We consider scattering of electromagnetic waves by a thin structure of high index of refraction. We first consider the Helmholtz equation, and show that if the squared refractive index scales as $O(1/h)$ where h is the thickness of the scatter, an approximate solution based on perturbation analysis can be obtained which involves solving a 2D integral equation for a 3D problem. We then discuss extensions to Maxwells' equations in this context while accounting for material jumps, and the calculation of resonant frequencies by this asymptotic approach.
This work involves coauthors D. Ambrose, J. Gopalakrishnan, F. Santosa and J. Zhang