Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

Abstract

Abstract Considered is the plane‐wave scattering from and absorption by a thin circular dielectric disk. The analysis uses a set of the singular integral equations for the effective electric and magnetic currents, derived using the generalized boundary conditions on the disk median section. Following the recently developed analytical preconditioning procedure, these equations are discretized by the Galerkin technique with judiciously chosen expansion functions, which provide for the Fredholm second‐kind nature of the resulting matrix equations. This guarantees the code convergence and high efficiency. It is demonstrated that the developed technique delivers the most important features of thin dielectric disks–the resonances on the natural modes. In the resonances on the slab modes, the disk can be well‐transparent and the shadow is created only by its rim; in the whispering gallery mode resonances, the scattering occurs mainly in the disk plane.

Keywords

• electromagnetic wave scattering
• Fredholm integral equations
• Galerkin method
• integral equations
• matrix algebra
• method of moments