Induced Focusing of Optical Beams in Self-Defocusing Kerr Media

Abstract

Self-focusing is a well-known nonlinear phenomenon. In a Kerr medium in which the refractive index n varies with intensity I as n=n0+n2I, an optical beam can overcome the natural diverging tendency and become self-focused as a result of the converging wavefront imposed on it by self-phase modulation (SPM). This occurs only for Kerr media for which n2 >0. By contrast, SPM imposes a diveraging wavefront when n2 <0. Optical beams then spread faster than diffraction, and are said to be self-defocused. In this paper we show that an optical beam can be focused even in a self-defocusing medium if it propagates together with an intense pump beam that itself experiences self-defocusing. We refer to this phenomenon as induced focusing. The physical mechanism behind induced focusing is cross-phase modulation (XPM), a nonlinear effect through which the phase of an optical beam is affected by other copropagating beams. Even though such a coupling does not lead to an energy transfer, it can redistribute the energy within each beam. In general, the XPM-induced coupling reshapes the beam profile through transverse modulation instability.1 It can lead to induced focusing under certain conditions discussed below. Induced focusing can also occur in a self-focusing medium.2