theory related to DOEs can be translated to LC-SLMs. For instance, the fundamental equation governing diffraction off a periodic structure indicates that light will emerge at diffraction angles θ satisfying

1mλ=psin(θ),

where m is the diffraction order, λ is the wavelength and p is the grating pitch. This tells us where the light will be diffracted, which can be useful for various applications. For instance, in a holographic display system, the viewing angle is double the maximum diffraction angle. In order to display a 3D image with a wide angle of view, an LC-SLM’s pixel pitch has to be sufficiently smaller than the wavelength. However, even with the finest 8K LC-SLM with a pixel pitch of 3.5 μm, the viewing angle is limited to about 10 degrees. The diffraction equation only provides information on the direction of diffracted light, but how much light will be going in a particular direction. The answer to this, the diffraction efficiency, depends largely on the type of periodic structure (binary, blazed, sinusoidal, etc.) whereas the function of the element depends largely on the spacing of the pitch in space, e.g., p(x,y). For instance, the diffraction efficiency for a 2^N level binary function is given by

2η=[sin(πm/2N)πm/2N]2,

where η is the power into the m order, and the non-zero orders are given by m = qN +1 where q is any integer.

What remains is to determine what the light looks like. Diffraction can be divided into two categories, analytic diffraction and numeric diffraction. Analytic diffraction is designed based on ray tracing, as the phase profile can be defined analytically on an infinitely thin interface. Examples of typical analytic elements include lenses, gratings, and interferograms, which may be a single element or in combination with refraction or reflection elements to create a hybrid optical system. On the other hand, numeric diffraction is calculated iteratively as a black box. The incoming wavefront and the desired output wavefront are specified, with the incoming wavefront being a particular amplitude or phase function, and the output field being an amplitude-only function located either in the far field or near field. Iterative algorithms are then used to reduce the specific cost of the diffraction efficiency in a given order, such as reconstruction uniformity, signal-noise-rate, or root-mean-square error between a desired reconstruction and an actual reconstruction. Examples of typical numeric elements include diffusers, beam splitters, beam shapers, CGHs, Fourier filters, spot array generators, and so on. As shown in Fig. 4(a) and 4(b), LC-SLM can replace typical analytic and numeric elements to realize the modulation of the light field in amplitude, phase and polarization. Holograms on LC-SLMs can be designed or calculated analytically, whereas numeric diffraction requires numeric optimization through iterative algorithms since there is no analytical solution to the diffraction problem. Depending on the input wavefront and the signals provided by the computer, LC-SLMs can produce various types of beams and images, either as single or compound images. In this section, we are interested in structured light, and so we briefly cover the common beam types that are typically created by LC-SLMs. Apparatus of LC-SLM and SLM holograms that produce different types of beams are illustrated in Fig. 4(c) and 4(d), illustrating the diverse capabilities of this technology.

Bessel beams have a transverse intensity profile according to the family of Bessel functions⁴⁷. A zeroth-order Bessel beam has a transverse intensity profile with a bright central core surrounded by bright concentric rings. Unlike Gaussian beams, a Bessel beam has a transverse intensity profile that does not spread as it propagates over a finite distance. Bessel beam can reconstruct around obstructions placed in the beam path, which makes Bessel beam useful for stacking multiple objects along the beam’s central core. Bessel beams are exact solutions to the free-space Helmholtz wave equation in cylindrical symmetry and are mathematically given by

3E(ρ,φ,z)=E0Jl(ktρ)exp(kzz)exp(ilφ),

where ρ and φ denote the polar coordinates, z denotes the axial coordinate, J_l is the Bessel function of order l, k_t is the transverse component of the wave vector k, and k_z is the longitudinal component of the wave vector k.

The two common methods to generate Bessel beams are based on a conical lens (axicon) for near-field creation, and a ring aperture (annular slit) for far-field creation. Even though both can be encoded as a hologram on the SLM, the former is more efficient. The transfer function of an axicon is described by

4t(ρ,φ)=exp(iktρ).

The transverse component of the wave vector k_t can be expressed in terms of the angle α of the axicon as

5kt=α(n−1)k,

where n is the refractive index of the axicon. Bessel-Gauss beams generated in the laboratory are Bessel beam enveloped with a Gaussian beam of radius w₀ and thus have a finite propagation distance described by

6zmax=w0kkt.

