Asymptotic theory of pulse compression in dispersive media

Abstract
This paper deals with the long distance propagation of FM pulses in dispersive media. The treatment is based on an asymptotic theory which utilizes space-time rays and plane wave dispersion surfaces as well as integral representations. The discussion includes the propagation of prescribed FM signals in homogeneous media as well as synthesis of signals to achieve maximum pulse compression. Special attention is given to the caustics and foci exhibited by the space-time ray system when pulse compression takes place, and to the description of the field in the corresponding space-time transition regions where simple asymptotic constructs are inadequate. While the theory is presented for media with relatively arbitrary spatial and dispersive characteristics, detailed calculations are carried out for a homogeneous isotropic cold plasma for which results can be obtained in explicit form.

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