Visualizing a Nonlinear Response in a Schrödinger Wave

Abstract

We demonstrate for the first time that the nonlinear response of a medium can be mapped directly onto a dynamical wave profile as governed by a generalized nonlinear Schr\"odinger equation. As analyzed in an accelerating coordinate, the intrinsic gravitylike potential helps ``isolate'' the effects related to a strong repulsive nonlinear interaction from the dispersion or diffraction in a steady state. Thus, under appropriate conditions, the associated nonlinear response curve can be read out directly in the profile of the nonlinear state. A simple scheme is proposed to approach adiabatically these modes through a shaped input wave profile. Our analysis is further verified experimentally by directly visualizing a Kerr (saturable) nonlinearity experienced by an optical pulse (beam) in a nonlinear fiber (photorefractive crystal), validating the versatility of this approach for different types of optical nonlinearities.