Time-dependent Lorentz-Mie-Debye formulation for electromagnetic scattering from dielectric spheres

Abstract

Canonical solutions to frequency domain Maxwell’s equations, in the spherical coordinate system, have found extensive use as is evident from citations in the scientific literature. What is conspicuous by its absence is lack of such expressions for transient Maxwell systems. The existence of such expressions or approximations, provide the means to glean interesting physics in a variety of applications as well as validate existing numerical fullwave solvers. However, developing these expressions is beset with challenges; direct inverse Fourier transforms of frequency domain expressions are unstable. Successful approaches that ameliorate this instability are more recent endeavor. In this paper, we generalize our earlier contribution to this effort by exploiting a novel representation of the retarded potential to derive expressions for scattering from a dielectric sphere. Several results are provided that demonstrate the stability and accuracy of the method.