Dispersive and dissipative medium response to an ultrashort pulse: A Green's function approach

Abstract

The propagation of an ultrashort pulse in a dispersive and dissipative medium may conveniently be described by using a Green's function analysis. The advantage would be that all details of the initial pulse, however short, could be probed by an "infinitely" sharp δ-pulse and subsequently deciphered in a modified form, after the influence of the medium, at a later time and at a new observation point.The Green's function for a dispersive and dissipative, plasma or dielectric (molecular) medium, is constructed for an infinitely extended three-dimensional case by using symbolic algebra for time-differential operators. The solution consists of two parts: a displaced δ-function part and a Bessel-function part, describing a wake field which for dominating dispersion is of oscillatory nature. For a certain ratio between the dispersive and dissipative parameters (plasma frequency and damping) a critical limit is found where the wake oscillations disappear completely.In the particular limits of vanishing dispersion or vanishing dissipation one recovers from the generalized solution the well-known results for a pure conductor (metal) and a pure dispersive medium (cold collisionless plasma) described by the Klein-Gordon equation.The response of the medium to an initially localized ulrashort electromagnetic pulse, of an arbitrary shape, can be expressed by an integral in time and space, of the product of the Green's function and the initial pulse.