| A spatial optical soliton which is resulted from a balance between difrac-tion and self-focusing, is such a kind of nonlinear localized bound state that canmaintain its shape and energy during propagation. In last two decades, this re-search area attracts much attention from all over the world. Among the mostpopular topics, self-defection of screening photovoltaic spatial solitons, incoher-ent photorefractive spatial solitons, and azimuthons are discussed in detail in thisthesis. Meanwhile, fber laser amplifers which can be placed to a category of thetemporal solitons are also involved. The primary achievements obtained are thefollowing:1. Large self-defection of bright and dark screening photovoltaic soli-tonsIt is numerically demonstrated that large self-defection of both bright anddark screening photovoltaic solitons exit in LiNbO3crystal under an externalapplied feld, and it is also demonstrated that the self-defection not only connectswith the acceptor concentration NAbut also connects with the external appliedfeld E0. With a fxed value of E0, the lower the value of NA, the more obviousof the self-defection; with a fxed value of NA, the higher the value of E0, themore obvious of the self-defection. It is also found that self-defection of thebright screening spatial soliton and that of the dark one are diferent: the brightscreening photovoltaic soliton defects obviously; while only one side of the darksoliton defects, its extreme value point and the other side nearly do not defect.2. Existence of quasi-bright and gray-like incoherent photorefractivespatial solitons, and the splitting of the dark incoherent photorefrac-tive spatial solitonsIncoherent solitons are diferent from coherent solitons, because there is no relation among the phases at diferent points across an incoherent beam andincoherent beams spread much more quickly than coherent beams. In light ofthe sources are mostly incoherent in nature, it is very meaningful to study in-coherent solitons. Propagation properties of bright and dark incoherent beamsare numerically studied in photovoltaic-photorefractive crystal and in logarith-mically saturable nonlinear media by using coherent density approach and beampropagation method.Numerical simulations not only exhibit that bright incoherent photovoltaicquasi-soliton, gray-like incoherent photovoltaic soliton, incoherent soliton doubletand triplet can be established under proper conditions, but also display thatthe spatial coherence properties of these incoherent beams can be signifcantlyafected during propagation by the photovoltaic feld Eph.In logarithmically saturable nonlinear media, it is illustrated that nonlin-ear coefcient ν plays an important role on the propagation of incoherent soli-tons. Dark incoherent solitons will change into gray-like incoherent solitons uponpropagtion if ν is not so high. With increasing of ν, doublet or other higher evennumber stripes will appear under even initial conditions and triplet or otherhigher odd number stripes will appear under odd initial conditions. It is alsodemonstrated that the coherent length will increase close to the notch and de-crease sharply at the right notch place.3. Azimuthons can rotate rigidly in circular waveguides, while insquare waveguides the rotation is related to the modulation depthof the azimuthonsAzimuthons are azimuthally modulated beams, that exhibit steady angularrotation upon propagation. They can be considered as azimuthally perturbedoptical vortices, i.e. beams with singular phase structure.It is found that azimuthons in circular waveguides always rotate rigidly dur-ing propagation and the analytically predicted rotation frequency is in excellentagreement with numerical simulations. On the other hand, azimuthons in square waveguides may experience spatial deformation during propagation. Moreover,it is shown that there is a critical value for the modulation depth of azimuthonsabove which solitons just wobble back and forth, and below which they rotatecontinuously. By using the concept of energy diference between diferent orien-tations of the azimuthons, these dynamics are explained.4. Gaussian input and hyperbolic secant input can both converge tothe parabolic pulses in a optical fbre amplifer, while the speed isafected by its gain proflePulse propagation in a normal-dispersion optical fbre amplifer with an ar-bitrary longitudinal gain profle by self-similarity techniques. The functionalform of the development of low-amplitude wings on the parabolic pulse in thischapter, which are associated with the evolution of an arbitrary input pulse tothe asymptotic parabolic pulse solution. It is found that for the increasing gainthe amplifer output corresponding to the input Gaussian pulse converges to theasymptotic parabolic pulse solution more quickly than the output obtained withthe input hyperbolic secant pulse, whereas for the decreasing gain the input pulseprofles have nearly no efect on the speed of convergence to the parabolic pulsesolution. These theoretical results are confrmed by numerical simulations. |