By adding the term exp(ilφ) to Eq. (3), we can get the transfer function of a high-order Bessel beam, which is given by

7t(ρ,φ)=exp[ikα(n−1)ρ]exp(ilφ).

Thus, the mathematical expression to generate a phase hologram for the SLM with the above transfer functions takes the form of

8ΦSLM(x,y)=mod[kα(n−1)x2+y2+larctan(y/x)+2π(Gxx+Gyy),2π].

Another solution to the paraxial wave equation is given in terms of the Airy functions, which are called Airy beams⁴⁸. The mathematical expression for these beams is given by

9A(sx,sy,ξ)=Ai[sx−(ξ2)2]Ai[sy−(ξ2)2]⋅exp[iξ2(sx+sy−ξ33)],

where A_i is the Airy function,sx=x/x0 andsy=y/y0 represent dimensionless transverse coordinates, x₀ and y₀ are the transverse scale parameters,ξ=z/kx02 is a normalized propagation distance. By imposing certain restrictions to Eq. (9), a very good approximation to the ideal Airy beam can be realized in the optical regime, described by

10A(sx,sy,ξ=0)=Ai(sx)Ai(sy)exp[b(sx+sy)],

where b is a positive parameter, typically smaller than one that limits the energy of the Airy beam. The final expression for this “finite-energy Airy beam” is described by

11A(sx,sy,ξ)=Ai[sx−(ξ2)2+ibξ]Ai[sy−(ξ2)2+ibξ]⋅exp[b(sx+sy)−bξ2+ibξ2−ξ36+iξ(sx+sy)2].

For the finite energy, Airy beam maintains its non-diffractive properties over a finite distance only.

The experimental generation of these beams can be achieved by encoding a hologram corresponding to the inverse Fourier transform of A₀. The phase encoding on the SLM is described by

12ΦSLM(x,y)=mod[x3+y33,2π].

Hermite-Gauss modes are a set of solutions to the paraxial wave equation in Cartesian coordinates⁴⁹. The mathematical representation is given in terms of a Gaussian function and the Hermite polynomial H_n(x) as

13HGnm(x,y,z)=1w(z)21−n−mπn!m!Hn[xw(z)]Hm[yw(z)]⋅exp[i(n+m+1)ξ(z)]exp[−(ρw(z))2]⋅exp(−ikρ22R(z))exp(−ikz),

where n and m are the positive integers. Other parameters are described by

14ρ=x2+y2,

15w(z)=w01+(zzR)2,

16R(z)=z[1+(zRz)2],

17w0=zλzRπ,

18ξ(z)=arctan(zzR).

Equation (13) represents a paraboloidal wave with the radius of curvature R(z), beam waist w₀, and beam size w(z). z_R is a constant known as the Rayleigh range, which is used to measure the distance over which the beam remains well collimated. ξ(z) is an additional phase shift that the wavefront acquires upon propagation through the beam waist, which is known as the Gouy phase.

Hermite-Gauss beams can be generated by employing complex amplitude modulation. The amplitude term and the phase term are given by

19AHG(x,y,z)=1w(z)21−n−mπn!m!Hn[xw(z)]⋅Hm[yw(z)]exp[−(ρw(z))2],

20ΦHG(x,y,z)=exp[i(n+m+1)ξ(z)]⋅exp(−ikρ22R)exp(−ikz).

Thus, the encoded hologram takes the form of

21ΦSLM=fHG⋅sin(ΦHG+Gxx+Gyy),

where f_HG is the amplitude phase function and can be found numerically from the relation

22J1(fHG)=AHG.

Laguerre-Gauss modes are another solution to the paraxial Helmholtz equation in cylindrical coordinates⁵⁰. They are mathematically described by

23LGpl(ρ,φ,z)=w0w(z)2p!π(|l|+p)![2ρw(z)]|l|⋅Lpl[2(ρw(z))2]exp[i(2p+|l|+1)ξ(z)]⋅exp[−(ρw(z))2]exp(−ikρ22R)exp(−ilφ),

whereLpl is the Laguerre function and the rest of the parameters are the same as in theHGnm modes.

Laguerre-Gauss beams generated by SLMs are approximated using complex amplitude modulation. The amplitude term and the phase term are given by

24ALG=w0w(z)2p!π(|l|+p)![2ρw(z)]|l|Lpl[2(ρw(z))2]⋅exp[−(ρw(z))2],

25ΦLG=exp[i(2p+|l|+1)ξ(z)]⋅exp(−ikρ22R)exp(−ilφ).

