Propagating solution of point source excitation electromagnetic wave in time-varying media sphere space

The electromagnetic propagation solutions of point source in a time-varying media of higher space were studied. According to the boundary conditions, inhomogeneous wave equation of point source before the media changing abruptly and the homogeneous wave equation after the media changing abruptly were constructed. Employing the traditional separation of variables, the solutions of the equations were obtained and figures in the one dimensional case were depicted to testify the solutions. After the media changing abruptly, the initial wave was split into the forward traveling wave and backward traveling wave. Two phenomena were generated, one was called energy focusing the other was called frequency shift.