Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation

Recently a new approach to the modeling of one-way wave propagation in Kerr media was proposed [1]. Within this approach the solution of the nonlinear Helmholtz equation is approximated by a series of solutions of iterative parabolic equations (IPEs). It was also shown that IPEs take the nonparaxial propagation effects into account. In this study we develop an efficient pseudospectral numerical method for solving the system of IPEs. The method is a generalization of an exponential time differencing (ETD) method for the nonlinear Schrödinger equation [2]. The ETD technique is well-suited for the system of IPEs, as it allows to reduce the order of the derivative in the input term.