Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes

Abstract

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Soliton dynamics in a fractional complex Ginzburg-Landau model

“…The realization of the FSE theory in optical fields provides abundant possibilities for studies of the fractional-order beam-propagation dynamics. Subsequently, the propagation of beams in FSE with different external potentials and nonlinear terms was investigated [13][14][15][16][17]. In this vein, various soliton states based on FSE in Kerr nonlinear media and lattice potentials were reported recently [18][19][20][21][22][23].…”

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

“…Since then, interesting results on generating and manipulating linear and nonlinear propagation dynamics of laser beams in such fractional optical models were obtained. Some typical works include: Gaus- * zengjh@opt.ac.cn sian beams either evolved into diffraction-free beams [14] or undergone conical diffraction [15] during propagation without a potential, PT symmetry [16] and propagation dynamics of the super-Gaussian beams [17] , optical beams propagation with a harmonic potential [14,15,17] (which supports spatiotemporal accessible solitons too [18,19]) and periodic potentials [16,20], propagation management of light beams in a double-barrier potential [21], in the context of linear FSE regime; and in terms of nonlinear fractional Schrödinger equation (NLFSE) regime [22][23][24][25][26][27][28], including optical solitons (or solitary waves) without external potential [23,24], solitons supported by linear [25][26][27] and nonlinear [28] periodic potentials which refer, respectively, to optical lattice and nonlinear lattice as described below.…”

Beam propagation management in a fractional Schrödinger equation

“…Note that the experimental setting for the realization of beam propagation in the FSE was proposed very recently 30 . In the context of nonlinearity, nonlinear effects tuned by varying the Lévy index 33 and stable lattice solitons in focusing/defocusing Kerr media 34 have been uncovered.…”