Morphology-Dependent Resonances in Two Concentric Spheres with Variable Refractive Index in the Outer Layer: Analytic Solutions

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system are derived in the closed form of both modes. Our numerical results are provided with discussion.