Waveguide propagation of electromagnetic step signal

Propagation of the transient electromagnetic field in a waveguide with the perfectly conducting surface of arbitrary cross-section and filled with a lossy medium is considered. The time domain method of waveguide evolutionary equations has been used, and original initial-boundary value vector problem for Maxwell´s equations has been reduced to integrating of the one-dimensional Klein-Gordon scalar equation. Its solution is obtained as an expansion in terms of a suitable for time domain method basic set. The expansion coefficients are readily derived through the same decomposition of the input signal. Analytical forms of early- and late-time approximations for propagating electromagnetic signal are presented, and the validity conditions for the explicit formulas are discussed