Comparative Analysis of the Analytical and Numerical Solutions of Transient Wave Propagation Problem

The nonstationary three-dimensional radiation problem is transformed into the problem for one-dimensional evolutionary equations by means of the construction of modal basis for electromagnetic field with arbitrary time dependence. Transient electromagnetic fields in infinite space filled with inhomogeneous in radial direction transient medium without losses are presented by spherical modes. The expansion coefficients of transient electromagnetic field on the modal basis are found from the set of evolutionary equations which describe independent propagation of the spherical modes. The transient electromagnetic field can be found without Fourier transform application directly by means of one-dimensional FDTD method for arbitrary medium or using Laplace transform and wave splitting for the case of homogeneous stationary medium. The above mentioned methods are compared with the three-dimensional FDTD method for the case of excitation of small loop by transient current