Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers

Abstract

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Levy index $\alpha$. The system represents linearly-coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment, which demonstrated the first observation of the wave propagation in an effectively fractional setup). By dint of numerical computations and variational approximation (VA), we identify the SSB in the fractional coupler as the bifurcation of the subcritical type (i.e., the symmetry-breaking phase transition of the first kind), whose subcriticality becomes stronger with the increase of fractionality $2-\alpha$, in comparison with very weak subcriticality in the case of the non-fractional diffraction, $\alpha =2$. In the Cauchy limit of $\alpha =1$, it carries over into the extreme subcritical bifurcation, manifesting backward-going branches of asymmetric solitons which never turn forward. The analysis of the SSB bifurcation is extended for moving (tilted) solitons, which is a nontrivial problem because the fractional diffraction does not admit Galilean invariance. Collisions between moving solitons are studied too, featuring a two-soliton symmetry-breaking effect and merger of the solitons.

to be published in Physical Review E

References in corpus (16)

• Spontaneous symmetry breaking in a nonlinear double-well structure
• Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons
• Experimental realisations of the fractional Schrödinger equation in the temporal domain
• Spatiotemporal accessible solitons in fractional dimensions
• Soliton dynamics in a fractional complex Ginzburg-Landau model
• Spontaneous symmetry breaking of solitons trapped in a double-channel potential
• Propagation dynamics of the circular Airy Gaussian vortex beams in the fractional nonlinear Schrödinger equation
• Symmetry breaking of spatial Kerr solitons in fractional dimension
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
• The Two-Dimensional Fractional Discrete Nonlinear Schrodinger Equation
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Reversible ultrafast soliton switching in dual-core highly nonlinear optical fibers
• Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy