An integral equation method for numerical computation of scattering resonances in a narrow metallic slit

Abstract

In this paper we present an efficient and accurate integral equation method to compute the scattering resonances for a subwavelength metallic slit structure. A new boundary integral equation is derived for the scattering problem, and the computation of scattering resonances is reduced to solving the eigenvalues of the corresponding homogeneous formulation over the complex plane. The integral operators are evaluated with high-order precisions by accurate calculations of the Green's functions for the layered medium and accelerated computation of the slit Green's function. The Newton's method is employed for solving the eigenvalues of the boundary integral formulation. We propose an effective strategy for obtaining the initial guesses of scattering resonances by introducing an approximate model for the scattering problem, for which the leading orders of the resonances are derived by asymptotic analysis. Numerical experiments are provided to demonstrate the accuracy, efficiency, and robustness of the method.