Use of decomposition of the wave equations and pseudo-differential operators for the description of nonparaxial beams and broadband wave packets

Abstract

We discuss the common approach for deriving the equations for the description of wave beams and wave packets in a wide range of angles and frequencies by decomposition of the initial equations into coupled equations of normal waves with the use of pseudo-differential operators. Estimates of accuracy of the one-wave approximation as a function of accuracy of approximation for the propagation-constant operator are given. We propose to use the method of moments for the description of pulses with a wide spectrum. The transition from the obtained to known equations is described. As an example of using the obtained equations, we analyze the self-focusing and modulation instabilities of plane waves in quartz in the range of transition from the normal to anomalous dispersion of the group velocity.