Wave-optical treatment of the shadow cast by a large sphere

TL;DR

This paper develops a wave-optical Mie theory to analyze the electromagnetic field in the shadow of a large sphere, showing that the shadow is devoid of EM field except for edge diffraction effects.

Contribution

It introduces a wave-optical Mie theory incorporating absorbing boundary conditions to accurately describe the EM field in the shadow of a large sphere.

Findings

No EM field deep in the shadow, except for edge diffraction.

The developed theory aligns with classical expectations of shadow regions.

Provides a detailed analytical solution for the EM field in the shadow zone.

Abstract

We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this treatment, we demonstrate that there is no EM field deep in the shadow, except for the field that is diffracted into the shadow by the edges of the sphere, as anticipated.