An attractive analytic solution of the Maxwell's equation

Abstract

In this paper, we aim to develop a closed-form solution of the standard Maxwell's equations that describe the propagation of electromagnetic waves in an isotropic homogeneous medium such as a vacuum. The proposed solution has a simple analytic structure that explains how initial conditions characterize the underlying electromagnetic wave. As such, it can be used as a tool to generate suitable electromagnetic waves in practice. The clean structure of the solution can also help us to derive closed-form solutions in a general medium with a non-zero current term. In this paper, we enhance the solution to cover a special case where the current comes from the contribution of an independent generator. We shall leverage the tools developed in this paper to derive similar closed-form solutions of Maxwell's equations in general mediums with non-zero currents in a separate paper.