Resonant combinatorial frequency generation in non-Hermitian hyperbolic metamaterials

The properties of the combinatorial frequency generation by the periodic semiconductor-dielectric multilayers with hyperbolic dispersion are explored. The nonlinear wave scattering process has been modelled in a self-consistent problem formulation, taking into account the nonlinear dynamics of carriers in semiconductor material. We show that incorporating gain within the multilayer system not only renders the compensation of the semiconductor loss but also significantly enhances the nonlinear interactions in the semiconductor stacks with resistive nature of nonlinearity.