Fig. 1. Comparison of second-harmonic build-up ($P_{2\omega }$) under the same propagation length ($z/l_c$) in domain-modification-based (i.e., $v=0.5$ or 0.75) NPCs, domain-erasure-based (i.e., $v=0$) NPCs, and domain-inversion-based (i.e., $v=-1$) NPCs. The cases for perfect PM and phase mismatching (i.e., $v=1$) are also drawn in this picture. Reproduced with permission from Ref. 114.

Fig. 2. Domain-modification-based quasi-3D NPCs in ${\mathrm{LiNbO}}_3$ crystals. (a) The setup for fabricating quasi-3D NPCs. (b) The fabrication routine of quasi-3D NPCs. (c) The end-face microscopic image of quasi-3D NPCs. Reproduced with permission from Ref. 112.

Fig. 3. Truly 3D NPCs written by femtosecond laser in ${\mathrm{LiNbO}}_3$ crystals. (a) The Čerenkov second-harmonic microscopic image of the first two layers in 3D NPCs. (b) The confocal second-harmonic microscopic image obtained from non-engineered (i.e., un-erased) and engineered (i.e., erased) areas. (c) The second-harmonic intensity distribution along the black line in panel (b). Reproduced with permission from Ref. 2.

Fig. 4. First domain-inversion-based truly 3D NPCs in ferroelectric BCT crystals. Panels (a) and (b) demonstrate the reciprocal lattice vectors of 2D NPCs and 3D NPCs, respectively. (c) The Čerenkov second-harmonic microscopic image of 3D NPCs. Reproduced with permission from Ref. 1.

Fig. 5. Femtosecond-laser-induced nanodomains in ${\mathrm{LiNbO}}_3$ crystals. (a) The 3D model of ruler-shaped nanodomains. Panels (b) and (c) show the PFM images on cross-sections of this ruler. (d) The PFM image of wide-angle nonlinear diffraction grating. The measured nonlinear Raman–Nath diffraction pattern is displayed in the inset. Reproduced with permission from Ref. 110.

Fig. 6. APP PM for nonlinear frequency conversion. (a) The schematic of birefringent PM in negative uniaxial crystals. (b) The schematic of quasi-PM in ferroelectric crystals. (c) The schematic of APP PM in arbitrary nonlinear optical crystals. (d) The amplitude of the second-harmonic field under PM, quasi-PM, APP PM, and phase mismatching. Reproduced with permission from Ref. 108.

Fig. 7. Femtosecond-laser-induced type-I and type-II modifications in ${\mathrm{LiNbO}}_3$ crystals. Panels (a) and (d) show refractive-index profiles of type-I modification and type-II modification, respectively. Panels (b) and (e) demonstrate refractive-index profiles at horizontal cross-sections in panels (a) and (d). Panels (c) and (f) are mode profiles at 633 nm, corresponding to modifications in panels (a) and (d), respectively. Reproduced with permission from Ref. 3.

Fig. 8. Schematic of typical 3D NPCs written by tightly focused femtosecond laser in nonlinear optical crystals.

Fig. 9. Femtosecond-laser-written NPCs in ${\mathrm{LiNbO}}_3$ crystals for photon pair generation. (a) The experimental setup for fabricating periodically-inverted domain structures in Ti-indiffused ${\mathrm{LiNbO}}_3$ waveguides. (b) Optical microscopic image of 2D periodically inverted domain structures. The small circles represent inverted domains. (c) The 3D profile of periodically inverted domain structures acquired by Čerenkov second-harmonic microscopy. Reproduced with permission from Ref. 125.

Fig. 10. The 2nd to 5th harmonic generation of 1030 nm in femtosecond-laser-written quartz NPCs. (a) The optical microscopic image of laser-written quartz NPCs. (b) The period length distribution of quartz NPCs. (c) The experimental setup for generating the 2nd to 5th harmonic generation of 1030 nm. (d) The photograph of the 2nd to 4th harmonic generation. Reproduced with permission from Ref. 127.

