Quaternionic equation for electromagnetic fields in inhomogeneous media

TL;DR

This paper demonstrates that Maxwell's equations in inhomogeneous media can be unified into a single quaternionic equation, extending the concept of generalized analytic functions to complex electromagnetic environments.

Contribution

It introduces a quaternionic formulation that simplifies Maxwell's equations in inhomogeneous media, providing a new mathematical framework for electromagnetic analysis.

Findings

Quaternionic equation equivalent to Maxwell's equations in inhomogeneous media

Extension of Vekua's generalized analytic functions to electromagnetic fields

Potential for simplified analysis of complex media

Abstract

We show that the Maxwell equations for arbitrary inhomogeneous media are equivalent to a single quaternionic equation which can be considered as a generalization of the Vekua equation for generalized analytic functions.