Fig. 1. (a) Side view (left) and top view (right) of MoS₂ atomic structure. The highlighted armchair direction and zigzag direction correspond to the top view. (b) Mechanical exfoliated MoS₂ with different layers^[16]. (c) 2H phase MoS₂ layers show diminishing the oscillation in SHG signal^[16]. (d) Optical image of artificial folded MoS₂(left) and its corresponding SHG image(right)^[31]. (e) Crystal structure of 3R phase MoS₂ and corresponding SH dipole^[32]. (f) 3R phase MoS₂ layers show quadratic enhanced SHG with the increase of layers^[32].

Fig. 2. CVD grown TMDCs with highly efficient SHG: (a) Optical image (left) and zoom in AFM image (right) of spiral WS₂ flake^[39]; (b) layer dependent SHG of spiral WS₂ flake^[39]; (c) schematic illustration of pyramid-like WS₂ structure^[41]; (d) pyramid-like WS₂ displays high intensity of residual edge SHG signal^[41].

Fig. 3. Polarization properties of SHG in TMDCs: (a) SHG polarization in monolayer MoS₂ shows six fold rotation symmetry^[16]; (b) top view of MoS₂ crystallographic orientation, where x represents armchair direction, y represents zigzag direction and θ is the angle between input laser and armchair direction ^[16]; SHG polarization in (c) WS₂/MoS₂ laterally epitaxial heterostructure^[44] and (d) WSe₂/WS₂ AA, AB vertical heterostructure^[45], where the insets shows correspongding SHG mapping; (e) superposition of SHG polarization by artificial stacks of two different 2D materials^[46]; (f)−(h) demonstration of distinguishing of different grain boundary in monolayer MoS₂ thin film be SHG polarization^[47].

Fig. 4. Exciton resonance properties of SHG in TMDCs: (a) Schematic illustration of SHG when two incident photons are resonant with 2p state of A exciton^[50]; (b) excitation wavelength dependent SHG of monolayer WSe₂ at T = 4 K^[50]; (c) second order nonlinear susceptibility and absorption served as the function of pump laser energy in monolayer (blue) and trilayer (green) MoS₂^[16]; (d), (e) illustration of SHG enhancement in spiral WS₂ flake when the excitation energy slightly above bandgap by comparison of reflective spectrum with SHG spectrum^[51]; (f) SHG spectra (dotted traces) of monolayer alloys and corresponding room-temperature PL spectra (solid traces)^[52]; (g), (h) CVD grown monolayer MoS₂ flakes show edge enhanced SHG^[47].

Fig. 5. SHG valley selection rules: (a) Circular polarization-resolved SHG spectra showing the generation of counter-circular SHG in monolayer WSe₂^[59]; (b) interband valley optical selection rules for SHG in 2D TMDCs^[59].

Fig. 6. Electric field modulated SHG: (a) Schematic illustration of bilayer MoS₂ microcapacitor device^[67]; (b) bilayer MoS₂ SHG intensity as the function of applied voltage and SHG emission energy^[67]; (c) reversible SHG induced by back gate in bilayer WSe₂^[66]; (d) optical image of monolayer WSe₂ transistor^[59]; (e) exciton resonant monolayer WSe₂ SHG spectra at selected gate voltage^[59]; (f) monolayer WSe₂ SHG intensity as the function of applied gate voltage and SHG emission energy^[59].

Fig. 7. Strain modulated SHG: (a) MoSe₂ SHG polarization changed by uniaxial tensile strain^[26]; (b) uniaxial strain map of MoS₂ monolayer flake^[75]; (c) schematic illustration (up) and SHG mapping (down) of TiO₂/MoS₂ structure^[77].

Fig. 8. Metasurfaces modulated SHG: (a) Schematic illustration of a MoS₂-gold phased array antenna steering SHG emission^[81]; (b) polar plot of the calculated (line) and measured (points) SH pattern along the intensity maximum when phase delay δ_x = δ_y = 0^[81]; (c) the SEM image of the fabricated gold metasurface with rectangular nanoholes of different orientation^[82]; (d) the experimental results of SHG focusing by using the hybrid metasurfaces^[82]; (e) schematic representations of steering second-harmonic waves on RCP pumping with monolayer WS₂^[79]; (f) evolution of the light field for the case shown in (c), “0” and “1” label the intensity order^[79].

Fig. 9. SHG enhancement by plasmonics: (a) Nano cavity strongly confines incident light field (up), and SHG enhancement by Ag nanoparticle in monolayer WS₂ (down)^[92]; (b) compare of SHG signal in different plasmonic array/semiconductor, where points 1, 2, 3 represent the area of nanorod, nanorod/bilayer WSe₂, and bilayer WSe₂, respectively^[93]; (c) SHG enhancement factor over 400 in monolayer WS₂ reached by Ag nanogroove grating^[94]; (d) SHG enhancement over 3 orders in monolayer WSe₂ by plasmonic structure on PDMS^[95].

Fig. 10. SHG enhancement by micro cavity and photonic crystal: (a) Enhancement of SHG from monolayer MoS₂ in a doubly resonant on-chip optical cavity^[100]; (b) enhancement of SHG by silicon waveguide^[105]; (c) CW excitation of SHG from GaSe/photonic crystal^[106].