Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrodinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too, in particular, for fast moving solitons and the results produced by the variational approximation. Moreover, dissipative solitons are briefly considered, which are governed by the fractional complex Ginzburg-Landau equation.

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The article reviews recent results on stable propagation of solitons and solitary vortices in models based on the NLSE, including fractional diffraction and nonlinear terms. The results are mainly numerical, with some analytical findings included for fast moving solitons. The article also briefly considers dissipative solitons governed by the fractional complex Ginzburg-Landau equation.