Thus, the encoded hologram has the form of

26ΦSLM=fLG⋅sin(ΦLG+Gxx+Gyy),

wherefLG is obtained by numerical evaluation

27J1(fLG)=ALG.

Vortex beams carry orbital angular momentum (OAM) by virtue of a helical twist to the wavefront, characterized by a phase function of the form ofexp(−ilϕ), resulting in photons withlℏ of OAM⁵¹. We have already seen that Bessel beams and Laguerre-Gauss beams have this form, but these are only two such examples. Ignoring the amplitude function, the desired phase profile can be experimentally generated with an SLM by encoding an azimuthal variation and blazed grating to separate the first order from the others. The phase encoding on the SLM is described by

28ΦSLM=mod[lϕ+2π(Gxx+Gyy),2π].

The unique properties of LC-SLMs make them well-suited for use as dynamic optical devices, which can replace conventional optical devices with a digital equivalent and also facilitate new functionality. In this section, we review the significant progress that has been made in the applications of LC-SLMs. The diverse range of these applications is captured in Fig. 5, including beam shaping and steering, holography, optical trapping and tweezers, measurement, wavefront coding, optical vortex, quantum applications, and more. We focus on revealing the unique dynamic flat-panel functionalities of the LC-SLMs.

Shaping the light field by changing its phase or intensity has enabled significant advances in optics. Refractive and reflective elements, such as lenses, prisms, and mirrors, are common devices for beam shaping and steering by deflecting the light paths. Elements that work with this diffraction effect are called DOEs. The propagating phase of light changes when it passes through the micro-structure pattern made on a substrate material. DOEs have become the first choice in many applications due to their flexible plasticity, absolute angular accuracy at designed wavelengths, small size, and flatness. However, LC-SLMs can change the phase pixel by pixel for the laser beam, and thus can replace traditional beam shaping and steering DOEs. Previous works have realized continuous phase and binary intensity modulation of beams with the help of beam shaping techniques based on LC-SLMs^52-57. Dispersion-free beam shaping has been achieved through the intermediate transversal light beam magnification, which balances the mismatch in the grating constants and leads to total residual angular dispersion compensation. LC-SLMs have also been used to achieve white light beam shaping⁵⁸ and axial sub-Fourier focusing of optical beams⁵⁹. In this approach, the generated beams have an axial focusing that is narrower than the Fourier limit. The generated beams are constructed from the superposition of Bessel beams with different longitudinal wave vectors, which realizes a super oscillatory axial intensity distribution. In beam steering, LC-SLMs enable the generation of dynamic gratings to steer the beam toward a specific direction or for beam scanning. Multifocal arrays have attracted considerable attention for their potential applications in parallel optical tweezers, parallel recording, and multifocal multiphoton microscopy. Methods of generating 3D dynamic and controllable multifocal spots in the focal volume of the objects have been proposed⁶⁰. Specifically, T. Zeng et al proposed a specific pseudo-period encoding technique to create 3D vectorial multifocal arrays with the capability of manipulating the position, intensity and polarization state of each focal spot, as shown in Fig. 6(a)⁶¹. The experiment demonstrates that the vectorial multifocal arrays have a tunable position and polarization state with high quality.

Beam shaping and steering techniques find wide applications in several domains, such as focusing light into materials or turbid media^62-64, measuring the transmission matrix in disordered media⁶⁵ or opaque materials⁶⁶, optimizing and characterizing optical properties^67-72, laser printing^{73, 74}, manufacturing equipment⁷⁵, detecting beams^{70, 76}, material processing^77-81, etc. Material processing utilizes beams projected onto the surface of the material to induce thermal effects for processing, including laser welding, cutting, marking, drilling, and micromachining. Among the techniques for generating structures of arbitrary complexity with sub-micrometer resolution and high efficiency, photopolymerization stands out as a powerful method. It allows for the simultaneous building of structures with diffractive patterns instead of multidimensional scanning of a single focus. Micro-supercapacitors, a promising miniaturized energy storage device, suffer from inefficient microfabrication technologies and low energy density, thus limiting their range of applications. Y. Yuan et al proposed a flexible and designable micro-supercapacitor, fabricated through a single pulse laser photonic-reduction stamping technique, as shown in Fig. 6(b)⁸². This unique technique has the potential to overcome the limitations of low energy density and high-throughput fabrication of micro-supercapacitors, thereby expanding their range of applications.

