Odyssey of Light in Nonlinear Optical Fibers

2 Waveguide electromagnetic pulse dynamics: Projecting operators method

Mateusz Kuszner and Sergey Leble

2.1 Introduction

In this review we discuss applications of the dynamical projecting method (DPM) [1] to problems of short pulse propagation in a dispersive medium. We concentrate on two basic mathematical formulations: the Cauchy problem and boundary regime propagation along a waveguide. The DPM method is a convenient way to specify the problems of a wave initialization for directed modes and for a given polarization account. A minimal version of such a study appears when one integrates across a waveguide with respect to transversal coordinates (e.g., [2]). More advanced theories include one-mode fiber description [3] and multimode waves ...