An approach to solving Maxwell's equations in time domain

Abstract

In this paper, we propose a new direct approach to solving Maxwell's equations in time domain. Completely different from the classic one, this approach is derived and analysed based on a strategy which is independent of the well-known Fourier (or Laplace) transformation and the corresponding inverse transformation. The analysis first decouples Maxwell's equations on the basis of a potential theory and then uses an operator-variation-of-constants formula (the Duhamel Principle) to achieve the expression of exact solutions of Maxwell's equations. We further illustrate the simplicity and multi-purpose applicability of the new approach in linear, homogeneous, isotropic and lossless (bounded or unbounded and source-free or source) medium (in rectangular, cylindrical or spherical coordinates). Moreover, we make a study on impulse electromagnetics. With this new approach, this paper bridges the gap between the time domain electromagnetics and the frequency domain electromagnetics.