Fig. 11. Second harmonic Hermite-Gaussian beam generation in femtosecond-laser-written 3D ${\mathrm{LiNbO}}_3$ NPCs. (a) The model and confocal second harmonic image of 3D ${\mathrm{LiNbO}}_3$ NPCs. (b) The second harmonic diffraction patterns pumped at 818 nm. (c) The dependence of the 1st-diffraction-order output power on fundamental wavelength. (d) The dependence of output power of second harmonic Hermite-Gaussian beam on fundamental power at 818 nm. Reproduced with permission from Ref. 111.

Fig. 12. Femtosecond-laser-written two-sequential 3D NPCs in ${\mathrm{LiNbO}}_3$ crystals for simultaneously reconstructing multiple second harmonic structured beams. (a) The schematic of quasi-PM mechanism for reconstructing multiple second harmonic structured beams at a single wavelength. (b) The schematic of two-sequential 3D NPCs for simultaneously reconstructing second harmonic structured beams composed of vortex beams and hexagonal diffracted beams. (c) Second harmonic structured beams emitted from the 3D NPCs, which are pumped with 834 nm. Reproduced with permission from Ref. 98.

Fig. 13. Nonlinear detour phase holography in femtosecond-laser-written SBN NPCs. (a) The schematic of the experimental setup for nonlinear holographic imaging. (b) The measured H-shaped far-field SHG holographic image. (c) The simulated SHG intensity distribution in the far-field. (d) The simulated result improved with a phase plate. Reproduced with permission from Ref. 89.

Fig. 14. Large field-of-view nonlinear holography in femtosecond-laser-written ${\mathrm{LiNbO}}_3$ NPCs. (a) 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. (b) The large-area hexagonal array is formed by combining the central, first, and higher orders of second harmonic fields. Reproduced with permission from Ref. 100.

Fig. 15. Schematic of typical 3D waveguide arrays written by tightly focused femtosecond laser in transparent materials.

Fig. 16. Topological photonics in femtosecond-laser-written waveguides. (a) Floquet TIs in a honeycomb lattice consist of helical waveguides. (b) Experimental observation of topological chiral edge states. (a), (b) Reproduced with permission from Ref. 161. (c) 3D Floquet TIs with photonic waveguides. (d) Experimental observation of the evolution of edge-wave packets in the 3D synthetic-space TI. (c), (d) Reproduced with permission from Ref. 175. (e) Fractal TIs in a fourth-generation Sierpinski lattice. (f) Experimental observation of topological edge transport in the Sierpinski lattice. (e), (f) Reproduced with permission from Ref. 176. (g) HOTIs in 2D SSH lattice. (h) Experimental observation of topological corner states. (g), (h) Reproduced with permission from Ref. 177.

Fig. 17. Non-Hermitian photonics in femtosecond-laser-written waveguides. (a) Passive PT-symmetric system in 1D femtosecond-laser-written waveguides. (a) Reproduced with permission from Ref. 192. (b) 2D PT-symmetric graphene lattice. (b) Reproduced with permission from Ref. 191. (c) Floquet PT-symmetry in photonic waveguides. (c) Reproduced with permission from Ref. 196. (d) PT-symmetric photonic Floquet TI. (d) Reproduced with permission from Ref. 197. (e) Schematic of Floquet non-Hermitian skin effect in a 1D optical array. (f) Experimental results of the non-Hermitian skin effect. (e), (f) Reproduced with permission from Ref. 198.

Fig. 18. Quantum photonics in femtosecond-laser-written waveguides. (a) PT-symmetric quantum interference in a coupled two-waveguide system. (a) Reproduced with permission from Ref. 205. (b) Dynamically localized quantum optical states in photonic lattice contain three waveguides. (b) Reproduced with permission from Ref. 206. (c) Quantum transport in the fractal lattice. (c) Reproduced with permission from Ref. 207. (d) 3D non-Abelian quantum holonomy. (d) Reproduced with permission from Ref. 208.

Table 1. Comparison of similarities and differences among three domain-modulation scenarios.

Table 2. Summary of the latest results for nonlinear frequency conversion in femtosecond-laser-written NPCs.

Table 3. Summary of the latest results for nonlinear beam shaping in femtosecond-laser-written NPCs.

Table 4. Summary of the latest results for nonlinear holography in femtosecond-laser-written NPCs.

Table 5. Summary of typical photonic applications of femtosecond-laser-written waveguide arrays.