A Spectral Method For Solving The Propagation Model Of Ultrashort Laser Pulse

The purpose of the paper is to provide a high-precision numerical algorithm for the solution of the ultrashort laser pulse propagation model.The theoretical background part starts from the Maxwell equations and combines the various ef-fects of ultrashort laser pulse in the transmission medium to derive the physical model of laser pulse propagation,then turns it into a mathematical equations by dimensionless.That said,this mathematical equation is a two-dimensional nonlinear Schrodinger equation.Then,we design a Galerkin spectral method based on Legendre polynomial and Fourier polynomial.We use the combination of the Galerkin spectral method and the finite difference method to solve the two-dimensional nonlinear Schrodinger equat,ion.The examples that one-dimensional linear Schrodinger equation and two-dimensional linear Schrodinger equation are used to illustrate the validity and accuracy of this method.Finally,we numerically simulated the nonlinear Schrodinger equations of one-dimensional and the two-dimensional respectively.Compared with the traditional finite difference method.this method can not only improve the accuracy of the spatial spectrum,but also reduce the computational time and computer memory requirements.The numer-ical results verify the accuracy and effectiveness of the method which indicates that the method is an effective method for solving the ultrashort laser pulse prop-agation model.