Normalization approach for scattering modes in classical and quantum electrodynamics

Abstract

We propose a scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogeneous medium outside the scatterer, we derive normalization conditions that only depend on the electromagnetic field on the surface of a sphere containing the scatterer. We pay special attention to the important cases of plane-wave illumination and illumination with a multipolar field, for which an explicit and easy-to-use normalization condition is derived. Our approach to normalize scattering modes is extremely versatile and of diverse use. We demonstrate the applicability by normalizing scattering modes of selected metallic and dielectric scatterers of different geometries in the context of different operation scenarios. Since every quantum mechanical treatment of light-matter interaction requires the proper normalization of electromagnetic fields, we deem our proposed normalization scheme beneficial because it provides normalized modes in arbitrary scattering scenarios.