Computation of scattering resonances for dielectric resonators

In this paper we present a numerical method to compute resonances and resonant modes for 2D electromagnetic scattering at a smooth homogeneous dielectric object in free space. The resonances are found as eigenvalues of a non-linear eigenvalue problem which comes from a formulation as a boundary integral equation and subsequent discretization by a Nystrøm approach, for which the integral kernels are regularized by singularity subtraction. The eigenvalues are computed by a predictor corrector strategy, which provides good initial guesses for an iterative corrector procedure. The resonances can be computed with very high accuracy due to an exponentially decreasing discretization error.