**5. Concluding Remarks**

In this review paper, an overview of various nonlinear optical processes studied in sub-wavelength periodic dielectric structures is presented. Dielectric structures are particularly attractive for nonlinear optical studies due to the ability to engineer field concentration to be located inside or outside the structure by design, high damage thresholds and ease of fabrication of complex structures. In particular, high refractive index dielectric structures are preferred for realizing such structures due to the high-quality factor of the resonances and the associated enhanced field strength. Resonant field enhancement mechanisms in such sub-wavelength structures are broadly classified here as guided-mode resonances and resonant metasurfaces. The physical mechanism behind the optical resonance phenomena in these structures are explained based on the guided-mode resonance phenomenon, EIT-like resonance and bound-state in continuum type resonances. The various nonlinear optical processes studied in these structures, which include second-/third-harmonic generation, four-wave mixing, sum-frequency generation, ultrafast optical switching based on Kerr and multiphoton absorption nonlinearities, photon acceleration of third harmonic generation signal, higher harmonic generation processes and hybrid resonant metasurfaces are discussed. Various dielectric structures in the form of one-dimensional gratings, two-dimensional arrays of nanodisks, bar-nanodisk structures, asymmetric bar dimers, asymmetric rectangular unit-cells, disordered nanodisk array, coupled GMR structures, heterogeneous structures are utilized for these nonlinear optical studies.

Looking ahead, such periodic dielectric structures are expected to find applications as miniaturized frequency converters in the form of intracavity photonic windows or as active fiber connectors [120,121]. The transition of this technology to practical, real world application does require improvements to certain aspects of this technology. In particular, scaling of the area of the metasurfaces, achieving higher conversion efficiencies, ability to extend to ultra-violet or infrared spectral windows with the exploration of novel structures and heterogenous integration capability will become essential. Optical metasurfaces are conventionally patterned using electron-beam lithography which renders it time consuming and difficult to scale to large area. The use of stepper lithography as used in standard electronic chip fabrication, interference lithography, imprint lithography or chemical synthesis techniques are promising to scale the metasurfaces to large areas [36,42]. The ability to combine multiple resonance phenomena such as quantum well based resonant nonlinearity with metasurface resonance is a promising direction to considerably improve the conversion efficiencies [116]. The use of high nonlinearity media on suitable low-index substrates, such as Gallium Phosphide on glass substrates [122] and high efficiency electro-optic polymers [123] are also possible direction to improve the efficiency. The use of multi-pass configuration, for example, in an intracavity application can also amplify the overall nonlinear process [120]. Furthermore, with emerging two-dimensional layered materials for photonic applications, the use of such materials in combination with dielectric metasurfaces is also seen as a promising direction [118]. The ability to switch or tune nonlinear optical functionality at high-speed will also be useful for fast optical modulation [124–126]. The exploration of high-quality factor resonances such as quasi bound-state in continuum is also an important direction to realize high efficiency resonant metasurfaces [83]. Overall, the emerging field of nonlinear optics in resonant metasurfaces and the resurgence it has given to guided-mode resonance platforms is creating lot of interest in nonlinear nanophotonics community. While practical applications are yet to emerge, the research efforts addressing this are in the right direction, which makes the future of this technology highly promising.

**Author Contributions:** Conceptualization, V.R.; writing—original draft preparation, V.R.; writing—review and editing, V.R., J.D., S.M., R.B. and L.K.A.S.; supervision, V.R.; project administration, V.R.; funding acquisition, V.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** VR acknowledges funding support from DST SERB Early career award, ISRO Space technology cell and DST Nano mission through the NNetra program.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


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