By periodically altering the optical properties (e.g., refractive indices and nonlinear optical coefficients) of transparent materials, a diverse range of periodic photonic structures can be created, including nonlinear photonic crystals (NPCs) and optical waveguide arrays.1^–3 The significance of NPCs lies in their applications for frequency conversion and beam shaping,4^–13 which are typically fabricated in nonlinear optical crystals using electrical poling techniques.14^,15 However, these NPCs are limited to one-dimensional (1D) and two-dimensional (2D) configurations, as the electrical poling method cannot produce three-dimensional (3D) NPCs. This limitation has significantly restricted the diverse photonic applications of NPCs in 3D space for an extended period.4^,16 Optical waveguides are fundamental components in the field of integrated optics,17^–30 allowing light to be confined to very small areas (on the microscale or even nanoscale) for nondiffractive propagation. Techniques such as ion implantation,31^,32 ion exchange,33^,34 and Ti-in-diffusion35^–37 have been employed to fabricate high-quality 1D and 2D optical waveguides in transparent materials; however, they are inadequate for creating 3D waveguide structures, particularly 3D optical waveguide arrays. Similar to the challenges faced in manufacturing 3D NPCs, conventional waveguide fabrication methods (e.g., ion implantation, ion exchange, and Ti-in-diffusion) lack the capability to produce 3D optical waveguide arrays, which hinders the advancement of high-performance and multifunctional 3D waveguide devices. The femtosecond laser direct writing technique presents a truly 3D processing approach,3^,38^–70 effectively addressing these challenges in the fabrication of both 3D NPCs and 3D optical waveguide arrays.

The femtosecond laser direct writing technique is characterized by high-precision, high-efficiency, and truly 3D processing, which has been widely applied in the fields of integrated optics, optofluidics, and biomedicine.3^,17^,64^,71^–82 Many important advances in femtosecond laser micro/nanomanufacturing technique have been made in recent years, such as rapid fabrication of reconfigurable helical microswimmers,83 fabrication of microclaw array with femtosecond Airy beam,84 and high-throughput two-photon 3D printing.85 The ultrashort pulse width and ultrahigh peak power are two distinctive features of femtosecond laser. The ultrahigh peak power can lead to a series of nonlinear interactions (e.g., multiphoton absorption, tunneling ionization, and avalanche ionization).3^,64 The ultrashort pulse width can suppress heat-affected zones, leading to ultrahigh machining accuracy. Usually, the incident femtosecond laser is focused by a microscope objective into transparent materials. At the femtosecond-laser focal point, some optical properties (e.g., refractive indices and ferroelectric domains) of transparent materials (e.g., nonlinear crystals and optical glasses) may be changed. The changes in optical properties of transparent materials are not only affected by material nature (e.g., hardness, dispersion, bandgap, thermal conductivity) but also are closely related to the selected femtosecond laser processing parameters (e.g., central wavelength, repetition rate, scanning velocity, pulse energy). Due to the above numerous advantages (i.e., high-precision, high-efficiency, and truly 3D processing) of femtosecond laser direct writing in material processing, it has been extensively applied to rapidly fabricate 3D micro-/nanoscale photonic structures in transparent materials.86 By carefully designing and optimizing the motion path of femtosecond laser in transparent materials, periodic modulation of material optical properties in 3D space can be easily realized. With femtosecond laser processing parameters continuously optimized, we can obtain the desired periodic photonic structures (e.g., 3D NPCs and 3D waveguide arrays) in specific transparent optical materials. Using the femtosecond laser direct writing technique to periodically modulate nonlinear optical coefficients of nonlinear crystals in 3D space, a variety of multifunctional 3D NPCs could be produced.16^,87 Today, a number of 3D NPCs have been successfully fabricated in diverse nonlinear optical crystals [e.g., lithium niobate (${\mathrm{LiNbO}}_3$) crystals,2${\mathrm{Ba}}_{0.77}{\mathrm{Ca}}_{0.23}{\mathrm{TiO}}_3$ (BCT) crystals,1${\mathrm{Ca}}_{0.28}{\mathrm{Ba}}_{0.72}{\mathrm{Nb}}_2{\mathrm{O}}_6$ (CBN) crystals,88 and ${\mathrm{Sr}}_{0.61}{\mathrm{Ba}}_{0.39}{\mathrm{Nb}}_2{\mathrm{O}}_6$ (SBN) crystals89] for a great deal of photonic applications, such as nonlinear frequency conversion,90^–96 nonlinear beam shaping,97^–99 and nonlinear holography.89^,100^–102 The femtosecond-laser-writing strategy of NPCs overcomes the fabrication challenge of NPCs in 3D space, providing the possibility for experimentally investigating 3D light-matter interactions in nonlinear optics. In addition to the application for modulating nonlinear optical coefficients, a tightly focused femtosecond laser can also be utilized to change refractive indices in transparent optical materials (including but not limited to nonlinear crystals and optical glasses).3^,17 Based on femtosecond-laser-induced refractive index changes, diverse waveguide structures have been fabricated in transparent materials, such as single-line, dual-line, and depressed-cladding waveguides,17 which can be applied to construct versatile 3D waveguide devices (e.g., 3D beam splitters and 3D waveguide arrays). Femtosecond-laser-written 3D waveguide structures are of great significance to the fabrication of multifunctional photonic devices in integrated optics and quantum optics. The laser-written 3D waveguide arrays, which are formed by periodically arranging optical waveguides in 3D space, provide a great photonic platform for studying interesting physical laws and phenomena in topological photonics.

Nowadays, a number of reviews have focused on femtosecond laser direct writing of NPCs,4^,16^,87 optical waveguides,3^,17 and micro-/nanoscale photonic structures.86 However, many latest research results are missing in these articles due to the rapid development of the femtosecond-laser-manufacturing field. Besides, there are few papers that summarize the recent advances of 3D periodic photonic structures written by femtosecond laser in transparent optical materials. This review article focuses on the state-of-the-art progress of femtosecond-laser-written 3D periodic photonic structures (i.e., 3D NPCs and 3D waveguide arrays) in transparent materials, including fabrication, characteristics, and selected photonic applications. In this review, Sec. 2 briefly introduces the basics of modulating optical nonlinearity in ferroelectric crystals and quartz crystals with a tightly focused femtosecond laser, followed by femtosecond-laser-induced refractive index changes in transparent materials. Section 3 demonstrates the selected applications of 3D NPCs in nonlinear optics, which are based on femtosecond-laser-induced periodic optical nonlinearity modulation. Section 4 presents the selected applications of 3D waveguide arrays in topological photonics, non-Hermitian photonics, and quantum photonics, which are based on femtosecond-laser-induced periodic refractive index changes. A concise summary and several potential study directions will be given in Sec. 5.

The optical nonlinearity (e.g., second-order nonlinearity) of nonlinear crystals can be effectively modulated using tightly focused femtosecond lasers. Ferroelectric crystals are a notable class of nonlinear crystals.15^,17^,29^,103^–107 The nonlinearity modulation in ferroelectric crystals is essential to modulate spontaneous polarization or ferroelectric domain (i.e., nonlinear optical coefficient). Due to the presence of a ferroelectric domain, the modulation of optical nonlinearity in ferroelectric crystals differs significantly from that in other nonlinear crystals. One of the most prominent distinctions is the phenomenon of ferroelectric domain inversion,103 where the sign of the nonlinear optical coefficient is reversed, whereas its absolute value remains unchanged. As for quartz crystals,108 which are ancient nonlinear crystals lacking ferroelectric domains, cannot reverse their nonlinear optical coefficients in the same manner as ferroelectric crystals. Femtosecond-laser-induced optical nonlinearity modulation in quartz crystals is chiefly realized by decreasing the nonlinear optical coefficients (even reduced to zero), i.e., the absolute value of the nonlinear optical coefficient will be reduced with sign unchanged. Section 2.1 presents the domain modulation in ferroelectric crystals and nonlinearity modulation in quartz crystals, including fundamentals, categories, and properties.

