Study On Spatial Solitons In Photorefractive Crystals With Both The Linear And Quadratic Electro-optic Effects

Since their unique features of formation at low laser power and potential important applications, photorefractive spatial solitons have attracted enormous interest and the rapid process has been achieved both in theory and experiments in a relative short period. So far, photorefractive spatial solitons resulting only from the linear electro-optic effect or quadratic electro-optic effect have been extensively studied and reported. However, a number of new photorefractive materials that have large electro-optic effects including both the linear and quadratic electro-optic effects near the phase-transition temperature have been found, such as KTaxNb1-xO3(KTN) crystals, Li Nb O3 crystals, [Pb(Mg1/3Nb2/3)O3](1-x)-(Pb Ti O3)x(PMN-x PT) single crystals, and so on. In this case, the refractive index changes in materials are simultaneously governed by both the linear and quadratic electro-optic effects. In this dissertation, the spatial solitons due to both the linear and quadratic electro-optic effects are investigated systematically.Based on Kukhtarev model and Castro-Camus model, the evolution equations of the incident optical beams propagating in biased single-photon or two-photon photorefractive crystals are firstly derived, which exhibit dark, bright and gray spatial soliton states under appropriate conditions. Moreover, the existence conditions and properties of these spatial solitons are discussed in detail. The evolution equations, analytic solutions and the expressions of soliton widths in the low-amplitude regime are presented. The dependences of soliton width on the applied biased field in the low-amplitude case are also investigated. Our results show that these solitons owe their existence to the co-effects of both the linear and quadratic electro-optic effects. Photorefractive effects can be enhanced, weakened or even counteracted because of the interaction of these two electro-optic effects.The incoherent coupling of two or multiple spatial solitons in biased single- photon or two-photon photorefractive crystals with both the linear and quadratic electro-optic effects is investigated. It is predicted that dark-dark, bright-bright, gray-gray and dark-bright soliton pairs(or dark, bright, gray and dark-bright spatial soliton families) can be supported provided that the incident beams have the same polarization, wavelength and are mutually incoherent. Furthermore, Manakov soliton pairs can be established in three possible realizations: dark-dark, bright- bright and dark-bright when the total intensity of two incident beams is much lower than the sum of the background and dark irradiance intensities.The stabilities of these spatial solitons or soliton families(pairs) are analyzed by means of beam propagation methods. It is found that bright spatial solitons or soliton families(pairs) are stable, i.e., incident beams can reshape theirself and evolve into a solitary wave after a short distance, whereas dark solitons or soliton families(pairs) cannot propagate steadily and will breakdown during propagation process against small perturbation.The effects of diffusion on self-deflection of steady-state bright spatial solitons are studied systematically by both the beam propagation methods and perturbation methods. Our results show that the soliton propagates along a parabolic trajectory, whereas the central spatial frequency component shifts linearly with the distance. Both the lateral displacement and angular deflection vary cubically with the applied bias field, and increase with considerably at higher values of applied bias field.The theoretical analysis of temperature effects on the stability, intensity profile, self-deflection process of bright spatial solitons in biased single-photon photorefractive crystals with both the linear and quadratic electro-optic effects is presented. Three physical factors related to the temperature, i.e., the dielectric constant, dark irradiance and diffusion effect are considered. It is shown that bright solitons can evolve into a new solitary wave in the vicinity of reference temperature 0T, whereas the incident beam cannot involve a stable bright soliton, but tends to experience lager cycles of compression and expansion and its maximum amplitude oscillates with propagation distance or to breakdown when the temperature of photorefractive crystal is far away from 0T. The intensity profile of bright solitons decreases as T increases. However, the temperature dependence of soliton width is related to the input power density 0r. The dark irradiance dominates the temperature dependence of displacements in range of phase-transition temperature. If the temperature continues to rise, the dielectric constant and diffusion effect will become more and more important in the self-deflection process and the dielectric constant will play decisive roles when T tends to Curie temperature, i.e.,CT â†'T.