One-way propagation in electromagnetic materials

Approaches to the characterization of the direction of wave propagation are examined, in the frequency and in the time domains, for electromagnetic materials with memory. In the frequency domain, the direction is characterized through the sign of the energy flux which is shown to decay as the wave propagates. In the time domain, a review is given of the wave-splitting approach for a dispersive dielectric. The result is a pair of decoupled equations, one being regarded to represent a forward propagating wave and the other a backward propagating wave, both of them involving an appropriate convolution kernel. To establish a connection between the two approaches, the Fourier components associated with the wave-splitting equations are examined. Owing to a thermodynamic restriction on the permittivity, the energy flux criterion, as well as the phase and amplitude criteria, implies that the direction is forward or backward depending on the value of the cosine transform of the convolution kernel and hence on the frequency.