The tightly focused femtosecond laser serves as a powerful tool for inducing changes in the refractive index of transparent materials, such as dielectric crystals and optical glasses.3 Femtosecond-laser-induced refractive index changes could be classified into two types, i.e., positive refractive-index change and negative refractive-index change.3 In general, positive refractive-index change is called type-I modification, and negative refractive-index change is called type-II modification. Section 2.2 introduces two types of refractive-index changes induced by femtosecond laser in transparent materials, including fundamentals, laws, and waveguiding properties.

This section will introduce the nonlinearity modulation of ferroelectric crystals from the following three aspects, i.e., domain modification, domain erasure, and domain inversion. Besides, as for nonlinearity modulation in quartz crystals, the nonlinearity modification and nonlinearity erasure will be briefly introduced.

Ferroelectric crystals are a distinctive class of nonlinear crystals characterized by their remarkable properties, particularly the phenomenon of spontaneous polarization within a specific temperature range.1^,99^,100^,109^,110 This spontaneous polarization can be reversed by applying an external electric field, thereby altering its direction. Ferroelectric crystals consist of numerous small regions known as ferroelectric domains. Within each domain, the direction of spontaneous polarization is uniform, while adjacent domains exhibit differing polarization directions. The nonlinear optical properties of ferroelectric crystals are significantly stronger than those of conventional nonlinear crystals, especially near the domain walls, which can enhance nonlinear processes. Today, ferroelectric crystals are widely utilized in various applications such as nonlinear frequency conversion, nonlinear beam shaping, and nonlinear holography, playing a vital role in the field of nonlinear optics.1^,2^,88^,111 For example, by periodically modulating the ferroelectric domains (i.e., nonlinear optical coefficients) of these crystals, one can create periodic photonic structures that enable quasi-phase matching, facilitating efficient nonlinear frequency conversion.103 The periodic photonic structures formed through periodically modulating nonlinear optical coefficients are called NPCs. The 3D NPCs will be fabricated if nonlinear optical coefficients are modulated by femtosecond laser in 3D space. According to variation of ferroelectric domains, femtosecond-laser-induced nonlinearity modulation in ferroelectric crystals can be divided into three categories: domain modification,112 domain erasure,2 and domain inversion.113

In ferroelectric crystals, domain modification, domain erasure, and domain inversion can all be utilized to fabricate 3D NPCs. However, there are significant differences among the three domain-modulation scenarios. Domain modification is to partly reduce the nonlinear optical coefficient. Domain erasure is to completely erase nonlinear optical coefficients. Domain inversion is just to reverse the sign of nonlinear optical coefficient. If $d$ and $d_0$ are defined as nonlinear optical coefficients of femtosecond-laser-irradiated and unirradiated regions, respectively. The $v=d/d_0$ represents a relative ratio of $d$ versus $d_0$. The relative ratio $v$ in domain modification ranges from 0 to 1 (i.e., $0<v<1$). For domain erasure, the relative ratio $v$ is 0 (i.e., $v=0$). In domain inversion, the relative ratio $v$ is $-1$ (i.e., $v=-1$). The original single crystal will become partially amorphous in domain-modification areas. In the regions of domain erasure, the original single crystal has become completely amorphous. However, the nonlinear properties of single crystals can be well preserved in domain-inversion areas. From the perspective of conversion efficiency, NPCs based on domain modification are relatively low, NPCs based on domain erasure are high, and domain-inversion-based NPCs are much higher. Why is there such a significant difference in conversion efficiency? The direct reason is that the modulation degree of the nonlinear coefficient varies, leading to different compensation for phase mismatch in the nonlinear frequency conversion. In 2020, Imbrock et al. calculated and compared second-harmonic build-up (see Fig. 1) in domain-modification-based NPCs, domain-erasure-based NPCs, and domain-inversion-based NPCs.114 As Fig. 1 depicts, the second-harmonic build-up ($P_{2\omega }$) of domain inversion (i.e., $v=-1$) is the highest under the same propagation length ($z/l_c$), followed by domain erasure (i.e., $v=0$), and finally domain modification (i.e., $v=0.5$ or 0.75). By comparison of $P_{2\omega }$ in Fig. 1, the effects of three domain-modulation scenarios on the conversion efficiency of NPCs have been intuitively demonstrated. For collinear phase matching (PM), the amplitude changes of fundamental and second-harmonic waves propagating along $y$ direction can be described with the following coupled-mode equations:114$$\frac{\text{d}}{\text{d}y}{A}_{\omega }{=-i\kappa }^{*}d(\mathbf{r})A_{\omega }^{*}{A}_{2\omega }\exp (-i\mathrm{\Delta }ky)-{\alpha }_{\omega }{A}_{\omega },$$(1)$$\frac{\text{d}}{\text{d}y}{A}_{2\omega }=-i\kappa d(\mathbf{r})A_{\omega }^2\exp (i\mathrm{\Delta }ky)-{\alpha }_{2\omega }{A}_{2\omega },$$(2)$${\kappa }^2=\frac{{2\omega }^2}{{ϵ}_0{c}^3}\frac{1}{n_{\omega }^2{n}_{2\omega }{S}_{\mathrm{eff}}},$$(3)$$\mathrm{\Delta }k=k_{2\omega }{-2k}_{\omega },$$(4)where $A_{\omega }$ and $A_{2\omega }$ are amplitudes of fundamental and second-harmonic waves, $\mathrm{\Delta }k$ is phase mismatch, and $S_{\mathrm{eff}}$ is the cross-section of overlap of the fundamental and second-harmonic modes. The ${\alpha }_{\omega }$ and ${\alpha }_{2\omega }$ are absorption coefficients of fundamental and second-harmonic waves, respectively. The $d(\mathbf{r})$ is the nonlinear coefficient, which could be modulated in any direction. Taking 1D quasi-phase-matching as an example, the nonlinear coefficient will be modulated only along the $y$ direction, which can be described with $d(y)=d_{\max }g(y)$. The normalized rectangular function $g(y)$ includes period $\mathrm{\Lambda }=2l_c=2\pi /\mathrm{\Delta }k$ to compensate for phase mismatch, where $l_c$ represents coherence length. The Fourier transform of $d(y)$ will generate an effective nonlinear coefficient $d_{\mathrm{eff}}$:114$$d_{\mathrm{eff}}=\frac{d_0}{\pi }(1-v).$$(5)

The $v=d/d_0$ represents a relative ratio, which has been mentioned above. Therefore, domain inversion (i.e., $v=-1$) possesses the largest effective nonlinear coefficient $d_{\mathrm{eff}}=(2d_0)/\pi$, domain erasure (i.e., $v=0$) has effective nonlinear coefficient of $d_{\mathrm{eff}}=d_0/\pi$, and domain modifications (i.e., $v=0.5$ and 0.75) have effective nonlinear coefficients of $d_{\mathrm{eff}}=d_0/(2\pi )$ and $d_{\mathrm{eff}}=d_0/(4\pi )$, respectively. These cases where $v$ equals different values have been manifested in Fig. 1.

