Study On Propagation Characteristics Of Spatial Solitons In Optical Lattices

Spatial solitons are optical modes that can propagate in nonlinear meidia while maintaining a constant shape and phase. Due to their unique properties, spatial solitons have found considerably potential applications in many fields such as optical switch, optical communication, data storage and particles manipulatation. Meanwhile, in optical lattices having a periodic refractive index distribution, the collective behavior of wave propagation exhibit many intriguing and unexpected phenomena that have no counterpart in homogeneous media. Combing the above two concepts(i.e., nonlinear effects and optical lattices) can further enrich the method of controlling and handling light. Thus study of dynamics of spatial solitons in optical lattices is of great importance. In this thesis, we first give a brief overview of the history and properties of spatial solitons in optical lattices, and then introduce the applied theoretical model and associated calculation methods, including plane-wave expansion method, Newton-Raphson iterative method, square-operator iterative method and split-step Fourier method. We chiefly study the existence and stability of spatial solitons in defective lattices, optical lattices with spatially modulated nonlinearity and PT-symmetric lattices. The main result are as follows:1. Surface defect gap solitons in two-dimensional optical latticesWe have studied surface defect gap solitons at an interface between two-dimensional optical lattices with a defect and uniform saturable Kerr nonlinear media. For negative defect, the surface defect gap solitons can exist in both semi-infinite gap and first gap. But in the semi-infinite gap, if e is lower than a critical value, there will no stable surface defect gap solitons. And in the first gap, the power of surface defect gap solitons is almost zero provided that the defect parameter e exceeds a threshold value. For the positive defect, surface defect gap solitons only exist in semi-infinite gap and stable in the low power region.2. Surface defect solitons at the interface between simple lattices and superlattices with spatially modulated nonlinearitiesWe have studied the properties of surface defect solitons at the interface between simple lattices and superlattices with spatially modulated nonlinearities. Numerical results reveal that for positive defects, surface defect soliton can only stably exist in low-power region of the semi-infinite gap and nonexistent in the first gap. While for the negative defects, surface defect solitons can stably exist in moderate-power region of semi-infinite gap, but in the first gap, surface defect solitons are stable in the most of the whole existence region. The threshold power for excitation of surface defect solitons grows with decrease of the refractive index in negative defects and vanishes for positive defects, and for fixed defect strength, the threshold power diminish following the drop in the nonlinearity modulation. Last but not least, the nonlinearity modulation may lead to a remarkable enhancement of the surface defect soliton’s mobility.3. Solitons in Gaussian potential with spatially modulated nonlinearityWe have studied the existence, stability and propagation dynamics of the solitons in Gaussian potential with both locally modulated nonlinearity and linear refractive index, including fundamental solitons and dipole solitons. The stability window of the fundamental solitons is continuous in the energy spectrum, while that of the dipole solitons is discrete and narrow; both of them shrink with an increasing nonlinear modulation depth. Also high power fundamental solitons may develop a significant power-dependent shape transformation if the nonlinear modulation is deep enough. The transverse mobility of fundamental solitons launched with a tilt angle was presented, and the critical tilt angles increase with a decrease of the propagation constant for soliton deflecting from the channel. In the region of small propagation constant only part of the soliton keeps oscillating in the channel and the other part would deflects away even if the tilt angle is smaller than the critical value.4. Solitons supported by defects of PT-invariant potentials with real part of dual-frequency latticesWe have studied the existence and stability properties of defect solitons in parity-time(PT) potentials whose real parts are dual-frequency lattices with a defect locating at the center. The impact of defect on the stability regions of defect solitons was investigated. For positive defects, fundamental solitons are always stable in the semi-infinite gap and nonexistent in the first gap. While for negative defects, in semi-infinite gap, fundamental solitons are stable in most of their existence region apart from low power region, but in the first gap, all the fundamental solitons are stable. The larger the modulation depth becomes, the narrower the stable region of fundamental soliton in the semi-infinite gap is and the wider that in the first gap is. Dipole solitons are unstable in the whole semi-infinite gap in spite of defects, but in the first gap they can be stable in the low power region for positive defects. The stable region of dipole in first gap broadens as the modulation depth becomes larger.5. Power-dependent shaping of solitons in PT-symmetric potentials with spatially modulated nonlinearityWe have studied the existence and stability of odd and even solitons supported by PT symmetric potentials with spatially modulated nonlinearity. Out-of-phase competition between the linear and nonlinear refractive indices not only substantially modifies the stability properties of both odd and even solitons, but also can result in a remarkable power-dependent shaping. The width of stability(instability) domain of odd(even) solitons shrinks quickly with the growth of nonlinearity modulation depth. In addition, the impact of variation of the amplitude of the imaginary part of the PT potential on the existence and stability of both odd and even solitons is also considered.