Spatial Optical Solitons In Nonlinear Media

Optical spatial solitons are light beams that do not broaden because of thebalance between diffraction and nonlinearity. They propagate and interact with oneanother while displaying properties that are normally associated with real particles. Inrecent years, a large number of studies are focused on optical solitons. The studies onoptical solitons have greatly enriched the knowledge about the interaction betweenoptical field and materials. There are huge potential industrial applications of opticalsolitons. Scientists in Bell laboratory have showed the possibility of using temporaloptical soliton technology in sihca optical fibers to improve the operation ofcommunication system therefore to increase the transfer rate. The possibility of usingspatial optical solitons to realize all-optical switching and all-optical router was alsoinvestigated. It can be expected that more and more applications of optical solitonscould be revealed as subsequences of the blooming of researches on optical solitons.The main objective of this thesis is the investigation of new techniques for solitoncontrol in nonlocal nonlinear media and optical lattice.In this thesis, we introduce the background about the studying of spatial opticalsolitons, the nonlinear media which can hold spatial optical solitons, all kinds ofspatial optical solitons, literatures reports on nonlocal spatial optical solitons andspatial optical solitons in optical lattice in Chapter1.Chapter2focuses the propagation of dark solitons in a weakly nonlocalself-defocusing Kerr-type nonlinear medium. Based on the variational principle, weget an analytical solution of such nonlocal dark solitons. We also clearly give theexpression describing the transverse velocity of the dark solitons. We find that thewidth of the dark solitons is related to the degree of nonlocality and the grayness ofthe solitons, that there exists a threshold of the degree of nonlocality for such nonlocaldark solitons, and that, as the degree of nonlocality increases, the velocity of thesolitons will decrease. We also demonstrate the stability of the nonlocal dark solitons.We investigate the existence and stability of dipole-mode solitons intwo-dimensional models of nonlocal media with anisotropic Kerr nonlinearity analytically and numerically in Chapter3. We obtain the approximate solution of suchelliptic dipole solitons by using the variational approximation. The dynamics of suchdipole-mode solitons is governed by the eccentricity of both the input beam and thenonlocal response function. We also compute the stability of the solitons by directnumerical simulations. The effects of the anisotropy of the nonlocal response functionon the propagation of the dipole beam are also discussed in detail.Chapter4treats both azimuthally and radially polarized vortex solitons in highlynonlocal nonlinear media. We get exactly analytical solutions of azimuthallypolarized vortex solitons with only polarization singularities and radially polarizedvortex solitons with both phase singularities and polarization singularities. Bothazimuthally and radially polarized vortex solitons can exist in nonlocal self-focusingnonlinear media with proper modulation of the beam power and the degree ofnonlocality. Contrary to those of radially polarized counterparts in local Kerr media,the topological charge can be any integer. When the topological charge m0, bothphase singularities and polarization singularities work. Only the polarizationsingularities work for the case m0. Azimuthally polarized vortex solitons withpolarization singularities corresponds to the linearly polarized vortex solitons withsingle charge. Our results show that polarization singularities work the same way asphase singularities in some sense.Chapter5is devoted to analyzing the stability of solitons in parity-time(PT)-symmetric periodic potentials (optical lattices) in both one-and two-dimensionalsystems. First we show analytically that when the strength of the gain-loss componentin the PT lattice rises above a certain threshold (phase transition point), an infinitenumber of linear Bloch bands turn complex simultaneously. Second, we show thatwhile stable families of solitons can exist in PT lattices, increasing the gain-losscomponent has an overall destabilizing effect on soliton propagation. Specifically,when the gain-loss component increases, the parameter range of stable solitonsshrinks as new regions of instability appear. Third, we investigate the nonlinearevolution of unstable PT solitons under perturbations, and show that the energy ofperturbed solitons can grow unbounded even though the PT lattice is below the phasetransition point.Finally, Chapter6summarizes the main results obtained in the thesis and discusses some open prospects.