Since Gabor invented holography, the field of holographic imaging and display has grown with the increasing use of LC-SLMs. A hologram is an interference recording of a 3D surface by calculating in reverse from the target image. Upon proper recording, reconstruction, and viewing conditions, unlike traditional 2D photography, the image appears to be 3D again. LC-SLMs are non-mechanical programmable wavefront modulation devices that introduce diversity into the image data. Three different techniques of single channel digital holography are discussed, including the joint object reference digital interferometer (JORDI), Fresnel incoherent correlation holography (FINCH) and Fourier incoherent single channel holography (FISCH)⁸³. Pixelated LC-SLMs can be implemented to encode complex modulation by means of appropriate CGHs, enabling the synthesis of fully complex fields with high accuracy. Methods of realizing hologram generation with maximum reconstruction efficiency, optimum bandwidth and high signal-to-noise ratio in CGH have been proposed^84-89, as shown in Fig. 7. Y. Zhao et al proposed a novel layer-based angular spectrum method of CGH, as shown in Fig. 7(a)⁸⁸. Experimental results show that the proposed method can perform high-quality optical reconstructions of 3D scenes with dramatically reduced computational load and precise depth performance. X. Sui et al realized complex amplitude modulation through spatiotemporal double-phase hologram⁹⁰. The method makes spatiotemporal double-phase holograms an appropriate way to digitally modulate static and quasi-static complex fields using existing LC-SLMs. In addition to the pure phase-based holography, LC-SLMs can realize amplitude or complex amplitude-based holography. This expanded capability allows for more versatile and sophisticated holographic applications, where both the phase and amplitude of light can be precisely manipulated to create complex and realistic holographic reconstructions.

Holographic displays have emerged as a powerful tool for constructing high-resolution and realistic 3D images, without the need for special glasses. Holography display techniques play a central role in diverse fields, such as scientific visualization, multimedia display, virtual reality, education and interactive designs. However, there is still a long way to go to improve it further. A material that takes all the advantages of holography does not exist. The performance characteristics of different materials have been analyzed to determine the advantages and limitations of different approaches⁹¹. Various methods have been proposed to accelerate the generation of color holograms^92-94, reduce speckle noise^{95, 96}, and implement time multiplexing⁹⁷. Additionally, researchers are exploring various algorithms and techniques to improve display properties^98-102. Optical see-through holographic near-eye displays have also been improved towards compactness, lightweight, low cost, and free of accommodation-convergence discrepancy^{100, 103, 104}. Recent progress in photo-electronic techniques and devices has enabled the real-time display of 3D images in free space, including the extraction of all depth cues such as motion parallax, occlusion, and ocular accommodation. Researchers have made significant strides in improving image quality while maintaining image size¹⁰⁵, implementing holograms with high contrast and per-pixel focal control¹⁰⁶, reconstructing high-definition 3D fields¹⁰⁷, and handling holographic images in real time¹⁰⁸.

Optical trapping and tweezers are tools that utilize highly focused laser beams to exert a micro force on microscopic dielectric objects, enabling physical manipulation, holding, and repulsion of the material. These techniques have become valuable tools in a wide range of applications, including trapping or manipulating cells and cell components^109-117, measuring the interaction forces and hydrodynamics^118-122, measuring the fluid flow^{123, 124}, and assembly of micro-structures^{125, 126}. However, precise spatial and temporal manipulation of multiple traps and independent manipulation of trapped micro-particles remains a challenging task in many applications. To address this, holographic or diffractive optical elements are widely implemented with LC-SLMs to form optical traps in multiple shapes^127-131, arbitrary arrays of traps or atoms^{132, 133}, and unique trapping structures^134-137. Typical applications of LC-SLMs in optical trapping and tweezers are shown in Fig. 8. In the field of quantum computation, quantum simulation and quantum many-body physics, it is essential to build a scalable neutral-atom platform. Optical trapping of atoms enables the construction and manipulation of quantum systems. To this end, H. Kim et al proposed a novel LC-SLM method to transport single atoms in real time with holographic micro-traps¹³². The method accomplished a 99% success rate for single-atom rearrangements for up to 10 mm translation. The technique can be further improved through increasing the number of atoms and initial loading efficiency. The application is not restricted to the preparation of an array, but can also be applied to many-body physics with ordered atoms and coherent qubit transports.

