分数衍射系统中部分pt对称孤子的对称破缺

Abstract

Objective Fractional diffraction effects and various novel phenomena produced by paritytime (PT) symmetric optics systems have become research hotspots in the field of optics. A large amount of theoretical research has proven the existence of the optical soliton in the fractional nonlinear Schrödinger equation containing PTsymmetric potentials.However, the existence, stability, and dynamics of partially PTsymmetric solitons in non -Hermitian nonlinear optical waveguides with fractional diffraction effect have not been explored yet. The phenomenon and mechanism of spontaneous symmetry breaking of the partially PTsymmetric solitons are still unclear. Meanwhile, the obtained research results provide new insights into the propagation and controlling of the partially PTsymmetric solitons in the non -Hermitian nonlinear optical waveguides with fractional diffraction.Methods We numerically solve partially PTsymmetric soliton solutions and asymmetric solutions. Specifically, the accelerated imaginary time evolution method is used to solve the stationary fractional nonlinear Schrödinger equation. Two types of solutions are obtained. The first type is the partially PTsymmetric solitons with real propagation constants, and the second is the asymmetric solutions with complex propagation constants. Then, the solutions of the perturbation are linearized through linear stability analysis, and the eigenvalue problem of the perturbation modes is transformed into the spectral space by using the Fourier collocation method. The spectrum of the eigenvalue problem of the perturbation modes is numerically solved. The propagations of the partially PTsymmetric solitons and the asymmetric solutions are numerically simulated using the splitstep Fourier method. Finally, the obtained results are compared with the results of linear stability analysis.Results and Discussions First, two types of solutions are confirmed to exist in the fractional nonlinear Schrödinger equation with the partially PTsymmetric potential. The first type of solution is the partially PTsymmetric solitons with real propagation constants, and the second type of solution is the asymmetric solutions with complex propagation constants. The results are shown in Fig. 2 and Fig. 3, respectively. Then, the critical power of the symmetry breaking bifurcation point of the partially PTsymmetric solitons is numerically determined and verified with the linear stability