Transients in dispersive media, part I: Theory

The asymptotic evaluation of complex frequency integrals arising in the theory of radiation from transient sources in dispersive media is reviewed and extended to accommodate phenomena observed at distant observation points at any observation time. Helpful graphical methods are emphasized and illustrated for a plasma medium discussed in detail in Part II of this paper. Results are interpreted in terms of space-time rays whose properties are reviewed, and these rays, together with the (
k, \omega
) dispersion surfaces for the medium, are utilized for the study of reflection and refraction processes at an interface.