Nonlinear propagation dynamics of Gaussian beams in fractional Schrödinger equation

Abstract

Abstract We investigated theoretically the nonlinear propagation dynamics of Gaussian beams in the fractional Schrödinger equation (FSE). When the nonlinearity is introduced into FSE without invoking an external potential, the evolution behaviors of incident Gaussian beams are modulated regularly and some novel phenomena arise. In the one-dimensional case, by changing the values of Kerr or saturated nonlinear coefficient, specific localized or diffracted phenomena appear in the corresponding intensity region, where the splitting angle of one-dimensional incident beam will be modulated flexibly to become larger or smaller in weak nonlinear region, besides, when the self-focusing strength is moderate, the energy of the beam is highly concentrated to form a breathing soliton structure. For two-dimensional case, Kerr or saturated nonlinearity will modulate the energy to the middle or edge in a certain nonlinear region, corresponding to the decrease or increase of the conical diffraction radius, it should be noted that there are two evolution periods under the saturated self-focusing nonlinearity. The work may provide more possibilities for beam modulation in FSE from a nonlinear perspective.