The Research Of Modulational Instability Based On The Exact Solution Of Optical Lattice Soliton

In this paper, we derived the soliton solutions of the nonlinearSchrodinger equations with lattice modulation by analytical method. Themodulation instability of the soliton solutions was studied by numericalmethod. Optical soliton is one of the focus research subjects in recentyears and the theory of the optical solitons has matured. The formmechanism of the optical soliton is the balance effect of the light pulsedispersion and self-phase modulation effects or the spatial beamdiffraction and the beam self-focusing. Optical lattice solitons recently hasbeen put forward as a new concept of the solitons; it is to create an opticallattice in transmission medium by a periodic or aperiodic modulation ofthe refractive index, which makes the soliton exist and stable. This opticallattice is kind of external potential. Compared with the traditional solitonmodels, the control of the solitons in optical lattice is convenient andflexible, and diversity. These characteristics makes the optical lattice agreat application prospects in optical switches, optical fiber communication, optical storage, optical control of light, beammanipulation of particles and other areas.1. We obtained the soliton solutions of the nonlinear Schrodingerequations (NLSE) with lattice modulation, and analyse its propagationcharacteristics. Finding exact solutions to these equations in latticemodulation is a problem of great significance. Soliton in optical lattice isbased on the NLSE, with optical lattice; the equation is complex and itssolution is hard to derive. Only part of the solution with certain conditionscan be derived. First we deduced the solutions of the (1+1) D NLSE withtime and spatial modulated. We find these solutions can be used indifferent kinds of external potentials, such as optical potential, parabolicpotential and double-well potential and so on. We can control thepropagation of the solution if we control the lattice modulation. Also wededuced the analytical solutions of the2D NLSE with Jacobean ellipticfunction modulated by an improved homogeneous balance principle andF-expansion technique. We study the influence of the chirp and diffractiveto the solution and study the evolution regulation of the solutions. 2. We analyse the modulation instability of the soliton solution.Result shows that the propagation characteristics of the perturbation areaffected by both the modulation depth and the period of the optical lattice,especially the period. Propagation of the beam with initial modulation willbe controlled if we choose the appropriate lattice modulation parameters.Stability is one of the important subjects of the soliton study. It is difficultto obtain the soliton solution of the NLSE with optical lattice, only smallclasses exact solutions with certain peculiar boundary condition areobtained; so modulation instability based on NLSE with optical lattice isnot carefully investigated, especially based on exact solutions. In thispaper, we obtained the exact solutions of the NLSE with optical lattice,and then added a perturbation to analysis the modulation instability. Wededuced the perturbation coupled equation, and use numerical method tosolve the coupled equation. The noise gain how to be affected by latticemodulation is investigated.