From the perspective of laser processing, the repetition rate of a femtosecond laser significantly influences the modulation of ferroelectric domains. For instance, a repetition rate of 1 kHz is sufficient to induce domain modification and domain erasure,2 while dozens of MHz is required to induce domain inversion.113 The thermal effect in light-matter interactions is negligible when a femtosecond laser of 1 kHz repetition rate is utilized to induce ferroelectric domains. However, the thermal effect is non-negligible if dozens of MHz repetition rate is used. Optical nonlinearity will be destroyed with varying degrees in domain modification and domain erasure schemes. Due to the thermal effect in the domain inversion scheme, ferroelectric domains are inverted by a thermoelectric field formed by ultra-high temperature gradient at laser focus. There is no damage to optical nonlinearity in domain inversion. Generally speaking, during the domain-inversion process, there are mainly two physical mechanisms that dominate the interactions between femtosecond laser and ferroelectric crystals.110 First, a tightly focused femtosecond laser will create a strong head-to-head electric field at the focal area. Second, due to laser-heating-caused reduction in domain wall pinning, the threshold field for domain inversion of ferroelectric crystals will significantly decrease, making it easier to invert ferroelectric domains at the focal spot of femtosecond laser. In addition, it has been reported that only the electric-field component antiparallel to spontaneous polarization can invert ferroelectric domains, whereas the others cannot.110 With in-depth investigations, more physical mechanisms of domain modulation will be revealed in the near future. In Table 1, the similarities and differences among the three domain-modulation scenarios have been summarized.

In 2013, Thomas et al. fabricated a type of NPCs in ${\mathrm{LiNbO}}_3$ crystals with a tightly focused femtosecond laser (central wavelength of 800 nm, pulse width of 170 fs, and repetition rate of 100 kHz),112 which is the earliest report about domain-modification-based quasi-3D NPCs. In this review, the optical nonlinearity has been periodically damped up to 20% (i.e., relative ratio $v=0.8$). With domain-modification-based quasi-3D NPCs, the frequency doubling of $1.55\mu \mathrm{m}$ light has been achieved. Compared with unmodified material, the frequency-doubling signal could be enhanced by a factor of 70. The corresponding fabrication setup [Fig. 2(a)], fabrication routine [Fig. 2(b)], and end-face microscopic image [Fig. 2(c)] of quasi-3D NPCs have been shown in Fig. 2. This pioneering review provides a new method to modulate optical nonlinearity in 3D space and paves the way to realize truly 3D nonlinear photonic devices.

In 2018, Wei et al. proposed a new scenario for fabricating 3D NPCs,2 called the femtosecond-laser-induced domain-erasure (i.e., relative ratio $v=0$) technique. Based on the domain-erasure technique, they presented the first experimental demonstration of truly 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals. It has been reported that a frequency doubling of 829 nm can be realized with a conversion efficiency of 0.012%. The central wavelength, pulse width, and repetition rate of femtosecond laser for domain erasure are 800 nm, 104 fs, and 1 kHz. Figure 3(a) shows Čerenkov’s second-harmonic microscopic image of the first two layers in 3D NPCs. The confocal second-harmonic microscopic image has been demonstrated in Fig. 3(b), which is obtained from non-engineered (i.e., un-erased) and engineered (i.e., erased) areas. Figure 3(c) shows the second-harmonic intensity distribution along the black line in Fig. 3(b). The minimal nonzero second-harmonic intensity in Fig. 3(c) means that the optical nonlinearity has not been completely erased in the experiment. Although the relative ratio is not exactly zero, an experimental value of 0.24 is approaching domain erasure. This review reported the first truly 3D NPCs, providing a promising platform for realizing 3D nonlinear frequency conversion, 3D nonlinear beam shaping, and 3D nonlinear holography.

In addition, in 2018, Xu et al. reported the first domain-inversion-based (i.e., relative ratio $v=-1$) truly 3D NPCs in ferroelectric BCT crystals.1 The central wavelength, pulse width, and repetition rate of femtosecond laser for domain inversion are 815 nm, 180 fs, and 76 MHz. As an example of nonlinear frequency conversion, second-harmonic generation with a conversion efficiency of $1.7\times {10}^{-6}{\mathrm{W}}^{-1}{\mathrm{cm}}^{-1}$ has been achieved under a fundamental wavelength of 1340 nm. Figures 4(a) and 4(b) show the reciprocal lattice vectors of 2D NPCs and 3D NPCs, respectively. In Figs. 4(a) and 4(b), it can be seen that a new degree of freedom has been added along the vertical direction. The Čerenkov second-harmonic microscopic image of 3D NPCs is displayed in Fig. 4(c). In the domain-inversion scheme, only the sign of the nonlinear optical coefficient will be reversed. Compared with domain modification and domain erasure, the domain-inversion scenario could provide a better compensation for phase mismatch, having many potential applications for fabricating high-efficient 3D nonlinear photonic devices.

More recently, Xu et al. proposed a non-reciprocal 3D femtosecond laser writing technique for nanodomain fabrication.110 With a non-reciprocal 3D laser writing technique, they have successfully fabricated nanodomain structures in ${\mathrm{LiNbO}}_3$ crystals in 2022. Figure 5 demonstrates femtosecond-laser-induced nanodomains in ${\mathrm{LiNbO}}_3$ crystals. Figure 5(a) shows a 3D model of ruler-shaped nanodomains, whose piezoresponse force microscopy (PFM) images on cross sections are displayed in Figs. 5(b) and 5(c). Figure 5(d) manifests the PFM image of wide-angle nonlinear diffraction grating constructed by nanodomains, with measured nonlinear Raman–Nath diffraction pattern shown in the inset. In Fig. 5(d), the linewidth and period are 250 and 500 nm, respectively. The central wavelength, pulse width, and repetition rate of femtosecond laser for inducing nanodomain inversion are 800 nm, 75 fs, and 80 MHz. In this review, it is the first time to push a femtosecond-laser-inverted ferroelectric domain to a nano-scale dimension (resolution to 30 nm), having potential applications in high-capacity memory, high-efficiency frequency conversion, and high-resolution linewidth manipulation.

Quartz crystals are a sort of ancient nonlinear crystals without ferroelectric domains, having relatively high transmission at deep-ultraviolet (DUV) bands.108^,115^,116 Due to without ferroelectric domains, the nonlinear optical coefficients of quartz crystals cannot be reversed similar to ferroelectric crystals. Analogous to domain modification and domain erasure in ferroelectric crystals, the femtosecond-laser-induced nonlinearity modulation in quartz crystals can be divided into two types: nonlinearity modification and nonlinearity erasure. If the nonlinearity decreases but does not reach zero, it is called nonlinearity modification. If the nonlinear coefficient drops to zero, it is called nonlinearity erasure. The nonlinearity modulation in quartz crystals is essentially the destruction of the lattice structure, which is decided by femtosecond-laser processing parameters. The most desired femtosecond-laser processing parameters are those that can reduce the nonlinear coefficient to zero with caused lattice damage as slight as possible because severe damage to lattice structure will bring about additional propagation losses in numerous applications of nonlinear optics. Through in-depth studies on interactions between femtosecond laser and quartz crystals, more physical mechanisms and optimum processing parameters will be reported successively. In 2020, Shao et al. proposed the additional periodic phase (APP) theory, to compensate for the mismatched phase during nonlinear frequency conversion inside arbitrary nonlinear optical crystals.108 As an experimental demonstration of APP theory, they have periodically erased the nonlinearity of quartz crystals and achieved DUV 177.3-nm coherent output with unprecedented conversion efficiency above 1‰. The central wavelength, pulse width, and repetition rate of femtosecond laser for inducing nonlinearity erasure are 1040 nm, 350 fs, and 200 kHz. Figures 6(a) and 6(b) demonstrate the schematics of birefringent PM and quasi-PM. The schematic of APP PM has been shown in Fig. 6(c), in which the areas of nonlinearity erasure are marked with “Disorder.” The amplitude of the second-harmonic field under PM, quasi-PM, APP PM, and phase mismatching has been displayed in Fig. 6(d). In Fig. 6(d), it can be seen that the amplitude of the second-harmonic field under APP PM is slightly lower than quasi-PM. Nevertheless, the application scope of APP PM is more extensive than quasi-PM. Due to the flexibility of laser processing and the good generality of nonlinear crystals, the APP theory and nonlinearity erasure technique reported in this review may lead to a next-generation revolution in nonlinear optics and quantum photonics.

