Simulation of Wave Propagation in Media Described by Fractional-Order Models

In this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell’s equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time domain (TD) and the frequency domain (FD). In the TD algorithm, the electromagnetic field is computed as a convolution of an excitation with Green’s function formulated based on an improper integral and the Mittag-Leffler function. On the other hand, the FD algorithm transforms an analytic excitation to FD, executes multiplications with phase factors, and finally transfers back result to TD. This algorithm involves elementary functions only, hence, computations are significantly faster and accurate with its use. However, applicability of the FD algorithm is limited by the sampling theorem. Numerical results and computation times obtained with the use of both algorithms are presented and discussed in detail.