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Self-focusing and azimuthal instabilities in graded-index optical fibers

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Abstract

Nonlinear beam propagation and self-focusing effects in graded-index optical fibers and waveguides have been the subjected of several studies in the past years (see, e.g.,[1-3]). As opposed to the most studied case of self-focusing in Kerr media descnbed by the three-d1mens10nal nonlmear Schri:idmger equation (NLSE), the guidmg provided by the radially-dependent refractive index profile allows for the existence of nonlinear self-trapped modes when the beam power is below the critical power for wave collapse. Most of previous studies have been concerned with the fundamental nonlmear TEM00 propagation mode and showed numencally its stability; vanat10nal [2] and scale-transformation [4] methods have been as well adopted to study nonlinear periodic beam refocusing in such structures. A still open question is the stability of higher-order nonlinear fiber modes as well as the existence of symmetry-breaking transverse instabilities, which are known to arise in analogous problems of beam self-trapping without any guiding structure [5,6]. In absence of index guiding, such an instability can be observed solely for a particular power level (usually high) corresponding to the self-trapping regime. Here we show that similar symmetry-breaking instabilities may occur in nonlinear parabolic-index fibers at power levels much lower than the critical power for beam collapse. Our analysis may be of relevance not only in the context of nonlinear fiber-optics or waveguides, but also in the field of Bose-Einstein condensation, where the mean-field equation describing the dynamics of the condensate 1s formally equivalent to the NLSE with a parabolic potential (see, e.g,, [7]).

© 2004 Optical Society of America

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