The femtosecond-laser-induced refractive index changes in transparent optical materials can be divided into two types, i.e., type-I modification and type-II modification.3 The type-I and type-II modifications are corresponding to positive and negative refractive-index changes at the focal point of the femtosecond laser. In the region with type-I modification, the refractive index is higher than the surrounding areas. Thus, type-I modification can be utilized to directly form optical waveguides in laser-irradiated regions. However, for type-II modification, the refractive index is lower than the surrounding areas. The optical waveguides cannot be formed in the region with type-II modification. However, one can use type-II modification to enclose a region with a relatively high refractive index in the middle, which is also a good strategy for constructing optical waveguides.

Generally speaking, low pulse energy is prone to induce type-I modification in transparent materials. Recently, it has been reported that type-I modification may be related to phase transition in laser-irradiated areas.117^,118 To induce type-II modification, the femtosecond laser with much higher pulse energy will be employed. The type-II modification will result in severe destruction of material structure and the formation of various defects. As an example, Fig. 7 shows femtosecond-laser-induced type-I and type-II modifications in ${\mathrm{LiNbO}}_3$ crystals. The refractive-index profiles of type-I modification and type-II modification are shown in Figs. 7(a) and 7(d), respectively. Figures 7(b) and 7(e) demonstrate refractive-index profiles at horizontal cross-sections in Figs. 7(a) and 7(d). In Figs. 7(b) and 7(e), it can be clearly seen that positive and negative refractive-index changes have been induced at laser focus. Figures 7(c) and 7(f) are mode profiles obtained at the wavelength of 633 nm, corresponding to type-I modification and type-II modification, respectively. It is evident that type-I modification can guide light but cannot guide light in type-II modification. For type-I modification in ${\mathrm{LiNbO}}_3$ crystals, femtosecond-laser-induced slight lattice distortion can lead to decreased spontaneous polarization and therefore an increment in refractive indices.3 However, as for type-II modification in ${\mathrm{LiNbO}}_3$ crystals, severe damage will be caused by a femtosecond laser at the focal area.3 It is the lattice expansion that results in a decrease in refractive indices.

Based on type-I modification and type-II modification, a variety of waveguide configurations have been constructed in transparent optical materials, such as single-line waveguides, double-line waveguides, depressed-cladding waveguides, and optical-lattice-like cladding structures.3^,17 The fabrication methods and wave-guiding properties of the abovementioned waveguide structures have been summarized in our previous review papers,3^,17 so we would not reiterate them here. In Sec. 4, the selected applications of 3D waveguide arrays are based on femtosecond-laser-induced type-I modification.

Femtosecond laser direct writing technique has brought revolutionary influence to the field of material processing, due to ultrashort pulse duration and ultrahigh peak power. The femtosecond laser direct writing technique has many advantages for inducing optical nonlinearity modulation in 3D space, such as high precision, high flexibility, and high efficiency. Nowadays, 3D NPCs, based on femtosecond-laser-induced optical nonlinearity modulation, have attracted considerable attention and intensive investigations. Figure 8 shows a schematic of typical 3D NPCs written by a tightly focused femtosecond laser in nonlinear optical crystals. In this section, the selected applications of 3D NPCs in nonlinear optics will be introduced, including nonlinear frequency conversion, nonlinear beam shaping, and nonlinear holography.

Nonlinear frequency conversion is one of the most important optical nonlinear processes, with which the frequency/wavelength of the input laser will be converted to other frequencies/wavelengths.92 Many conversion mechanisms could be applied to realize nonlinear frequency conversions, such as second harmonic generation (SHG),90 third harmonic generation,119 spontaneous parametric down-conversion (SPDC),120 difference frequency generation,121 and optical parametric oscillation.122 Nonlinear optical crystals serve as an ideal material platform to achieve nonlinear frequency conversion. Due to its ability to convert the frequency of light to other bands, light at different wavelengths could be generated with nonlinear frequency conversion. Nonlinear frequency conversion has many valuable applications, such as the generation of multi-wavelength lasers in laser technology. Nowadays, the fabrication challenge of 3D NPCs has been overcome using the femtosecond laser direct writing technique,1^,2 enabling the investigation of 3D nonlinear frequency conversion.

In 2013, Thomas et al. periodically modified ferroelectric domains in ${\mathrm{LiNbO}}_3$ crystals by femtosecond laser direct writing technique and successfully realized SHG of 1545 nm.112 This is the earliest report on nonlinear frequency conversion using femtosecond-laser-written NPCs. Two years later, in ${\mathrm{LiNbO}}_3$ crystals, Kroesen et al. combined femtosecond-laser-modified periodic domains with femtosecond-laser-written depressed-cladding waveguides, achieving SHG of 1064 nm with the conversion efficiency of $0.0637\%{\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$.123 This review paves the way to fabricate waveguide-based on-chip high-performance frequency converters in one step. In 2016, Chen et al. fabricated periodically inverted domain structures in Ti-indiffused ${\mathrm{LiNbO}}_3$ waveguides, obtaining SHG of 815 nm with a conversion efficiency of 17.45%.103 The domain-inversion-based NPCs reported in this review are the most promising candidates for implementing high-performance frequency converters. Two years later, two independent groups reported the femtosecond-laser-written 3D NPCs at approximately the same time. The SHG has been realized as well in both laser-written 3D NPCs. One is 3D NPCs fabricated by Wei et al. in ${\mathrm{LiNbO}}_3$ crystals, which are based on domain erasure.2 The other is 3D NPCs fabricated by Xu et al. in BCT crystals, which are based on domain inversion.1 These two pioneering reviews pave the way to study new physical phenomena and laws, having great potential applications in nonlinear frequency conversion, nonlinear beam shaping, and nonlinear holography.