The use of optical tweezers has revolutionized the field of micro-manipulation by enabling the trapping, assembling, and sorting of multiple particles in 3D^{111, 135, 138}. The inception of optical tweezers dates back to 1986¹³⁹. Intensity-modulated patterns projected by an LC-SLM enable the manipulation of microparticles dynamically. Typical setups for optical tweezers involve on-axis Fourier holograms. However, an advanced optical setup has been proposed that uses an off-axis Fresnel hologram, which increases the flexibility of diffractively steered optical tweezers¹⁴⁰. Rapid generation and analysis of optical tweezers meet the demand for development^{141, 142}. The advantage of optical tweezers is that it is possible to design any potential for the atom. The use of LC-SLMs in the design of arbitrary potentials has made optical tweezers a powerful tool in life science, material science, and particle physics.

Dynamic aberrations are a common problem in optical systems, and LC-SLMs offer a potential solution as an alternative to conventional deformable mirrors for aberration correction. Various high-accuracy correction systems and principles with liquid crystal wavefront correctors have been proposed^143-147. Phase calibration has been implemented in the field of stable real-time correction^148-150 and imaging¹⁴⁵ with LC-SLMs. Typical applications of LC-SLMs in measurement are shown in Fig. 9. R. Li et al proposed a phase calibration technique by dividing the LC-SLM panel into two zones, the grating zone and the measured zone, enabling efficient and visible in situ calibration, as shown in Fig. 9(a)¹⁵¹. This low-cost and highly efficient method is applicable for routine and frequent calibration. A. Jesacher et al proposed a method for correcting small surface deviations of the LC-SLMs with an optical vortex and a flexible non-interferometric technique, which can be applied to optical tweezers for optimizing trapping fields and imaging systems for optimizing the point-spread-function¹⁵². The surface distortion information is extracted from the shape of the optical vortex. The use of LC-SLM as a phase calibration device provides a way to obtain the surface quality of optical devices in applications, which require good characterization of amplitude, phase and polarization properties. Phase retrieval based on wavefront sensors has shown the capability of reconstructing the complex field from optical devices with high spatial resolutions. Adaptive optics (AO)¹⁵³ is one of the most promising techniques for calibrating wavefront distortions caused by atmospheric turbulence or other factors. LC-SLMs are versatile AO elements that can achieve high resolution and low temporal turbulence imaging systems for improved resolution performances and displays¹⁵⁴, wavefront correction for both low- and high-order aberrations in human eyes¹⁵⁵, etc. Combined LC-SLMs with AO techniques enable the observation of cells in their native state¹⁵⁶, recovery of biological or non-biological samples with near-diffraction-limited performance¹⁵⁷, better quality optical tweezers¹⁵⁸ and resolution improvements¹⁵⁹ in microscopy. In the context of colorful holographic images, and when dealing with broadband or incoherent light sources, the phase change of the LC-SLM at different wavelengths becomes a critical consideration. A careful calibration process is required to address the problem. This involves characterizing the phase response of the LC-SLM at different wavelengths and compensating for the wavelength-dependent phase changes. The calibration process might involve measuring the phase change introduced by the LC-SLM for various wavelengths and then applying appropriate corrections to achieve the desired holographic or wavefront manipulation. It is also possible to overcome the wavelength dependence by using a grating, but this comes at the expense of a small wavelength dependent loss factor⁵⁸.

