Wave Propagation in Time-Varying Media

This paper examines the propagation of waves in media which are spatially homogeneous but whose properties vary with time abruptly or continuously. Emphasis is placed on the excitation problem and on source-dependent phenomena which are not evident when attention is given only to the source-free case. After a presentation and interpretation of various exact closed-form solutions for simple nondispersive and dispersive media undergoing sudden or gradual temporal changes, attention is given to integral representations required under more general conditions. In the ensuing far-zone asymptotic analysis, dispersion surfaces and space-time rays are used extensively for identification of wave packets and other wave constituents descriptive of the field, and a comparison is made between the asymptotic results and the exact solutions noted above. Asymptotic field solutions are then derived by a direct ray procedure, without intervention of integral representations. The examples considered exhibit a variety of phenomena, among which the most interesting is the focusing of reflected waves when a dispersive medium undergoes a sudden change.