The 3D NPCs provide powerful platforms to manipulate and control quantum states in the field of quantum optics. In 2021, Xu et al. reported that 3D NPCs are of great significance in generating high-dimensional orbital-angular-momentum entanglement, having potential applications in quantum precision measurement, quantum computing, and quantum communication.124 In 2023, Dai et al. periodically inverted ferroelectric domains in Ti-indiffused ${\mathrm{LiNbO}}_3$ waveguides with femtosecond laser direct writing technique and realized photon pair generation by the SPDC process.125 This review proves that it is possible to fabricate integrated quantum sources with femtosecond-laser-written NPCs. Figure 9(a) shows the experimental setup for fabricating periodically inverted domain structures in Ti-indiffused ${\mathrm{LiNbO}}_3$ waveguides. Figure 9(b) is an optical microscopic image of 2D domain patterns. The Čerenkov second-harmonic microscopic image of NPCs is displayed in Fig. 9(c). More recently, Yang et al. reported the SPDC process in nanoscale-resolution ${\mathrm{LiNbO}}_3$ NPCs written by femtosecond laser.126 This review indicates the remarkable advantages of the femtosecond laser direct writing technique in fabricating nanoscale-resolution 3D NPCs, with which narrowband entangled photon pairs could be realized by the counter-propagation SPDC process.

Based on femtosecond-laser-induced nonlinearity erasure in quartz crystals, Shao et al. fabricated NPCs in 2020 and realized DUV 177.3 nm laser generation with SHG mechanism.108 In 2022 and 2023, based on SHG mechanism and laser-written NPCs in quartz crystals, they respectively achieved widely tunable DUV 221 to 332 nm laser generation,115 and the milliwatt power output at 177.3 and 167.8 nm.116 Their series of reviews are of great significance for generating high-performance DUV solid-state lasers and bringing revolutionary progress to studies of DUV laser sources. In 2024, Zhang et al. simultaneously realized the 2nd to 5th harmonic generation of 1030 nm in femtosecond-laser-written APP quartz crystals.127 This review paves the way to develop multi-wavelength solid-state laser sources using laser-written quartz NPCs. Figure 10(a) demonstrates an optical microscopic image of laser-written quartz NPCs (i.e., APP quartz crystals). The period length distribution of quartz NPCs is shown in Fig. 10(b), ranging from 6.5 to $10.5\mu \mathrm{m}$. The experimental setup for generating the 2nd to 5th harmonic generation of 1030 nm is displayed in Fig. 10(c). The photograph of the 2nd to 4th harmonic generation is shown in Fig. 10(d).

Regarding material as a clue, Table 2 demonstrates the latest results of nonlinear frequency conversion in femtosecond-laser-written NPCs, in which readers can easily get recent advances and obtain more details not mentioned above.

Nonlinear beam shaping is a technique that alters the wavefront shape of a light beam by utilizing nonlinear optical materials and principles.88^,111 It can be realized through nonlinear frequency conversion processes. For example, using quasi-PM technology in nonlinear optical crystals, the light beam at a fundamental frequency can be converted into a second harmonic light beam with a specific wavefront shape. The nonlinear beam shaping technique allows for simultaneous wavefront modulation and frequency conversion, leading to the generation of nonlinear vortex beams and nonlinear nondiffracting beams. Nonlinear beam shaping has a wide range of applications, including optical communication and super-resolution imaging. In addition, nonlinear beam shaping can also be employed for achieving 3D nonlinear holographic imaging.100 Nonlinear holographic imaging is a technology that stores optical information in a new frequency channel, enabling optical information reconstruction while frequency conversion, thereby improving the capacity and security of information storage (see Sec. 3.3 for more details). With the rapid development of NPCs, nonlinear beam-shaping technology is expected to be applied in more fields, such as optical data storage. The 3D NPCs written by femtosecond laser have shown many noticeable advantages in nonlinear beam shaping, such as a significant improvement in conversion efficiency. Overall, the development of nonlinear beam-shaping technology has brought new opportunities to the field of optics. It can not only improve the performance of optical systems but also promote the development of novel optical devices and applications.

In 2019, Liu et al. fabricated 3D NPCs in CBN crystals based on femtosecond-laser-induced domain inversion, successfully converting fundamental Gaussian beams into the second harmonic vortex, Gaussian, and conical beams.88 In the same year, Wei et al. fabricated 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals based on femtosecond-laser-induced domain erasure, successfully converting fundamental Gaussian beams into the second harmonic vortex and Hermite-Gaussian beams.111 As a showcase of beam-shaping results, the second harmonic Hermite-Gaussian beam generation has been depicted in Fig. 11. Figure 11(a) shows the model and confocal second harmonic image of 3D ${\mathrm{LiNbO}}_3$ NPCs for nonlinear beam shaping. The corresponding second harmonic diffraction patterns are displayed in Fig. 11(b), which are pumped at 818 nm. Figure 11(c) demonstrates the dependence of 1st-diffraction-order output power on fundamental wavelength. Figure 11(d) shows the dependence of the output power of the second harmonic Hermite-Gaussian beam on fundamental power at 818 nm. These two excellent reviews pave the way for achieving nonlinear beam shaping using femtosecond-laser-written 3D NPCs. In 2023, Wang et al. fabricated sequential 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals based on the domain erasure technique, successfully converting fundamental Gaussian beams into hexagonal diffracted, Hermite-Gaussian, and vortex beams.98 As an example, Fig. 12 demonstrates femtosecond-laser-written two-sequential 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals for simultaneously reconstructing multiple second harmonic structured beams. Figure 12(a) shows a schematic of a quasi-PM mechanism for reconstructing multiple second harmonic structured beams at a single wavelength. Figure 12(b) displays a schematic of two-sequential 3D NPCs for simultaneously reconstructing second harmonic structured beams composed of vortex beams and hexagonal diffracted beams. Figure 12(c) manifests second harmonic structured beams emitted from two-sequential 3D NPCs, which are pumped with 834 nm. This review provides a great strategy for simultaneously generating multiple nonlinear beams.

In 2023, Hu et al. fabricated NPCs in SBN crystals based on the domain inversion technique, successfully converting fundamental Gaussian beams into second harmonic optical bottle beams.99 This review opens up a new way for generating optical bottle beams at new frequencies, having potential applications in nonlinear optics and quantum photonics. More recently, in 2024, Wang et al. fabricated 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals based on a domain modification technique, successfully converting fundamental Gaussian beams into second harmonic flat-top beams.130 This review provides a great scenario to generate nonlinear flat-top beams, carrying important implications for generating other nonlinear beams with special wavefront.

Regarding material as a clue, Table 3 demonstrates the latest results of nonlinear beam shaping in femtosecond-laser-written NPCs, where readers can easily get recent advances and obtain more details not mentioned above.

Nonlinear holography is an advanced holographic technology that records and reproduces 3D image information through nonlinear optical processes.89^,100^–102^,133 With nonlinear holography technology, one can store more information and reconstruct it in different frequency channels, thereby increasing the storage capacity and security of information. It is the core of nonlinear holography technology to precisely control the amplitude and phase of light waves, using nonlinear optical materials (e.g., NPCs) and nonlinear optical processes (e.g., SHG). Nonlinear holography has been widely utilized in information storage, optical imaging, and optical communication.

Both nonlinear beam shaping and nonlinear holography aim to achieve precise control and manipulation of light waves through nonlinear frequency conversion processes in NPCs. However, there are key differences between these two technologies. First, nonlinear beam shaping is mainly utilized to change the wavefront and propagation characteristics of the beam, whereas nonlinear holography is used to record and reproduce 3D image information. Second, nonlinear beam shaping is commonly employed in the fields of optical communication and imaging, whereas nonlinear holography is more commonly used for information storage and display. Third, frequency conversion and wavefront modulation of the beam can be performed simultaneously in a nonlinear beam shaping process, whereas nonlinear holography primarily focuses on the reconstruction of optical information during frequency conversion.

