Fig. 1. Nonlinear processes and applications of optical crystals

Fig. 2. Phase mismatch. (a) Energy conservation in SHG; (b) momentum mismatch in SHG; (c) illustration of intensity variation of SHG during it propagates through an optical crystal

Fig. 3. Birefringent phase matching. (a) Refractive index of o- and e-wave as a function of wavelength; (b) birefringent phase matching incidence conditions; (c) momentum conservation in birefringent phase matching; (d) refractive index matching through birefringent effect

Fig. 4. Phase matching loss in birefringent phase matching^[63]. (a) Minimum phase matching wavelength and cut-off wavelength of different optical crystals; (b) phase matching loss of different optical crystals

Fig. 5. Quasi-phase matching. (a) Illustration of quasi-phase matching; (b) momentum conservation; (c) SHG intensity as a function of distance in birefringent phase matching, quasi-phase matching and phase mismatching

Fig. 6. Special quasi-phase matching. (a) Quasi-periodic optical superlattice for THG phase matching^[21]; (b) THG under 1570 nm excitation^[21]; (c) chirped periodic poled lithium niobate^[66]; (d) quasi-phase matching from SHG to 8^th harmonic generation^[66]; (e) illustration of the additional periodic phase (APP) matching^[67]; (f) effect of APP matching^[67]

Fig. 7. Two-dimensional optical crystals. (a) Crystal structure of NbOCl₂^[22]; (b) nonlinear coefficient of NbOCl₂ as a function of layer number^[22]; (c) 3R-MoS₂ for SHG^[23]; (d) thickness-dependent SHG enhancement^[23]; (e) rBN optical crystal^[24]; (f) conversion efficiency of different two-dimensional optical crystal materials^[24]

Fig. 8. Twist phase matching. (a) Schematic of twist phase matching^[27]; (b) illustration of the physical picture of the twist phase matching^[27]; (c) effect of twist phase matching^[27]; (d) multiwalled BNNTs with coherent stacking^[25]; (e) chiral SHG^[25]

Table 1. Features of different kinds of phase matching methods