A Study Of Optical Solitons In Fractional Diffraction Nonlinear PT Symmetric Waveguides

Parity time symmetry(PT-Symmetry)is derived from the concept of quantum mechanics.It requires that the physical quantities can be observed,so the eigenvalues corresponding to the eigenspectra of these operators must be real numbers.Therefore,Hamiltonian operators are required to be Hermitian.Until 1998,bender and his collaborators proved that the non Hermitian Hamiltonian with PT symmetry also has real eigenspectra,which also meets the requirement of observability of physical quantities.Because the wave equation describing microscopic particles in quantum mechanics and the propagation equation describing light wave in paraxial approximation in optics are consistent in mathematical form,the research of PT symmetric optics in linear and nonlinear optical systems has been widely concerned by researchers.However,the Hermitian non-linear and fractional Schrodinger optical systems may have less choice for the control of Hermitian non-linear and fractional Schrodinger optical systems.The propagation of beams in fractional diffractive nonlinear Kerr media is quite different from that in standard nonlinear Kerr media.In this paper,we study the propagation dynamics of soliton beams under the nonlinear Schrodinger equation based on fractional derivative to further deepen the understanding of the fractional Schrodinger equation.First of all a(1+1)dimensional theoretical model of beam propagation in a self-focusing Kerr nonlinear PT symmetric waveguide is established and described by the nonlinear Schrodinger equation.Then,the optical modes of the ground state,first,second and third excited states of the solitons are obtained by using the squared operator iterative method of power conservation.And PT symmetric linear system with nonlinear PT symmetric optical model of the system of the eigenvalue and the relationship between the gain/loss factor comparison,and then by the numerical method can clearly see the eigen spectrum and the relationship between the intensity of non Hermitian,finally through step by step Fourier method with random disturbance of soliton transmission is simulated.Then,we aimed at scores of diffraction Kerr nonlinear conditions of PT symmetric waveguide model,in the same way with the square of power conservation operator iteration method for the ground state of optical soliton in the system,the first,second and third excited state optical model,and studied the different levy index cases soliton propagation constant on the relationship between the imaginary part of PT symmetric potential modulation depth,It is found that the fusion point of PT symmetric eigenspectrum increases with the increase of Levy exponent.Then we introduced the linear stability analysis method,and through the linear stability analysis of the stability of the optical model,we found that under certain parameter conditions,the ground state and the first excited state is the linear stability of the soliton,for the second and the third excited state mode with the increase of imaginary part PT symmetric modulation depth by the first stable transformation to the linear instability.Finally,the dynamic evolution process of these optical modes is numerically simulated by the fractional Fourier method,and the effectiveness of the linear stability analysis method is proved by comparison.From this,we can get the influence of the modulation depth of the imaginary part of the Levy index and the symmetry potential on the nonlinear optical solitons,which provides a new degree of freedom parameter for the transmission stability and modulation of the laser beam.