Nowadays, femtosecond-laser-written 3D NPCs have been successfully applied in nonlinear holographic imaging, showing unique advantages and enormous potential. In 2021, Chen et al. reported quasi-phase-matching-division multiplexing holography in 3D NPCs,102 which are fabricated in ${\mathrm{LiNbO}}_3$ crystals based on femtosecond-laser-induced domain erasure. In this review, the patterns of the star, musical note, moon, and heart have been successfully reconstructed at the second harmonic wave. This review paves the way to realize high-efficient nonlinear multiplexing holography and is of great significance to high-security optical information storage. In the same year, Wang et al. reported nonlinear detour phase holography in SBN NPCs,89 which are fabricated based on domain inversion technique. They successfully demonstrated an H-shaped far-field second-harmonic holographic image, which can be seen in Fig. 13. Figure 13(a) shows a schematic of the experimental setup for nonlinear holographic imaging. Figures 13(b) and 13(c) demonstrate measured H-shaped far-field SHG holographic images and simulated far-field SHG intensity distribution, respectively. Figure 13(d) displays simulated results improved with a phase plate. It is the first time to extend the traditional detour phase method into nonlinear optics and successfully realize high-fidelity reconstruction of special optical beams, having potential applications in designing functional holograms.

In 2023, Chen et al. reported 3D NPCs at nano-resolution, which are fabricated in ${\mathrm{LiNbO}}_3$ crystals with domain inversion technique.101 With 3D ${\mathrm{LiNbO}}_3$ NPCs, 3D dynamic nonlinear holography and frequency-up-converted image recognition have been successfully demonstrated. The nano-resolution photonic platform reported in this review is of great importance for realizing high-capacity optical information storage. More recently, in 2024, Xu et al. reported large field-of-view nonlinear holography in ${\mathrm{LiNbO}}_3$ NPCs,100 which are fabricated with domain inversion technique. The large field-of-view nonlinear holography in experiments has been demonstrated in Fig. 14. Figure 14(a) displays the reconstruction of a cube at the second harmonic wave, corresponding to view angles of $-45\mathrm{deg}$, $-15\mathrm{deg}$, 15 deg, and 45 deg. Figure 14(b) shows a large-area hexagonal array formed by combining the central, first, and higher orders of second harmonic fields. It can be predicted that nonlinear holography reported in this review may play a critical role in wide-view imaging and display.

Regarding material as a clue, Table 4 demonstrates the latest results of nonlinear holography in femtosecond-laser-written NPCs, where readers can easily get recent advances and obtain more details not mentioned above.

Due to its capability for 3D modulation of the refractive index in transparent materials, the femtosecond laser direct writing technique has emerged as a powerful tool for fabricating 3D waveguide arrays. Figure 15 shows a schematic of typical 3D waveguide arrays written by a tightly focused femtosecond laser in transparent materials. Femtosecond-laser-induced type-I modification and type-II modification can both be utilized to construct 3D waveguide arrays. Perhaps due to the poor coupling effects between adjacent optical waveguides, there are relatively few reports on waveguide arrays based on femtosecond-laser-induced type-II modification. This section mainly focuses on the waveguide arrays based on type-I modification in optical glasses. In 1996, Davis et al. first fabricated optical waveguides based on type-I modification in optical glasses.135 Since then, optical waveguides based on type-I modification have been widely utilized to construct multifunctional waveguide devices and investigate interesting physical phenomena. In this section, the selected photonic applications of 3D waveguide arrays will be introduced, involving the fields of topological photonics, non-Hermitian photonics, and quantum photonics.

Topological photonics offers a unique path for manufacturing photonic devices immune to scattering losses and disorder.136^–142 Because of the pioneering theoretical predictions and experimental demonstrations of topologically protected electromagnetic edge states,143^–148 a series of studies on photonic topological insulators (TIs) have been successfully implemented in various experimental optical platforms,149 including photonic crystals,150 coupled resonators,151 metamaterials,152^–156 photorefractive waveguides,157^–160 and femtosecond-laser-written waveguides.161^–173 For instance, in 2009, the first experimental realization of the Su–Schrieffer–Heeger (SSH) model in the photonic context was achieved using photorefractive waveguides.174 Meanwhile, photonic topological surface-state arcs connecting topologically distinct bulk states were observed in metamaterials.152 Femtosecond-laser-direct-written waveguides represent a significant class of topological systems for light manipulation, providing several advantages for precision material machining. These advantages include the flexibility to fabricate 3D waveguides, the ability to achieve ultra-compact and large-scale integration of micro- and nanostructures on a chip, in situ rapid fabrication capabilities, and a wide range of adjustable processing parameters that can be customized to meet specific fabrication needs.

A famous example is the photonic TIs implemented in 2013 by Rechtsman et al., through Floquet engineering, which enables one-way transmission of light in 2D systems.161 Their design featured a pattern of helical waveguides arranged in a graphene-like honeycomb lattice, disrupting time-reversal symmetry, as depicted in Fig. 16(a). The topologically nontrivial states can be induced via “z-periodic” driving rather than via magnetic or spin-orbit effects. Thus, a topologically protected chiral edge state can be observed by tuning the helicity radius, as shown in Fig. 16(b). This approach has demonstrated the capability of Floquet engineering to convert a traditional system into a topological one, unveiling distinct topological features that are absent in static systems. More importantly, this review opens the door to the study of photonic TIs in femtosecond-laser-written waveguides. For instance, a 3D photonic TI with protected topological surface states was first demonstrated in femtosecond-laser-written waveguides by Lustig et al.175 Using femtosecond laser direct writing technique, they designed and established helical waveguides with a specific effective index of refraction, as shown in Fig. 16(c). Using this approach, they introduced an additional modal dimension, transforming a 2D photonic system into a 3D topological system. This innovation enabled them to successfully demonstrate a 3D photonic TI that supports topologically protected edge states propagating along 3D trajectories, facilitated by a dislocation. This achievement marks the first realization of a Floquet 3D TI and paves the way for exploring higher-dimensional topological phases in both theoretical and experimental contexts. Figure 16(d) shows the experimental observation of the evolution of edge-wave packets in the 3D synthetic-space TI.175 In 2022, Biesenthal et al. experimentally demonstrated fractal TIs in photonic femtosecond-laser-written waveguides.176 By fabricating periodically driven photonic lattices with Sierpinski geometry [see Fig. 16(e)], they observed robust light transport along both the outer and inner edges of the fractal landscape [see Fig. 16(f)]. Importantly, their work challenges the conventional theoretical framework of bulk-boundary correspondence by demonstrating the existence of chiral topological edge states in the absence of bulk insulating states. In 2023, Li et al. achieved the first experimental realization of fractal photonic anomalous Floquet TIs based on a dual Sierpinski carpet using the femtosecond laser direct writing technique.178 They observed high-visibility (over 90%) quantum interference of multiple single-photon chiral edge states that dynamically transport along various boundaries of the fractal lattice. The femtosecond-laser-written fractal photonic anomalous Floquet TIs, utilizing fewer waveguides, not only support a greater number of chiral edge modes but also enable the perfect hopping of topological quantum states. These results suggest a promising new avenue for manipulating the topological transport of light using engineered structures. Furthermore, the exploration of higher-order topological systems, characterized by non-trivial bulk polarization, is an emerging research direction. To date, photonic higher-order topological insulators (HOTIs) have been realized in a series of femtosecond-laser-written lattices.168^,177^,179^–185 For example, Noh et al. experimentally demonstrated the existence of photonic HOTIs in a ${\mathrm{C}}_{6\mathrm{v}}$ symmetric hexagonal lattice using the femtosecond laser direct writing technique.179 This review enabled the observation of 0-dimensional corner-localized mid-gap states that are topologically protected by chiral symmetry. In addition, Cerjan et al. revealed that topologically protected corner states can exist within the topological bands themselves rather than solely in the gaps between them.177 They experimentally confirmed the presence of higher-order topological bound states in the continuum (HOTBICs) in a nontrivial 2D SSH lattice formed by femtosecond-laser-written waveguides, as illustrated in Fig. 16(g). Unlike traditional HOTIs in 2D systems, where corner states are confined within the band gap, HOTBICs can support unconventional corner states that remain isolated from the surrounding bulk states, even in the absence of a band gap. By employing an auxiliary waveguide to excite zero-energy states that spatially overlap within the array, they demonstrated the remarkable localized properties of HOTBICs [Fig. 16(h)]. These topological corner modes pave the way for exciting applications in energy harvesting and lasing.

