The Application of Mutual Energy Theorem in Expansion of Radiation Field in Spherical Waves

TL;DR

This paper refines the spherical wave expansion method for electromagnetic fields by redefining the inner product to limit it to a Hilbert space, enabling the application of the mutual energy theorem to expand the radiation field.

Contribution

It introduces a new inner product definition that restricts the wave expansion method to a Hilbert space, facilitating the use of the mutual energy theorem in electromagnetic field analysis.

Findings

Redefinition of inner product to Hilbert space

Application of mutual energy theorem to spherical waves

Enhanced theoretical framework for electromagnetic field expansion

Abstract

In recent years the shperical wave expansion method has been widely applied to the theory and calculation of electromagnetic fields. But the inner product exist in reference[1] is defined on the Banach space[2]. Through redefining the inner product this article limits the wave expansion method to Hibert space[3]. For this reason the mutual energy theorem is introduced.