Fig. 1. Development roadmap of nonlinear chiroptical effects. (a) Optical nonlinear effect was first discovered by Franken in 1961^[8]; (b) in 1965, Bloembergen published the Nonlinear Optics to establish the relevant theoretical framework^[9]; (c) Shen Yuanrang systematically explained nonlinear optics principles in The Principles of Nonlinear Optics in 1984^[10]; (d) Berger established nonlinear photonic crystal theory at the end of the 20th century^[11]; (e) in the early 21st century, Zharov introduced nonlinear optics into metamaterals for the first time^[12]; (f) research on the second-order nonlinear characteristics of L-shaped gold nanoparticles array is the pioneering work of nonlinear metasurface^[13]; (g) symmetry selection rule reveals the macro-control mechanism of the nonlinear effect of metasurface structure^[14]; (h) guided mode resonance mechanism was used to enhance the chiral THG^[15]; (i) enhancement and modulation of chiral SHG based on Mie resonance nanoparticles^[16]; (j) Mie-resonant nanohelices significantly amplified THG signals^[17]; (k) BIC nonlinear metasurface enhanced the chiral THG^[18]; (l) BIC metasurfaces achieved maximal chiral THG^[19]; (m) by chiral and achiral unitcell coupling, the DFG is used to generate terahertz waves^[20]; (n) based on the symmetry-breaking tetrameric metasurface structure of silicon nanodiscs, efficient chiral HHG was achieved^[21]; (o) up-conversion of linearly polarized or arbitrarily polarized pump light into circularly polarized nonlinear signals based on rotationally symmetric double-layer metasurfaces^[22]

Fig. 2. Schematic diagrams of polarization response and frequency conversion of nonlinear effects. (a) SHG is the interaction of two photons of the same frequency ω0 to generate a new photon with double frequency 2ω0^[8], and THG is the incident process of light field of frequency to generate light field of frequency 3ω0^[27]; (b) coupling of two beams (ω1,ω2) with different frequencies can generate ω1+ω2 (SFG) ^[23] or ω1-ω2 (DFG) ^[24]; (c) HHG is caused by the interaction between a high-intensity laser pulse and a medium, which produces light with a frequency that is an integral multiple of the frequency of the incident laser nω0^[30]; (d) in the SPDC process, the pump light ωp with frequency is incident, and the photon pair (ωs,ωi) with frequency and is generated^[26]; (e) FWM refers to the frequency mixing of four photons of different frequencies in a medium, where the incident light frequencies ω1、ω2、ω3 are combined ω4^[28]; (f) interaction of incident light with a frequency ω of with a nonlinear medium generates a direct current or a low-frequency polarization field through a second-order nonlinear process, which is known as optical rectification effect^[25]; (g) incident light with a frequency of ω induces a third-order nonlinear process in the medium, resulting in a change in refractive index of Δn∝|E(ω)|2, frequency of the output polarization field remains the same as ω, and this phenomenon is called optical Kerr effect^[29]

Fig. 3. Chiral SHG. (a) Chiral Ge nanospiral array and SHG-CD^[83]; (b) spin-unlocked SHG vortex light based on nonlinear chiral metasurfaces^[85]; (c) achiral dielectric nanoparticles enable chiral SHG^[86]; (d) C₃ symmetric chiral metasurface and SHG intensity curves^[22]; (e) chiral nano-kirigami metasurface and SHG-CD spectrum^[87]; (f) relationship between evolution of nonlinear polarizability singularities and nonlinear emission directions in torsional double-layer metasurfaces^[93]

Fig. 4. Chiral THG. (a) Chiral nonlinear metasurface to realize four-channel THG holographic image^[94]; (b) nonlinear geometric phase modulation for a nanopillar with off-centered hole and C₁ symmetry^[96]; (c) quasi-BIC mode of chiral silicon metasurfaces achieves high THG conversion efficiency and near-perfect nonlinear CD^[18]; (d) THG output power of chiral metasurfaces and corresponding nonlinear THG-CD^[100]; (e) chiral response of the third harmonic Rayleigh scattering of silver nanohelix^[101]; (f) hBN metasurface supporting quasi-BIC mode to achieve strong THG conversion efficiency and high nonlinear CD ^[103]

Fig. 5. Chiral SFG, DFG, HHG, and other nonlinear chioptical effects. (a) Chiral and achiral structure coupling realize DFG to generate THz vortex beam^[20]; (b) SFG-CD signal was significantly enhanced by the chiral gold nanohook structure^[108]; (c) an inclined double-elliptic half-disk metasurface with half-integer topological charges and its FHG-CD response^[99]; (d) significant HHG-CD response of nano-topological insulators^[109]; (e) chiral metamaterals of varactor diodes with strong chiral four-wave mixing^[110]; (f) terahertz radiation induced by optical rectification effect in silver-based chiral metamaterials and its relationship with pump power^[111]; (g) dielectric chiral lithium niobate dimer metasurface supporting quasi-BIC to realize second-order nonlinear processes such as SPDC^[89]; (h) nonlinear chiral metasurfaces based on GMR and the variation of polarization angle and ellipticity of transmitted light with incident power^[112]