A finite element contour integral method for computing the resonances of metallic grating structures with subwavelength holes

We consider the numerical computation of resonances for metallic grating structures with dispersive media and small slit holes. The underlying eigenvalue problem is nonlinear and the mathematical model is multiscale due to the existence of several length scales in problem geometry and material contrast. We discretize the partial differential equation model over the truncated domain using the finite element method and develop a multi-step contour integral eigensolver to compute the resonances. The eigensolver first locates eigenvalues using a spectral indicator and then computes eigenvalues by a subspace projection scheme. The proposed numerical method is robust and scalable, and does not require initial guess as the iteration methods. Numerical examples are presented to demonstrate its effectiveness.