Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals

TLDR

Quadratic nonlinear photonic crystals feature a spatially modulated second-order susceptibility while the linear susceptibility remains uniform, contrasting with conventional photonic crystals where the linear index is modulated, and their nonlinear processes are governed by phase matching set by the crystal’s reciprocal lattice. The study investigates three-wave mixing in nonlinear photonic crystals with periodic, quasi-periodic, radially symmetric, or random modulation, and proposes new all-optical methods to control beam spatial and polarization properties. The authors analyze both one-dimensional and two-dimensional modulations of the nonlinear susceptibility to explore these wave-mixing processes. Modulating the nonlinear susceptibility enables engineering of spatial and spectral responses in three-wave mixing and supports efficient generation of new optical frequencies in multiple directions.

Abstract

Abstract Quadratic nonlinear photonic crystals are materials in which the second order susceptibility χ (2) is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three‐wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi‐periodic, radially symmetric or even random. We discuss both one‐dimensional and two‐dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all‐optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.