Nonreciprocal nonlinear wave scattering by loss-compensated active hyperbolic structures

The combinatorial frequency generation (CFG) in active periodic semiconductor-dielectric structures has been explored through illumination by a pair of pump waves with dissimilar frequencies and incidence angles. We study the influence of gain on linear refraction properties of the stack and on the efficiency of the mixing processes by the system with the resistive character of nonlinearity. We demonstrate that the introduction of gain dielectric material inside the stack not only compensates for losses caused by the collisions of the electrons in semiconductor media but also improves the efficiency of the CFG. We show that in systems with weak asymmetry of linear response we can get significant nonreciprocity of nonlinear interaction.