Doubly-Resonant Photonic Crystal Cavities for Efficient Second-Harmonic Generation in III-V Semiconductors

Second-order nonlinear effects, such as second-harmonic generation, can be strongly enhanced in nanofabricated photonic materials when both fundamental and harmonic frequencies are spatially and temporally confined. Practically designing low-volume and doubly-resonant nanoresonators in conventional semiconductor compounds is challenging owing to their intrinsic refractive index dispersion. In this work we review a recently developed strategy to design doubly-resonant nanocavities with low mode volume and large quality factor via localized defects in a photonic crystal structure. We built on this approach by applying an evolutionary optimization algorithm in connection with Maxwell equations solvers; the proposed design recipe can be applied to any material platform. We explicitly calculated the second-harmonic generation efficiency for doubly-resonant photonic crystal cavity designs in typical III-V semiconductor materials, such as GaN and AlGaAs, while targeting a fundamental harmonic at telecom wavelengths and fully accounting for the tensor nature of the respective nonlinear susceptibilities. These results may stimulate the realization of small footprint photonic nanostructures in leading semiconductor material platforms to achieve unprecedented nonlinear efficiencies.