Nonlinear Subwavelength Resonances in Three Dimensions

ABSTRACT In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high‐contrast resonators with Kerr‐type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the extra experimentally observed eigenmodes that are induced by the nonlinearities.