Propagation of the main signal in a dispersive Lorentz medium

TL;DR

This paper analyzes how a sine-modulated pulse signal propagates through a Lorentz dispersive medium, deriving asymptotic representations and illustrating the results with numerical examples.

Contribution

It introduces uniform and non-uniform asymptotic descriptions of signal evolution in a Lorentz medium and clarifies conditions for their reduction.

Findings

Derived uniform and non-uniform asymptotic formulas

Identified conditions for reducing uniform to non-uniform representations

Provided numerical examples illustrating the theoretical results

Abstract

Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and non-uniform asymptotic representations for the signal are found. It is shown when the uniform representation can be reduced to the non-uniform one. The results obtained are illustrated with a numerical example.