Interaction Between Solitons And Radiation & The Theoretical Study On Spatial Soliton Families In Logarithmically Nonlinear Medium

The main work of my thesis is composed of four parts, as follows:(1) Interaction between solitons and radiation is investigated by variational approach. It is analyzed in details by using the model of particles in the potential well .The pulse width probably exhibit three different evolution behaviors (contraction, broadening and periodical oscillation) in different conditions. The variation of potential function p( ) with the pulse width is strongly dependent of the values of amplification factor and field amplitude E0. The approximate analytical expressions of pulse width and chirp factor are obtained , and it is shown that the optical pulse oscillationly varies in the course of evolution because the nonlinear contraction or the radiation broadening dominates alternatively.(2) The explicit formula of Jost function pairs in the case of pure radiation is derived by using the dressing method , and the analysis of the interaction between solitons and radiation is made. It is found that the optical pulse, whose amplitude decays, finally evolves into the form of soliton-like wave in the absence of radiation. It is revealed that the factor plays an important role in the spectrum structures for the optical pulse output. The dynamic behavior of the soliton-like waves during the interaction between solitons and radiation is also analyzed. It is found that a mutual attraction of solitons appear due to the radiation scattering, which is unfavorable for the optical pulses in long-haul fiber communication.(3) The dynamic evolution equation for optical beams in the logarithm nonlinear medium is derived from Helmholtz Equation. The necessary condition for the existence of the bright, dark and gray spatial solitons in such medium is obtained by choosing some correct trial solutions of the equation. And further , we draw a conclusion that such proposition mentioned above is correct. The steady-state solutions to the bright, dark and gray spatial solitons described in the form of the equation's integral is made. Their relevant properties are alsodiscussed. Beam width for such spatial solitons dramatically decrease with the increasing power. When the peak power is low, the system exhibits some good nonlinear effects. The variation of beam width of all the spatial solitons is slow and becomes constant when the peak power of its pulse gradually increases to some extension. The physical origin of creating such phenomena is different for self-focusing and self-defocusing logarithm medium. In former case it derives from the material's saturation property. In latter case it results from the slow increase of its own nonlinearity.(4) It is shown that incoherently coupled bright-bright, gray-gray , dark-dark and bright-dark soliton pairs propagating collinearly can exist respectively in the logarithm medium under some steady-state conditions provided that they have the same polarization and wavelength.(a) A good synchronization is exhibited for the propagation of coupled bright-bright, gray-gray , dark-dark soliton pairs; (b) The intensity of the two beams plays an important role in the stable propagation of the coupled soliton pairs; (c) Only can the coupled dark-bright soliton pairs, which requires that the intensity of the dark component is slightly higher than that of the bright , propagate steadily in self-defocusing logarithm medium due to Modulation Instability(MI). It is revealed from our results that the coupled bright, dark and bright-dark hybrid soliton families are possible in such medium if we extend the physical model mentioned above to that of the multi-beams. Incoherently coupled soliton pairs can be reduced to the Manakov solitons for the case of a low power. The dark-dark, bright-bright and dark-bright soliton pair solutions can be solved exactly under steady-state conditions. Furthermore, the stability of such Manakov soliton pairs via the linear stability approach is analyzed.