Using Lorentz’s theorem for studying the propagation wave packets in a nonlinear medium

Abstract

We obtain integral relationships expressing the amplitude of wave-packet field on the output surface of a layer via the field amplitude on the input surface, the field on the side surface of the layer, and the integral of the nonlinear currents inside the layer at the previous times in the spectral and spatiotemporal forms. These relationships allow one to perform studies and develop numerical simulation algorithms of propagation and interaction of wave packets which have wide frequency and angular spectra, including calculations of excitation of evanescent waves in the case of sharp focusing or formation of supernarrow filaments. Using the obtained relationships, we propose an algorithm that employs a simple iteration of the first order and allows one to significantly speed up the calculations. The possibility of using the fast Fourier transform to develop algorithms for numerical simulation of the boundary-value problems of nonlinear optics is demonstrated.