Fig. 1. Simulated second harmonic (SH) distribution at different nonlinear interfaces^[45]. (a) Structure diagram of nonlinear medium; (b) bulk LN medium; (c) domain wall; (d) LN crystal surface

Fig. 2. SH distribution at different nonlinear interfaces^[45]. (a) C₁=C₂; (b) C₁=1, C₂=0; (c) C₁=1, C₂=10

Fig. 3. Experimental setup and angle measurement of SH radiation^[45]. (a) Experiment setup; (b) relationship between nonlinear Cherenkov radiation angle generated at the boundary of BBO crystal and the interface of BBO-LN crystal and incident angle of fundamental frequency light

Fig. 4. Intensity comparison of the second harmonic generated at two nonlinear interfaces^[45]. (a) BBO-LN interface; (b) single BBO crystal surface

Fig. 5. Spectra of fundamental frequency light and second harmonic wave generated at the boundary of BBO or LN crystal^[62]

Fig. 6. Intensity of second harmonic wave generated at the interface of BBO-LN and the boundary of BBO^[62]

Fig. 7. Three approaches to generate vortex beams^[104]. (a) Spiral phase plate; (b) hologram with spiral phase; (c) fork-shaped grating

Fig. 8. Generation and propagation of the Airy beam^[72]. (a) Phase diagram of Airy beam generated in one dimension; (b) Airy beam generated by the far field and variation of light beam with propagation distance

Fig. 9. Vector beams^[80]. (a) Experimental setup for generating vector beam; (b) vector beams with m=1 and φ₀=0, π/4, π/2, 3π/4, respectively; (c) vector beams with m=2,3,5 and φ₀=0

Fig. 10. Schematic of nonlinear harmonic wave manipulation in structured light field^[112]

Fig. 11. Generated second harmonic wave of fundamental frequency (FW) light with different phase structures^[117]. (a)(d) Phase structure of the FW; (b)(e) phase-matching geometries of the nonlinear Raman-Nath second harmonic generation under non-diffraction assumption of the FW; (c)(f) SH diffraction patterns in the far field; (g) FW light shape at exit surface of the crystal

Fig. 12. Nonlinear vortex beam array generation^[119]. (a) 1D; (b) 2D

Fig. 13. Dynamic nonlinear holographic generation^[121]. (a) Schematic of the experimental setup for realizing dynamic holography; (b) phase-matching diagram of the non-collinear second harmonic; (c) experimentally realized running horse

Fig. 14. Schematic of the experimental setup for realizing frequency conversion of vector light field by using cascaded nonlinear crystals^[122]

Fig. 15. Second harmonic focusing through a scattering medium via feedback-based wavefront shaping method^[66]

Fig. 16. Speckle patterns and spot focusing patterns^[129]. (a)(c) Speckle pattern of fundamental frequency light and second harmonic light before optimization; (b)(d) spot focusing pattern of fundamental frequency light and second harmonic light after optimization

Fig. 17. Polarization method of PPLNOI. (a) Schematic of the x-cut LNOI poling method; (b) x-cut periodic polarization LNOI^[135]; (c) schematic of the z-cut LNOI poling method; (d) z-cut periodic polarization LNOI^[137]

Fig. 18. Cascaded nonlinear process in LN microdisks^[142-143]. (a) Microscopy image; (b) scanning electron microscope (SEM) image; (c) simulated fundamental mode; (d) cascaded third harmonic generation; (e) cascaded four-wave mixing frequency effect

Fig. 19. Theoretical simulation of cyclic phase matching of TE mode in microcavities^[149]. (a) Schematic of phase matching; (b) relationship between effective refractive index and angle; (c) relationship between wave vector mismatch and angle; (d) relationship between effective nonlinear coefficient and angle; (e) relationship between second harmonic wave intensity and angle

Fig. 20. Structural design, mode electric field distribution, and nonlinear coefficient of the corresponding region of the ordinary and semi-nonlinear integrated optical waveguides^[150]

Fig. 21. Electro-optical polarization controller in PPLNOI ridge waveguide and its applications^[151-153]. (a) Cascading processing of electro-optical polarization coupling and second harmonic; (b) schematic of single-photon generation and polarization control; (c) coincidence count as a function of the applied voltage

Fig. 22. Broadband electro-optical frequency comb in LN microring cavity^[157]. (a) SEM image of LN microring cavity; (b) spectrum of broadband electro-optic optical frequency comb

Fig. 23. Experimental setup of frequency conversion and spectral compression of broadband single-photon-level weak coherent light^[173]

Fig. 24. Spectra and relative frequency of the positively chirped laser pulse and up-converted laser pulse^[173]. (a) Spectra; (b) relative frequency

Fig. 25. Experimental setup of nonlinear interaction between two broadband single-photon-level weak coherent light^[175]

Fig. 26. SFG efficiency and number of SFG photons^[175]

Fig. 27. Experimental setup of the single-photon frequency convertor^[177]

Fig. 28. Experimental setup of SPDC photon-pair preparation^[177]

Fig. 29. Two-photon interference patterns^[177]. (a) Before frequency conversion; (b) after frequency conversion

Fig. 30. Entanglement between two independent photons^[185]. (a) Entanglement-swapping-based DWDM quantum network; (b) SFG between two non-entangled photons

Fig. 31. SFG efficiency of non-entangled photons and fidelity of generated entangled states^[185]. (a) SFG efficiency of non-entangled photons; (b) fidelity of the corresponding entangled states