Irradiation of Medium by Plane Disk with Uniform Distribution of Transient Current

The problem of irradiation of a perfect medium by transient electromagnetic wave radiated by the aperture with arbitrary distribution of electrical current is solved analytically by means of the method of evolutionary equations. This source generates TE-wave in free space. As an example the radiation of the plane disk with uniform distribution of current with steplike time dependence is considered. Using Riemann function and separation of variables methods the general solutions for the incident, transmitted, and reflected waves are obtained. Application of boundary conditions permits to derive analytically coefficients of modal expansion of field in the form similar to the Fresnel formulas. Generalization of the obtained expressions for arbitrary time dependence of source can be made by Duhamel integral.