Does the Nonlinear Schroedinger Equation Correctly Describe Beam Propagation?

Abstract

The effect of self-trapping and self-focusing of light beams in nonlinear media was predicted in the early 1960s [1,2]. The evolution of light beams in self-focusing media has always been described by the nonlinear Schroedinger equation (NLSE) ever since the very first works devoted to this question [3,4]. It takes the diffraction and nonlinearity into account in a simple way, and describes the field evolution with high accuracy, unless time dependence and dispersion are involved [5]. Thus, the NLSE is a convenient approximation; it provides the possibility of using a powerful tool such as the inverse scattering method [6] for its investigation. In fact, a variety of exact solutions can be obtained for the 1-D NLSE using even simpler approaches [7]. This equation, with variable coefficients adjusted for a layered medium, has been used widely for describing nonlinear wave propagation in optical waveguides and interfaces [8]. It is also important to note that many fast and convenient calculation methods have been developed [9] for numerical simulations of solutions of the NLSE.