Optical theorem in the 3-D scattering from a locally perturbed lossless or lossy thin dielectric plate: silver disk-sealed hole analysis

Abstract

This paper is aimed at devising a new optical theorem formulation for the 3-D plane-wave scattering from an infinite resistive plane and, more generally, a thin dielectric plate with a finite-size inhomogeneity shaped as a hollow or sealed hole. This formulation is further modified to cover the case of the plane guided wave scattering from the same inhomogeneity. For the lossless plane, the diffracted field combines a classical outgoing spherical wave, satisfying the Silver-Muller radiation condition, with an outgoing cylindrical guided wave supported by the plane; the power absorbed in the lossy filling is finite. When a lossy plane is involved, a complication appears: the total absorbed power is infinite. However, a change in the inhomogeneity characteristics perturbs the absorbed power density, thus suggesting the perturbative absorption analysis. After developing the analytical procedure for the resistive plane case and the corresponding generalization to the thin dielectric plate case, we illustrate the significance of the new optical theorem by the numerical analysis of the visible-light scattering from a dielectric plate with a circular nanosize hole sealed with a silver disk. Our analysis uses the in-house code having mathematically guaranteed convergence; it reveals the scattering and absorption resonances on the plasmon modes of the silver nanodisk. The derived optical theorem allows us to see that, in the resonances, the power carried by the guided waves can be comparable to the power scattered into the free space.