Measurement with LC-SLM refers to the use of these devices to manipulate optical wavefronts for various purposes, which enables precise control over the characteristics of optical beams. This dynamic control enables researchers and engineers to tailor optical systems for various experimental, research, and practical purposes, ultimately enhancing the capabilities of optical technologies across diverse fields. Interferometric measurement is a powerful tool that can measure the phase profile of samples at subwavelength resolution. In the field of optical nondestructive testing, the extraction and classification of faults is a major task in industrial quality control. Interferometric fringes contain valuable information about faults in the sample, making them an important tool for defect detection. In traditional interferometry, the image-carrying light wave is coherently superposed on the reference wave, resulting in closed interference fringes that form contour lines. However, it can be challenging to distinguish between elevations and depressions using this approach. One solution to this issue is the use of a spiral phase optical element, which produces spiraled interference fringes instead of closed contour lines, enabling accurate identification of elevations and depressions¹⁶⁰. The theoretical derivation of spiral interferometry and various demodulation methods based on interferograms have been extensively studied^161-163. Researchers have also reported new quantitative phase imaging approaches based on a self-reference holograph that improves the accuracy of phase maps by superposing three on-axis interferograms with different phase filters¹⁶⁴. Interferometric measurement has been successfully applied in many areas, including calculating the skew angle of a Poynting vector¹⁶⁵, depth measurement of polymer-coated steel samples¹⁶⁶, wavefront interferometry¹⁶⁷, detection of scattering materials¹⁶⁸, and measuring the optical index^169-171. Overall, interferometric measurement is an essential tool for nondestructive testing and provides valuable information for various applications in the field of optics.

Imaging typically involves the integration of a specifically coded aperture with a coded phase mask in an optical system. One common type of device used for coded aperture imaging is the LC-SLM¹⁷². A diffractive lens was used in the advanced optical system of coded aperture correlation holography (COACH), which was proposed by A. Vijayakumar et al to enable 4D imaging of objects at three spatial dimensions with a spectral dimension¹⁷³. In the same year, A. Vijayakumar et al proposed a new digital holographic imaging technique, called interferenceless coded aperture correlation holography (I-COACH), which does not rely on two-wave interference. The technique simplifies the optical systems, increases working efficiency, and eliminates complicated alignment procedures¹⁷². LC-SLM was employed by N. Dubey et al to generate a coded phase mask to enhance imaging resolution, as shown in Fig. 10(a)¹⁷⁴. The principle of operation of endoscopic interferenceless coded aperture correlation holography (EI-COACH) is based on simulating the endoscopic setting. The annular coded phase mask is produced on the computer and displayed on the LC-SLM. The LC-SLM’s internal region, surrounded by the annular coded phase mask, serves to deflect unwanted light through display a diffractive optical element. The diffraction optical element consists of a quadratic phase function and a linear phase function, which are used to focus unwanted light from the sensor. Thus, only the light that passes through the annular coded phase mask reaches the image sensor, and the rest dissipates around.

Random scattering of light in materials like paint, milk, and biological tissues can cause the incident wavefront to become seriously distorted, leading to a loss of spatial coherence. This results in the formation of a volume speckle field that lacks correlations over distances larger than the wavelength of light. The serious scrambling of the field makes it impossible to control the propagation of light using established wavefront calibration methods and prevents direct retrieval of the information encoded in the light. However, with active control methods, random scattering can be beneficial rather than harmful for applications such as focusing^{175, 176}, imaging^177-179, speckle analysis^{180, 181}, phase conjugation^182-185, etc. Although challenging, effective focusing of light into or through scattering media is highly desirable in many fields. Optical scattering due to the non-uniformity of the refractive index in the scattering media makes it difficult to efficiently deliver optical intensity. Z. Cheng et al proposed a novel ultrasound-assisted technique called ultrasound-induced field perturbation optical focusing (UFP), which uses the brighter zeroth-order photons diffracted by the ultrasonic guidestar as information carriers to guide optical focusing, as shown in Fig. 10(b)¹⁸⁶. The new technique allows for the focusing of light to the location where the field perturbation occurs in the scattering medium. The technique broadens the scope of optical control in scattering media and challenges conventional notions about the usefulness of ultrasound guidestar. Biological specimens mostly consist of optical inhomogeneities, which seriously degrade imaging performances. The demand for live and real-time microscopic imaging of biological samples is high. 3D reconstruction must be fast enough to capture the dynamical properties of living cells or biological objects. True physiological imaging of subcellular dynamics requires no undue stress on the sample and characterizing the cells within their parent organisms. Therefore, wide-field in situ and native state metrology^{187, 188}, and other biological imaging methods have been proposed^189-195.

