Controllable inversion and focusing behaviors of Swallowtail-Gaussian beams in fractional Schr?dinger equations
By transferring a one-dimensional swallowtail catastrophe to an optical field,the evolution dynam-ics of the Swallowtail-Gaussian(SG)beams in fractional Schrödinger equations(FSE)with different poten-tials,which include the linear,parabolic,and Gaussian potential and non-potential cases,were investigated using the split-step Fourier method.In a non-potential case,the SG beams split into two sub-beams,and their splitting trajectories along straight lines can be curved with a larger Lévy index in FSE.In a linear potential case,periodic inversion and focusing behaviors are found,and a larger Lévy index can strengthen their peak intensities at focusing points and curve trajectories.However,the period distance of inversion and focusing is only affected by linear potentials rather than the Lévy index.In a parabolic potential case,the beams evolve from chaos interference into an apparent period in inversion and focusing of main and side lobes with a lar-ger Lévy index,where the inversion and focusing position are combined and determined by parabolic poten-tial and the Lévy index.In a Gaussian potential case,the evolution dynamics are evidently constrained with-in potential barriers.In a narrow barrier,the periodic inversion and focusing display chaotic behavior be-cause of the interference of both the reflected main and side lobes.In contrast,the periodic evolution in a wider barrier becomes more prominent owing to the attenuation of the side lobes.The study of the SG beam in FSE offers the possibility of optical modulators and switches through the utilization of the higher-order swallowtail catastrophe wave fields.
Swallowtail-Gaussian beamFractional Schrödinger equationLévy index
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