Nonlocal Spatial Optical Solitons In The Numerical Study

The width of optical beams undergo broaden for the natural diffraction when they propagate in linear isotropic media. But in some nonlinear materials, the power of optical beams can induce the change of refractive index and arose the self-focusing effect. In this way, the beam's width does not spread again when the self-focusing effect balances the diffraction effect. This is called a spatial soliton.If the spatial soliton propagate in the nonlocal nonlinear medium, it would be called the nonlocal spatial soliton. The nonlocal soliton had been found such as in the nematic liquid crystals, emieonduetor electronie, Bose-Einstein condensation,C2S and so on. Its equation is seem not complex and the theory is not abstruseness in the first see. But people still connot find a effective mathematics technique for its mathematic analytical solution. The focus of this work is to discuss the property of solitary wave propagating in the nonlocal nonlinear materials, which would play important role in the all-optical control and all-optical communication in the future.First of all, a nonlinear schrodinger equation is obtained from the Maxwell equation in the condition of the optical beams propagating in the strongly nonlocal nonlinear media, and a approximate analytical solution of Gauss beams is found in the 2D strongly nonlocal nenlinear media. The optical beams width is a sine function, the beam width and the period of the beam width relate to the input power. Recurrence formula which describes optical beams propagating in the nonlocal media is obtained from the split-step Fourier method. The analytical solution is compared with the numerical solution in this part, and numerical method is made use of simulate the reciprocity of two optical beams.In the second place, more apices structure H-G solution is obtained based on the 3D nonlinear schrodinger equation. The property of ellipse Gauss optical soliton propagating is discussed in the nonlocal nonlinear materials and this dissertation analyse the influence of the series and the input power about the optical beams width, and the beams interaction in the condition of different series or input optical power.The propagation of spatial soliton is investigated in the nematic liquid crystals. Base on the theory of liquid crystalline continuous elastomers and theory of minimizing of the total free energy, The response function of nematic liquid crystals is found in the laser input and make use of difference alternate method and split-step Fourier method to numerical simulate property of nematic liquid spatial soliton. In the end, this dissertation compare the propagation of the general single optical beam with the single soliton and study the interaction of two soliton in the nematic liquid. It is found that the solitons always attract each other and connot be affected by their phase.