Fig. 1. Second-harmonic intensity versus propagation distance in nonlinear crystal under conditions of perfect phase matching, quasi-phase matching,and non-phase matching

Fig. 2. Schematics of nonlinear photonic crystal and involved phase-matching^[8]. (a) 1D nonlinear photonic crystal and its phase-matching condition; (b) 2D nonlinear photonic crystal and its phase-matching condition; (c) 3D nonlinear photonic crystal and its phase-matching condition

Fig. 3. Formation of inverted domains in LiNbO₃ crystals by combining femtosecond laser processing with thermal treatment^[37]. (a) Femtosecond-laser induced filaments in sample; (b) inverted domains below filaments after thermal treatment; (c) Čerenkov second-harmonic generation micrograph of lower surface of inverted domain lattice; (d) 3D Čerenkov second-harmonic generation micrograph of inverted domain lattice

Fig. 4. Fabrications of 1D and 2D nonlinear photonic crystals in LiNbO₃ crystals by femtosecond laser domain inversion. 3D Čerenkov second-harmonic generation micrographs of square lattice inversion domain structure (a) at depth of 15 μm in surface layer and (b) at large depth inside crystal^[38]; (c) optical micrograph of inverted domain structure in waveguide^[47]; (d) 3D Čerenkov second-harmonic generation micrograph of inverted domain structure^[47]

Fig. 5. Fabrication of 3D nonlinear photonic crystals in CBN crystal by femtosecond laser domain inversion^[49]. (a) 3D inverted domain structure visualized by Čerenkov second-harmonic generation micrograph; (b) second-harmonic pattern obtained for hexagonal inverted domain structures fabricated in multidomain crystal; (c) second-harmonic pattern obtained for inverted domain structures fabricated in monodomain crystal

Fig. 6. 1D nonlinear photonic crystals fabricated inside LiNbO₃ by femtosecond laser. (a) Schematic of erasing nonlinear coefficients by femtosecond laser line scanning^[56]; (b) microscopy image of cross section of fabricated quasi-phase matching structure^[56]; (c) femtosecond laser direct writing waveguide and erasing nonlinear coefficients in waveguide^[57]; (d) quasi-phase matching structures with one period and four periods embedded in waveguides^[58]; (e) temperature tuning curves of waveguide embedded with four parallel quasi-phase matching structures^[58]

Fig. 7. 3D nonlinear photonic crystal fabricated by erasing nonlinear coefficients in LiNbO₃ crystals with femtosecond laser^[55]. (a) First two-layer structure and (b) partial three-layer structure of 3D nonlinear photonic crystal visualized by Čerenkov second-harmonic generation micrographs; (c) optical micrograph of top layer structure of 3D nonlinear photonic crystal; (d) schematic of second harmonic emission enabled by 3D quasi-phase matching

Fig. 8. Femtosecond laser fabrication of two-dimensional nonlinear photonic crystals for nonlinear structured light generation. (a) Second-harmonic images of HG₁₀, HG₁₁, HG₁₂ holographic patterns fabricated by femtosecond laser selective erasing ferroelectric domain^[59]; (b) beam profiles at first diffraction order in output from HG₁₀, HG₁₁, HG₁₂ structures^[59]; (c) integrating function of fork grating and axicon into nonlinear photonic crystal to generate second harmonic beam of perfect vortex light^[60]; (d) nonlinear micrographs and (e) intensity distribution of emitted second harmonic beam of fabricated structures with different topological charges^[60]

Fig. 9. Nonlinear beam shaping with 3D photonic crystals fabricated by femtosecond laser domain inversion^[61]. (a) Three-layer structure comprised of fork gratings with different orientations; (b) 3D three-layer fork structure visualized by Čerenkov second-harmonic generation micrograph; (c) far-field second-harmonic pattern emitted from three-layer fork structure; (d) three-layer structure comprised of fork, linear and circular gratings; (e) 3D three-layer structure comprised of different gratings visualized by Čerenkov second-harmonic generation micrograph; (f) far-field second-harmonic pattern emitted from three-layer structure comprised of different gratings

Fig. 10. High-efficient beam shaping with 3D nonlinear photonic crystals fabricated by femtosecond laser. (a) 3D nonlinear photonic crystal visualized by second-harmonic micrographs in x-z and x-y planes^[62]; (b) second-harmonic diffraction patterns at different input wavelengths and their corresponding quasi-phase matching configurations^[62]; (c) designed nonlinear volume holographic pattern^[63]; (d) fabricated nonlinear volume hologram in CBN crystal; (e) second harmonic vortex beam reconstructed from nonlinear volume hologram^[63]

Fig. 11. Detour phase coded holograms processed by femtosecond laser for nonlinear holographic imaging^[64]. (a) Fabricated whole detour phase coded hologram and four basic units visualized by second-harmonic micrographs; (b) experimentally measured second harmonic holographic image of letter in far field; (c) simulated second harmonic holographic image of letter in far field with improved quality obtained by increasing numbers of hologram pixels

Fig. 12. 3D nonlinear photonic crystals processed by femtosecond laser for quasi-phase-matching-division multiplexing holography^[66]. (a) Schematic of quasi-phase-matching-division multiplexing nonlinear holography; (b) detour phase encoding in LiNbO₃ realized by femtosecond laser erasing nonlinear coefficients; (c) far-field second harmonic imaging results of three-channel quasi-phase-matching-division multiplexing holography

Fig. 13. Femtosecond laser processing quasi-phase-matching structure in quartz crystal for deep-ultraviolet coherent output. (a) Experimental setup of deep-ultraviolet second harmonic generation^[71]; (b) second harmonic signals in quartz crystal with nonlinear structure and as-grown quartz crystal^[71]; (c) angle regulation of multilayer quasi-phase-matching structure in quartz^[72]; (d) tuning second harmonic generation wavelength and effective second-order nonlinear coefficient of crystal by varying phase-matching angle^[72]