Theoretical Study On Holographic Optical Solitons

In optically materials, cross-phase modulation (XPM) has been traditionally believed to be always accompanied by self-phase modulation (SPM). However, a new kind of spatial solitons, holographic solitons, has been suggested theoretically in photorefractive media and can be supported by strong XPM but lack SPM altogether. For holographic solitons, the interference of two mutually coherent beams will induce a grating in refractive index and lead to simultaneous trapping of the two beams in a form of spatial solitons via XPM, arising from Bragg diffraction from the induced grating. The presence of both beams is required and each beam is a necessary component of a holographic soliton, since each beam alone cannot survive as a soliton if the other beam is absent. A considerable research interest has been invested in the study of holographic solitons due to its specialty.In this dissertation we investigate theoretically the properties of waveguide induced by holographic solitons in Hamiltonian system, and the stability of holographic soliton solutions in dissipative system (DHS), and holographic soliton solutions with two significantly different components in both Hamiltonian system and dissipative system.Based on the theoretical model of holographic solitons in Hamiltonian system, we analyze the properties of waveguided induced by bright holographic solitons with two identical components. We find that the number of possible guided modes in such waveguide is solely dependent on the intensity ratio of the soliton, which is the ratio between the soliton max intensity and the sum of background illumination. The number of guided modes increases monotonically with increasing intensity ratio. We perform numerical simulation of the wave guiding in such waveguide for guided mode beams and cosine waves and sine waves. The results imply that it is possible to realize the wave guiding in the bright holographic soliton-induced waveguide for a probe beam periodic in one dimension and with slowly varying amplitude.In a proposed model for DHS, one beam can act as pump beam to supply energy for the other beam, which behaves as the signal beam. And the intensity of pump beam has been considered as constant so that the evolution of pump beam is ignored. Based on such model, a numerical study is performed on the stability property of DHS solutions through analyzing the role of every single system parameter, such as the linear loss of the crystal, the external biased field. For comparison, a theoretic analysis on the stability of DHS solutions is presented. Both numerical result and theoretic result indicate the signal soliton beam is stable against small perturbation under the assumption that the evolution of pump beam is ignored. However, further investigation reveals that the assumption of constant pump beam intensity will bring the depleted effect and the modulational instability (MI) on pump beam, which can greatly influence the stable propagation of signal beam. Proper DHS solutions should be obtained in the model with the evolution of pump beam.In order to obtain the holographic soliton solutions with two constituents significantly dissimilar, a mode coupling method is applied in Hamiltonian system. The coupling between two modes of the same mode-order will give rise to single hump-single hump, two humps-two humps, and multihumps-multihumps holographic soliton solutions with arbitrary amplitude. And the coupling between two modes of different mode-order can generate single hump-two humps, two humps-multihumps, and single hump-two humps holographic soliton solutions. These results will lead to the enormously various shapes for holographic solitons and greatly enriches the form of holographic solitons, and expand the range of parameters of holographic solitons. On the other hand, the mode coupling method can be extended to dissipative system and find the corresponding DHS solutions without the MI on pump beam. Moreover, a clear vision on XPM can be available through such mode coupling processes, especially the influence induced by mode-order as well as the peak intensity of soliton on XPM.