Recent advancements in the theory of non-Hermitian systems, particularly regarding exceptional point singularities, have significantly transformed our understanding of photonics. Non-Hermitian systems that exhibit parity-time (PT) symmetry challenge the conventional view that real eigenvalues are exclusively linked to Hermitian observables, generating considerable interest in this field.186^–189 Typically, non-Hermitian systems display complex eigenvalues due to their energy exchange with the environment. However, in a PT-symmetric system, real eigenvalues can arise in the presence of gain and loss, provided the condition [PT, H] = 0 is met. Notably, the transition of eigenvalues from real to complex indicates a PT symmetry phase transition, which is invariably associated with the emergence of exceptional points. These developments in non-Hermitian physics not only facilitate the manipulation of gain and loss in electromagnetic waves using imaginary potentials but also encourage us to rethink established frameworks by integrating gain and loss as new degrees of freedom. In general, a PT-symmetric non-Hermitian system is characterized by the presence of both gain and loss, which is referred to as an active PT-symmetric system. However, it has been observed that by introducing global loss, the gain component of the active PT-symmetric system can be offset, resulting in a passive PT-symmetric system that features only loss. Unlike the active PT-symmetric system, the passive PT-symmetric system merely alters the reference level of gain and loss without changing the relative relationship between gain and loss among the waveguides. Consequently, this has no significant impact on the underlying physical phenomena. By contrast, passive non-Hermitian systems are widely utilized in experiments because they simplify the experimental setup by requiring only the implementation of loss, thereby reducing overall complexity. Until now, non-Hermitian phenomena have been achieved in many optical platforms.190^,191 Notably, femtosecond-laser-written waveguides have become one of excellent platforms for exploring non-Hermitian phenomena,191^–199 because they can easily introduce tailed loss through the implementation of “wiggling” waveguides, “intermittent” waveguides, and artificial scatterers.

In 2013, Eichelkraut et al. experimentally demonstrated the first passive PT-symmetric system in 1D femtosecond-laser-written waveguides,192 as illustrated in Fig. 17(a). To introduce additional and tailored losses in every second waveguide, they spatially modulated the waveguides in a sinusoidal pattern, with a transverse amplitude of A = 3 mm. This induced curvature facilitated radiation and, consequently, enhanced losses. Through this approach, they observed the coexistence of ballistic and diffusive transport in a static, ordered system driven by non-Hermiticity. Importantly, their findings showed that the critical distance is determined solely by the level of dissipation, rather than the coupling between the waveguides. This research paves the way for utilizing femtosecond-laser-written waveguides to explore non-Hermitian physics. Meanwhile, Kremer et al. experimentally demonstrated a 2D PT-symmetric system using femtosecond-laser-written waveguides with designed refractive index landscape and alternating loss.191 They developed a novel technique to introduce losses by incorporating artificial scatterers into the waveguides, which caused tailed losses during fabrication. Through this approach, they successfully established a 2D PT-symmetric graphene lattice, as illustrated in Fig. 17(b). Their findings revealed that the 2D non-Hermitian topological phase transition coincides with the emergence of mid-gap edge states. Moreover, Kang et al. experimentally demonstrated a scheme for tuning the localization of HOTBICs through non-Hermiticity.195 Utilizing the femtosecond laser direct writing technique, they fabricated a 2D non-Hermitian SSH lattice by designing “intermittent” waveguides to introduce tailored loss. This approach allowed them to systematically explore the interplay between PT symmetry and higher-order corner states, providing insights into the physical mechanisms that mitigate finite-size effects. The strong 3D processing capabilities of the femtosecond laser direct writing technique have enabled researchers to apply Floquet engineering to non-Hermitian phenomena, resulting in a series of novel physical effects. In 2024, Liu et al. designed and employed periodic spatial modulation of loss in femtosecond-laser-written waveguides to achieve Floquet PT-symmetry in integrated photonics,196 as shown in Fig. 17(c). By carefully tuning the Floquet period, they demonstrated PT-symmetry phase transitions and achieved precise control over the system’s response through excitation ports, allowing for real-time switching between suppression and amplification regimes. Concurrently, Fritzsche et al. experimentally developed a periodically driven Floquet model that dynamically distributed non-Hermitian components across both spatial and temporal dimensions,197 as shown in Fig. 17(d). This model exhibited a non-Hermitian TI with a purely real spectrum. Another recent groundbreaking achievement is the realization of the non-Hermitian skin effect in waveguide systems. In 2024, Sun et al. theoretically designed and experimentally demonstrated that structured loss can induce the non-Hermitian skin effect in a periodically driven system.198 By introducing staggered loss into a 1D optical array of helical waveguides [see Fig. 17(e)], they observed the non-Hermitian skin effect in femtosecond-laser-written photonic waveguides, as illustrated in Fig. 17(f). The complex spectrum of the non-Hermitian system reveals that gapless unidirectional edge states, which span the topological band gap, can acquire a nontrivial point-gap winding topology. This indicates the presence of the non-Hermitian skin effect, driven by the nonreciprocal flow of these edge states. This review paves the way for further exploration of the non-Hermitian skin effect in photonic waveguide systems.

