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.

Morphology-Dependent Resonances: The Effective Potential

This chapter examines the effective potential for morphology-dependent resonances (MDRs). In the cross-section for scattering of electromagnetic energy by a dielectric sphere, a series of sharp peaks that occur as a function of the size parameter can be observed. These peaks are a manifestation of scattering resonances in which electromagnetic energy is temporally trapped inside the particle. These resonances are the MDRs. The chapter first considers the case of a scalar plane wave impinging in the direction θ‎ = 0 on a sphere of radius a before finding the solution of the Schrödinger equation that describes the motion of a particle in the effective potential in the presence of a centrifugal barrier. It also discusses the characteristics that are necessary to define a resonance appropriately.