Epsilon-near-zero phase-matching for second-harmonic generation in semiconductor-based nanowire hyperbolic metamaterial

Abstract

Hyperbolic metamaterials have been widely used for nonlinear optical applications. Their unique functionality for nonlinear optics enhancement due to the hyperbolic dispersion is induced by a strong shape anisotropy. In this work, we numerically investigated the second-harmonic generation (SHG) in two-dimensional periodic arrays of aluminium gallium arsenide (AlGaAs) nanowires embedded in ordered porous aluminum oxide (Al2O3) or the nanowire hyperbolic metamaterial (NHMM). Under local effective medium approximation, the homogenization of the NHMM was achieved due to deep sub-wavelength size of each nanowire radius. Then this medium was classified as an effective uniaxial medium with anisotropic electric permittivity. The NHMM provided the spectral position of second-harmonic (SH) wavelength, which is determined at the epsilon-near-zero (ENZ) by the optimal design of NHMM structural parameters such as AlGaAs radius or fill fraction. Consequently, a gigantic increment of SHG conversion efficiency was achieved because of dramatic phase-matching at ENZ point. This mechanism is attributed to electric field enhancement of SHG inside the metamaterial. According to numerical results, the NHMM can be applied as nonlinear frequency converters in integrated nanophotonic systems.