In this thesis, we study the nonlinear properties of various solid-state nanosystems and evaluate their performance towards applications in nonlinear nanophotonics.
Nonlinear nanophotonics is an exciting avenue of research, translating nonlinear optical phenomena to modern platforms such as on-chip technologies. The optical and infra-red length-scale regime matches the interaction length scales of the waves
in the medium, lifting the phase-matching constraints of bulk nonlinear optics.
We explore different materials with strong nonlinear strength quantified by the nonlinear susceptibility.

Firstly, we show second-harmonic generation from a 410 nm thin film of epitaxially grown gallium phosphide and demonstrate that its absolute efficiency is comparable to a bulk wafer over the pump wavelength range from 1060 to 1370 nm. Additionally, we show that for third-order nonlinear processes, amorphous GaP thin films are an alternative that even exceeds the efficiencies of the crystalline samples at third-harmonic efficiency.

Secondly, we study nonlinear effects at the band-edge of FAPbBr3 nanocrystals and report the maximum absolute value third-order nonlinear susceptibility as 1.46 x 10-19 m2/V2 at 1560 nm excitation wavelength. We show a spectral dependence of the SHG from WS2 bulk TMDC, which we attribute to excitonic effects near the bandgap. Furthermore, we find the third-order nonlinear susceptibility for four TMDC at the telecommunications wavelength (1500 nm) to be of the order of magnitude 1 x 10-18 m2/V2, which is one order of magnitude larger than monolayer
materials.

We conclude by showing that nanophotonic design principles can enhance nonlinear effects in the nanoscale regime. We use the resonant anapole
mode of high-refractive-index WS2 nanoantennas to generate enhanced third harmonic.
Furthermore, we couple plasmonic antennas to epsilon-near-zero material films to boost nonlinear response (measured via four-wave-mixing) by 15
000.