Generalized Higher-Order Nonlinear Evolution Equation for Multi-Dimensional Spatio-Temporal Propagation

Abstract

There is currently great interest in nonlinear spatio-temporal propagation phenomena. Advances [1] in short-pulse laser technology and in the measurement of pulse amplitude and phase [2] have allowed for the experimental study of phenomena that have been predicted theoretically using simple models of propagation. These studies have also revealed new phenomena, which have resulted in the development of new propagation models as well. Typically, one or more terms are added to the multi-dimensional nonlinear Schrodinger (NLS) equation in an attempt to explain these phenomena, but to date, no generalized higher-order spatio-temporal propagation equation has been obtained. Here, we present the results of the derivation of such a generalized envelope equation directly from Maxwell’s equations. This result uncovers physics that is not directly revealed in Maxwell’s equations in the form of higher-order terms in the NLS equation which allow for the description of the propagation of optical radiation with large spatial and temporal bandwidths.