Optical vortex beams, with their unique properties, have found applications in diverse areas of research. An optical vortex beam with anexp(−ilϕ) phase structure carries an orbital angular momentum oflℏ per photon, wherel is the topological charge andϕ is the azimuthal angle. Whenl takes on integer values, a vortex or helices is formed in the wavefront with a single screw-phase dislocation on the beam axis. Whenl takes on non-integer values, a complex-phase structure is formed in the wavefront, which contains many vortices at differing locations in the cross-section of the beam. Whenl takes on half-integer values, a line of alternating charge vortices near the radial dislocation is formed¹⁹⁶. Optical vortices generically arise when laser beams are combined. A few laser beams with optical vortices can be combined to form optical vortex knots, links or loops^{197, 198}. LC-SLMs can efficiently synthesize the helical modes of the beam and generate novel optical vortices^199-202. Fundamental studies on optical vortex beams include intrinsic measurement and analysis^203-214, mode generation and transformation^215-219, laser beam engineering^220-222, metrology¹⁶⁹, polarization nano-tomography²²³, image reconstruction^{224, 225}, and more. The OAM cannot be completely eliminated when two optical vortex beams with different topology charges are superimposed coherently. The remaining OAM in the superimposed beam, which is located in different concentric circles, may have the opposite orientation due to the difference in charge. When the different charges of the two beams are large, the remaining OAM can be detected through the rotating micro-particles^{226, 227}.

Optical vortex has been widely used in optical communication due to its capability of providing more degrees of freedom and expanding the bandwidth^228-233. Typical applications of LC-SLMs in optical vortex are shown in Fig. 11. M. Malik et al proposed an OAM modal for a free-space 11-dimensional communication system²³². By combining LC-SLM with binary phase filters, the transmission bandwidth of multimode fibers can be largely increased. G. Jing et al proposed a fractional orbital angular momentum (FOAM) mode recognition method with a feedforward neural network (FNN)²³⁴. The experiment result showed that the method can break the limitation of precision measurement in the turbulence environment of practical FOAM applications. To further increase the data transmission rate, in addition to OAM, A. Trichili et al demonstrated the use of both radial and azimuthal degrees of freedom for multiplexing and demultiplexing, as shown in Fig. 11(b)²³⁵. The novel holographic technique allowed over 100 modes to be encoded and decoded in one hologram, in a wide wavelength range through a wavelength-independent manner. Optical vortex beams offer immense potential for developing innovative optical communication techniques and are an active area of research.

Quantum optics has traditionally been executed experimentally using qubit quantum states based on polarization, for which the optical toolkit is very mature. The birth of spatial modes of light as a basis to realize high-dimensional quantum states has opened up many new quantum processes and protocols^{236, 237}, all facilitated by LC-SLMs embedded as quantum state creators and detectors, as shown in Fig. 12(a). The birth of this field can be traced back to the seminal work in 2001 where DOEs were used as OAM projectors to show OAM conservation down to the single photon level, and OAM entanglement in 2D subspaces²³⁸. The DOEs, which were hardcoded for particular projections, were later replaced by LC-SLMs for rewritable quantum projectors, one for each photon in the experiment. This was a crucial step, particularly when considering that there are many spatial basis to select from, and an infinite number of modes in each. This implies the need to have versatility in the detection step, a condition made possible with SLMs. For instance, the introduction of LC-SLMs into quantum optics enabled dynamic quantum state tomography, first for OAM qubits²³⁹ and later for any dimensional state on any basis²⁴⁰. This was quickly followed by seminal work on Bell inequality violations using digital holograms²⁴¹, uncertainty principle tests²⁴² and the realization of ultra-high entangled state characterization using just a few measurements^{243, 244}. LC-SLMs have likewise proven essential in tailoring the entanglement spectrum either at the creation step^245-247 or the detection step^{248, 249}. This realization and control of multidimensional quantum states have led to both new physics and advanced quantum applications, with LC-SLMs proving crucial in quantum random number generation²⁵⁰, quantum key distribution^{251, 252}, quantum communication^{253, 254}, quantum secret sharing²⁵⁵ and for quantum entanglement swapping²⁵⁶ and teleportation²⁵⁷, reaching states of up to 100 × 100 dimensions²⁵⁸. Figure 12 illustrates the typical applications of LC-SLMs in the field of quantum. The quantum application that is most leveraged in the use of SLMs is quantum ghost imaging^259-262, where digital objects are encoded on one photon and digitally detected on the other photon. Here the SLMs facilitate computational approaches to be used, for instance, to allow single pixel imaging with random masks on the SLMs.

