Failure of the Quasimonochromatic Approximation for Ultrashort Pulse Propagation in a Dispersive, Attenuative Medium

Abstract

The dynamical evolution of an ultrashort pulse, whose initial temporal envelope is infinitely smooth with compact support, is considered as it propagates through a temporally dispersive, attenuative medium characterized by two resonance lines. As the propagation distance increases, the accuracy of the popular group velocity description decreases monotonically, whereas the accuracy of the mathematically well-defined asymptotic description and its derivative energy velocity description increase.