Energy flow in lossy waveguides for impulse wave propagation

The paper is dealt with pulse wave propagation in a waveguide uniformly loaded with lossy medium. Maxwell's equations are solved directly in time-domain by modal basis method [O.A. Tretyakov, 1989, 1993, 2002]. Electromagnetic fields of the time-domain modes are products of some functions of the transverse waveguide coordinates, which originate the modal basis, and the modal amplitudes, which are some functions of axial coordinate z and time t. Modal amplitudes are governed by evolutionary equations which can be reduced to the Klein-Gordon's equation. The solution to this equation is written in the integral form. The energy flow is under study. Some diagrams with space-time distributions of energy density and energy flow speed are plotted for Lagerr impulse wave propagation.