Propagation of the ultrashort pulsed beam with ultrabroad bandwidth in the dispersive medium

Abstract

In this paper we have investigated the propagation of the ultrashort pulsed beam with ultrabroad spectral width in the dispersive medium. A general $(3+1)$-dimensional $[(3+1)\mathrm{D}]$ propagation equation first order in the propagation coordinate is derived by using the extended paraxial approximation, which does not resort to the envelope and carrier frequency. This equation can provide an accurate description of the evolution of the ultrashort pulsed beam through the nonlinear dispersive medium, with the numerical value of the spectral bandwidth being bigger than the carrier frequency and considering the absolute frequency. The dispersive and loss coefficients are introduced, and their impacts on the pulse propagation are discussed. In the case of linear propagation, a family of exact solutions of the $(3+1)\mathrm{D}$ equation in dispersive media has been obtained, which represents the ultrashort pulse evolving due to gain (loss), dispersion, and diffraction.