Time Domain Analysis of Impulse Electromagnetic Field on the Interface of Two Media

The method of evolutionary equations is applied to the problem of transient wave falling into interface between two media. The transversal distribution of a wave is similar to a wave generated by plane electrical current in form of circle. Using method of separation of variables the general solution of the problem in time domain is obtained. The unknown coefficients of field expansion by Bessel functions are received using properties of orthogonality of membrane functions. The application of Duhamel's integral to describe fields generated by a source with arbitrary time dependence gives the analytical expressions for fields along longitudinal axis. The cases of different impulse time shapes are illustrated by numerical simulations.