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Transient response of nonuniform dispersive media Thorleifson, Jon Michael

Abstract

The transient response of one-dimensional nonuniform dispersive media is studied through the use of numerical techniques for the inversion of the Laplace transforms of the transient signals. The media considered are those in which the permittivity varies in one spatial dimension only and for which an analytical or numerical solution of the wave equation can be obtained. Two numerical techniques for the inversion of Laplace transforms are used, one in which the inverse transform is obtained in terms of a series of generalized Laguerre polynomials and the other in which the inverse is obtained by direct numerical integration of the complex inversion integral. Responses are calculated for the following cases; (a) a uniform isotropic plasma, (b) dielectric media with a piecewise linear variation in permittivity and (c) isotropic cold plasmas with a piecewise linear variation in electron density, for step-modulated and rectangular-pulse-modulated carrier input signals. It is shown that the results for case (a) compare favorably with the known exact solution, for a unit-step-modulated carrier input signal.

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