Quantum photonics is a rapidly developing field that merges fundamental science with technology, where quantum effects are central to its principles and applications.200^–204 Quantum photonics explores the interactions between quantized light and matter, emphasizing the manipulation and active control of these interactions at the quantum level. Among various optical artificial platforms, femtosecond-laser-written photonic waveguides stand out for their true 3D processing capabilities and high-precision fabrication mechanisms. To date, a series of quantum phenomena have been successfully demonstrated in femtosecond-laser-written waveguides.205^–218 For instance, Klauck et al. experimentally demonstrated two-particle quantum interference in a passive PT-symmetric system.205 They utilized the femtosecond laser direct writing technique on fused-silica glass to establish a passive PT-symmetric system comprising two waveguides, as illustrated in Fig. 18(a). The system incorporated loss through a slight sinusoidal modulation of the left waveguide, which introduced additional tunable bending losses. By launching pairs of indistinguishable photons with a wavelength of $\lambda =815\mathrm{nm}$ into the samples, they observed a counterintuitive shift in the position of the Hong–Ou–Mandel dip within the integrated lossy waveguide structures, moving it to shorter propagation distances. Jiang et al. experimentally demonstrated dynamic localization for quantum-correlated biphotons, addressing both generation and propagation aspects.206 Utilizing the femtosecond laser direct writing technique, they fabricated a photonic system containing three waveguides with varying modulation periods and amplitudes, as illustrated in Fig. 18(b). They recorded biphoton coincidence count rates, providing evidence of robust biphoton generation. By analyzing the quantum correlations of biphotons at the output of the waveguide array, they revealed dynamic localization features in both spatial and temporal domains. These findings indicate that the dynamic modulation of the waveguides indirectly influences the generation of quantum states by localizing the pump light while directly regulating the evolution of correlated photon pairs. This review paves the way for exploring complex physical processes using photonic femtosecond-laser-written waveguides. Moreover, Xu et al. conducted an experimental investigation of quantum transport in fractal networks using continuous-time quantum walks in fractal photonic lattices,207 as shown in Fig. 18(c). They employed the femtosecond laser direct writing technique to create three types of fractal lattices, allowing them to study the interplay between quantum transport and the geometric or fractal characteristics of these networks. This research not only enables the quantitative verification of physical laws but also provides a detailed understanding of transport dynamics, thereby paving the way for deeper insights into more complex quantum phenomena influenced by fractality. Meanwhile, Neef et al. experimentally demonstrated non-Abelian quantum holonomy in both 2D and 3D femtosecond-laser-written photonic waveguides,208 as shown in Fig. 18(d). They designed the waveguide arrangement to form a star-graph configuration, which features a central mode along with radial modes. By utilizing either one or two indistinguishable photons as input states, they harnessed a unique degree of freedom inherent to bosonic systems. This review paves the way for the development of quantum optical analogs that can illuminate aspects of quantum chromodynamics.

Regarding key characteristics as a clue, Table 5 demonstrates a summary of typical photonic applications of femtosecond-laser-written waveguide arrays, where readers can easily get recent advances and obtain more details not mentioned above.

In this review article, recent advances in femtosecond-laser-written 3D periodic photonic structures (i.e., 3D NPCs and 3D waveguide arrays) in transparent materials have been summarized, including fundamentals, properties, and applications. First, this paper provides a brief introduction to NPCs, optical waveguides, and waveguide arrays, involving basic concepts, great significance, common processing methods, and fabrication challenges in 3D space. The femtosecond laser direct writing technique, as a true 3D processing method, is identified as the preferred approach for fabricating 3D NPCs and 3D waveguide arrays. The characteristics and advantages of the femtosecond laser direct writing technique, especially in the fabrication of 3D periodic photonic structures, have also been introduced. Second, we offer a concise overview of the optical nonlinearity modulation and refractive index changes induced by femtosecond lasers in transparent materials, which serve as the foundation for constructing 3D NPCs and 3D waveguide arrays. Third, we review the latest advancements in 3D NPCs, focusing on their applications in nonlinear frequency conversion, nonlinear beam shaping, and nonlinear holography. Finally, the advances of 3D waveguide arrays in the fields of topological photonics, non-Hermitian photonics, and quantum photonics have been discussed.

Due to the remarkable advantages of the femtosecond laser direct writing technique in fabricating 3D NPCs and 3D waveguide arrays, a great number of significant achievements have been made in the past decade, as briefly introduced in this review paper, for example, the fabrication of nanoscale-resolution 3D NPCs in ${\mathrm{LiNbO}}_3$, the DUV 177.3 nm laser generation with output power over 30 mW in APP quartz crystals, and simultaneous 2nd and 5th harmonic generation of 1030 nm in APP quartz crystals. However, several challenges and difficulties remain. For instance, in ferroelectric crystals, inducing domain inversion with dimensions exceeding millimeter scales poses significant challenges, which hinder the fabrication of large-scale, high-efficiency frequency converters for industrial applications. In addition, when employing femtosecond-laser-written 3D NPCs for nonlinear frequency conversion, issues such as high absorption losses and high scattering losses have yet to be adequately addressed, resulting in relatively low conversion efficiency. Furthermore, due to the extreme complexity of light-matter interactions, the effects of various femtosecond laser processing parameters (e.g., central wavelength, repetition rate, and pulse energy) on optical nonlinearity modulation and refractive index changes have not been thoroughly investigated.

Based on the analysis above and recent advancements in light-matter interactions, several potential research directions are proposed as follows. First, a combination of beam shaping techniques (i.e., light manipulation techniques) with femtosecond laser direct writing could be explored. For instance, using Bessel beam shaping in conjunction with femtosecond laser direct writing (i.e., replacing traditional femtosecond Gaussian beam with femtosecond Bessel beam) may provide an effective solution for inducing domain inversion in ferroelectric crystals at millimeter scales. Second, an investigation into the physical mechanisms underlying the interactions between femtosecond lasers and nonlinear crystals is recommended. For example, the formation mechanism of domain wall during domain inversion, if this mechanism is revealed, the absorption losses and scattering losses in nonlinear frequency conversion may be decreased. Third, developing a model that illustrates the effects of various femtosecond laser processing parameters on optical nonlinearity modulation and changes in refractive index is essential. With this physical model, one can rapidly fabricate desired photonic structures and achieve specific functions. Fourth, the direct writing of lithium niobate on insulator (LNOI) or lithium tantalate on insulator (LTOI) using femtosecond lasers should be explored. For example, constructing frequency converters on thin films (e.g., LNOI and LTOI) with femtosecond-laser-induced periodic domain structures could significantly enhance the performance and integration of these devices. Fifth, it is important to study novel physical phenomena and laws by combining femtosecond-laser-induced type-I modification with type-II modification. For example, in 3D waveguide arrays constructed by numerous type-I modification areas, introducing a type-II modification region can disrupt the coupling between neighboring waveguides, providing a promising platform for investigating symmetry-related problems in topological photonics.

In summary, significant progress has been made in the femtosecond laser direct writing of 3D periodic photonic structures. This review article provides an overview of recent advancements in this field (e.g., high-efficient DUV laser generation at 177.3 and 167.8 nm with milliwatt power in APP quartz crystals based on second-harmonic mechanism, as well as successful applications of nanoscale-resolution 3D ${\mathrm{LiNbO}}_3$ NPCs in SPDC process and large field-of-view nonlinear holography), analyzes current challenges (e.g., relatively low conversion efficiency), and proposes several potential avenues for future research (e.g., formation mechanism of domain wall, and laser direct writing technique based on femtosecond Bessel beam). With the rapid development of femtosecond laser direct writing techniques and an intensified investigation into light-matter interactions, we can anticipate the emergence of more efficient photonic devices and intriguing physical phenomena in the near future.

Bin Zhang is currently a research associate at the School of Physics, Shandong University. He received his PhD from Shandong University, Jinan, China, in 2021. From 2021 to 2023, he was a post-doctor at the State Key Laboratory of Crystal Materials, Shandong University. His current research interests include femtosecond laser micro-/nanofabrication, optical waveguides, nonlinear photonic crystals, and nonlinear frequency conversion.

Wenchao Yan received his PhD from Nankai University, Tianjin, China, in 2022. He is currently a post-doctor at the School of Physics, Shandong University. His current research interests include topological photonics, nonlinear photonics, and non-Hermitian photonics.

Feng Chen is currently a professor at the School of Physics, Shandong University. From 2003 to 2005, he was at the Clausthal University of Technology, Germany, as an Alexander von Humboldt Research Fellow. His research interests include material modifications by ultrafast laser writing, ion beam modification of materials, waveguide devices, plasmonics, nonlinear optics, and topological photonics. He is a fellow of the Institute of Physics (IOP), Optica (formerly OSA), and SPIE. He also serves as the Executive Editor-in-Chief of Chinese Optics Letters.