LC-SLMs have had a profound impact on various research areas and applications, ranging from optical interconnections at the component level to quantum entanglement. This review paper provides a comprehensive analysis of recent developments in LC-SLMs by discussing liquid crystal devices, exploring light shaping through diffraction, and highlighting the promising applications of LC-SLMs. The review demonstrates the potential of LC-SLMs to achieve unique functionalities, but also outlines the technical challenges that need to be addressed to advance this field further. One significant challenge is the lack of compact and fast enough LC-SLMs, especially in long-wave wavelengths. Additionally, designing LC-SLM systems involve trade-offs among various factors, such as resolution, modulation range, and damage threshold. Reducing pixel size and increasing the number of pixels in an image can improve image clarity and quality, but may also compromise fill factor, surface flatness, diffraction efficiency, and light utilization. Presently, the maximum matrix resolution is 4160×2464 and a linear array of 1×12288. Several methods have been proposed to achieve large-angle holographic displays, but there is a trade-off between modulation range and refresh rate. Furthermore, the high concentration of laser energy can cause deformation or complete damage to the inside or surface of the medium. This damage is related to the processing of optical components, such as the coating methods and the purity of the film material. Short response time is crucial in applications that require real-time modulation of optical wavefronts. This is particularly important in dynamic applications. Long response time can limit the ability of LC-SLMs to keep up with rapidly changing optical signals, leading to degraded performance and reduced effectiveness. Overcoming this challenge requires the development of LC-SLMs technologies that can swiftly modulate phase and amplitude while maintaining accuracy. High resolution refers to the number of pixels per unit area on the LC-SLM. For precise modulation of optical wavefronts, a high resolution is crucial. However, increasing the pixel density presents challenges related to manufacturing, controlling individual pixels, and managing heat dissipation. Higher resolution demands better control over individual pixels, which can lead to difficulties in maintaining uniformity and minimizing cross-talk between adjacent pixels. Advanced manufacturing techniques, pixel addressing schemes, and materials engineering are being explored to pursue higher resolution without compromising performance. Fringe field effects occur due to interactions between pixels on an LC-SLM, resulting in unintended phase or amplitude changes in neighboring pixels. These effects can lead to image artifacts, reduced modulation fidelity, and inaccurate wavefront manipulation. Mitigating these effects requires precise pixel addressing and calibration techniques, as well as the development of pixel structures that minimize cross-talk. As these challenges are overcome, LC-SLMs are becoming more versatile tools for dynamic optical control, holography, imaging, and many other fields where precise wavefront manipulation is essential.

We conclude by providing our opinions on the opportunities and technical challenges in the rapidly developing field of metamaterials and metasurfaces. Metamaterials have been a research hotspot and offer the ability to modulate various properties of light such as bandwidth, polarization, wavelength, and time dependence. By incorporating metamaterials into LC-SLMs, a substitute optical modality is possible. Ongoing research in this realm aims to improve the usefulness of long-wave metamaterial imaging, which has significant implications for non-invasive cancer detection, infrared thermography, and other medical imaging scenarios. Another promising direction is the use of metasurfaces, which can perform wavefront regulation at the sub-wavelength scale. Metasurfaces can be implemented in designing and fabricating optical elements and systems with capabilities that surpass the performance of conventional DOEs. By integrating metasurfaces with LC-SLMs, one can make LC-SLMs more powerful in wavefront engineering, modulation of polarized light, holography, and other applications. S. Mansha et al proposed a novel design that allows small pixel and multi-spectral operations with a metasurface-based LC-SLM²⁶³. Their design is based on LC-tunable Fabry-Perot nanocavities, which are designed to support multiple resonances in the visible range, including RGB wavelengths, providing continuous 2π phase modulation with high reflectance. It is foreseeable that with the improvements in manufacturing techniques, computing power and further exploration of dynamic modulation techniques, the performance of LC-SLMs could be further improved. The incorporation of metamaterials and metasurfaces into LC-SLMs opens up new exciting possibilities for research and applications in various fields. However, there are still technical challenges that need to be addressed, such as improving the usefulness of long-wave metamaterial techniques, optimizing the design and fabrication of metasurface-based LC-SLMs. Nonetheless, we are optimistic about the future of LC-SLMs and the potential impact they can have on the field of optics and beyond.

We are grateful for financial supports from National Natural Science Foundation of China (No. 62235009).

The authors declare no competing financial interests.