Fig. 1. Nonlinear resonant metasurfaces for second- and third-harmonic generation. (a) Scanning electron microscope (SEM) micrograph of BaTiO3 nonlinear metasurface that operates in the near-UV spectral range. Inset: atomic force microscopy (AFM) height profile along the red dashed line [44]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. (b) Schematic illustration of ZnO-based nonlinear metalens focusing self-generated vacuum-UV second harmonic. Inset: SEM image of the fabricated metalens. Adapted from Ref. [80]. Licensed under CC BY-NC 4.0. (c) Schematic of crystalline transition-metal-dichalcogenide truncated cone metasurface that enables single-beam second- and third-harmonic generation. The bottom-right inset shows the SEM image of the fabricated MoS2 metasurface. Reprinted with permission from Macmillan Publishers Ltd. [49]. Copyright 2021. Licensed under CC BY. (d) Artistic representation of the dielectric metasurface with THG at frequency 3ω generated via cascaded SHG and sum-frequency generation process: 3ω=ω+2ω. Reprinted with permission from Ref.  [81]. Copyright 2022 American Chemical Society. (e) Design of Si metasurface on a gold mirror that enables BIC resonance for THG enhancement. The inset shows the cross section of the unit cell with corresponding materials. Reprinted with permission from Ref. [29]. Copyright 2022 American Chemical Society. (f) SEM image of a three-layer GaAs-based nonlinear metasurface for second-harmonic generation (SHG). Adapted from Ref. [82]. Licensed under CC BY 4.0.

Fig. 2. Asymmetric generation of third-harmonic images with nonlinear nonreciprocal metasurfaces. (a) Directional formation of images achieved at the third-harmonic-generation frequency by using nonlinear anisotropic dielectric metasurfaces with asymmetric geometry and strong magneto-optical coupling [110]. The unit cell is composed of subwavelength nanoresonators based on silicon nitride and amorphous silicon. (b) Experimental realization of the bilayer metasurface: scanning electron microscopy image of the sample, before its embedding into the homogeneous environment. (c) Experimental results. Nonlinear optical response detected in transmission at the third-harmonic frequency for forward and backward excitation at a wavelength of 1475 nm. Each experimental image is assigned its own individual minimum and maximum levels of camera counts. Adapted from Ref. [103]. Copyright 2022 Springer Nature Ltd.

Fig. 3. Examples of enhanced nonlinear chiral response of metasurfaces. (a), (b) Optical chiral quasi-BIC metasurface composed of arrays of meta-atoms resonantly transmitting RCP light but transforming it to LCP light. (c) Experimentally measured THG intensities for chiral metasurface, compared to Si thin film. Inset shows a photographic image of the light spot of THG. Adapted from Ref. [116]. Licensed under CC BY 4.0. (d) Measured third-harmonic chiral dicroism spectrum in nonlinear dielectric metasurface that supports multiple quasi-BIC resonances. Dashed lines are guide for eyes. The resonant wavelengths are marked with solid vertical lines [118].

Fig. 4. Observation of self-action effects and high-harmonic generation with resonant silicon metasurfaces. (a) Scheme of the ultrafast self-action effects in the metasurface supporting quasi-BIC resonances. (b) Experimentally measured dependence of THG spectra on pump power; each spectrum is normalized to the third power of its pump intensity. Right: measured (dots) and simulated (solid lines) evolution of the spectral position (blue) of the THG peak and its linewidth (red) with an increase of the pump power density. Inset shows an SEM image of the resonant metasurface. Adapted with permission from Ref. [121]. Copyright 2021 American Chemical Society. (c) Spectrum of high harmonics generated by 100 fs laser pulses. The pale blue area is the spectral range not covered for a particular spectrometer. Right: power dependence of the generated fifth to eleventh harmonics for 100 fs pump pulses. Adapted with permission from Ref. [122]. Copyright 2022 American Chemical Society.

Fig. 5. (a) Artist’s representation of SPDC from a LiNbO3 metasurface: the pump ωP is incident from the substrate side; photon pairs ωs and ωi are collected in reflection. (b) Spectrum of production of photon pairs enhanced by Mie resonance in LiNbO3 metasurface shown by red diamonds, referenced to unpatterned film of the same thickness shown by gray stars. Reprinted with permission from Ref. [141]. Copyright 2021 American Chemical Society. (c) Schematic illustration of multiplexed entangled photon generation in a multi-resonance semiconductor metasurface. Inset shows SEM image of GaAs metasurface that supports BIC resonance before metasurface was transferred on the transparent substrate. (d) Measured SPDC spectra of non-degenerate photon pairs in GaAs metasurface where the signal photon is emitted at the electric dipole BIC mode wavelength (purple vertical solid line). (e) Measured SPDC spectra of GaAs metasurface when two types of non-degenerate photon pairs are produced: signal photons are emitted at wavelengths of electric dipole BIC resonance (orange solid vertical line) and the magnetic dipole BIC resonance (green vertical solid line) [142].

Table 1. Even-Order Nonlinear Processes in All-Dielectric Metasurfaces^a

Table 2. Odd-Order Nonlinear Processes in All-Dielectric Metasurfaces^a