Abstract

A uniform asymptotic approximation of Maxwell's equations for propagation of a short pulse in Kerr media yields the well- known nonlinear Schrödinger equation $\begin{array}{l}2ik\left(\frac{\partial A}{\partial z}+k^{\prime }\frac{\partial A}{\partial t}\right)+{\nabla }_{\perp }^2-k{k}^{″}\frac{{\partial }^{2}A}{\partial t^2}\\ +\frac{2k^2{n}_2}{n}{\left|A\right|}^{2}A=0,\end{array}$, (1) which describes the dynamical evolution of the light pulse subject to diffraction, normal dispersion, and cubic nonlinearity. This equation reproduces many of the features associated with short-pulse propagation that are observed experimentally.

© 1994 Optical Society of America