Electromagnetic wave propagation in a time-variant medium: A state-space approach via the spatial fourier domain

In this paper we consider a three-dimensional electromagnetic field in a homogeneous and time-variant medium. After a spatial Fourier transformation we solve Maxwell´s equations for the electric and magnetic flux densities and write the solution in terms of the so-called transition matrix. This matrix can be given in terms of the well known Peano-Baker series and we show that in the constant impedance case this series simplifies to the matrix exponential operator. This operator can explicitly be transformed back to the spatial domain resulting in explicit space-time domain expression for the electromagnetic field.