Theoretical background for the time-domain analysis of complex open resonant structures

The paper deals with the theoretical and methodological background for the time-domain (TD) study of complex open resonant structures. We discuss the formulation and solution of model initial boundary-value problems of the theory of open resonators (OR), the analytical relations between spatial-temporal and spatial-frequency representations for the solutions, the problem of choice of the pulse source allowing one to extract a reliable information about dispersive properties of OR from the general solutions, and some numerical results relating to free oscillations in classical OR, in resonant quasi-optical structures, and in resonant antennas.