Surplus of energy for time-domain waveguide modes

Abstract

In this study, a problem for electromagnetic fields produced by a time dependent source function in a waveguide with perfect electric conductor surfaces is considered by a direct analytical time-domain method called Evolutionary Approach to Electromagnetics. The previous works are revisited for energy and surplus of energy of time-domain modes in the waveguides. A complete set of transverse electric and transverse magnetic waveguide modes is obtained in time-domain, directly. Every field component of the modes is product of two factors: First one is a vector function of transverse waveguide coordinates which corresponds to a modal basis problem. It is specified via well studied Dirichlet and Neumann boundary eigenvalue problems. Physically, these vector functions are distributions of the modal force lines in the waveguide cross-section. The second one is a scalar function corresponds to a time-dependent modal amplitude problem. This is obtained as the solution of Klein-Gordon equation depend on the waveguide's longitudinal coordinate and time. Consequently, the problem of time-domain signal propagation in the waveguide is solved analytically in compliance with a causality principle. The graphical results are shown for the cases when the energy and surplus of the energy for the waveguide time-domain waveguide modes are represented via the first kind Bessel functions of semi-integer order.