An arbitrary signal propagation in waveguides

Transient electromagnetic wave propagation in a hollow waveguide of arbitrary cross section with perfectly conducting walls is considered. The time domain method employed is faithful to the nature of transients and thus is an efficient one. By means of the evolutionary waveguide equations method, the original vector electromagnetic problem is reduced to integration of the scalar one-dimensional Klein-Gordon equation. With the separation of variables method, its solution is obtained as an expansion in terms of the special basic set for the Klein-Gordon equation. The expansion coefficients are readily deduced by making use of the definition of an input signal. Analytical forms of the signal near its front, and numerical computations in other space-time domains are represented.