Spin Orbit Coupling Effect On Dynamics Of Linear And Nonlinear Waves In Optical Lattices

In condensed matter physics,spin orbit coupling（SOC）refers to the coupling be-tween the spin angular momentum and the orbit angular momentum of the charged par-ticles.SOC is a necessary condition for various unique physical phenomenon,including spin Hall effect,topological insulator,Majorana fermions,and so on.However,cou-pling between spin and orbit depends on the intrinsic properties of material in the con-densate physics and difficult to engineer.Therefore,physicists make their efforts to"synthesize"spin-orbit coupling in a variety of physical systems to make this type of SOC tunable,thus we can systematically study abundant of novel physics related to SOC.In this thesis,two kinds of platforms,namely Bose-Einstein condensates（BECs）dressed by Raman lasers and photon-exciton-coupled semiconductor microcavity sys-tem,are used to synthesize the SOC.While optical lattice is introduced in these two systems,we can systematically explore the strength of pseudo-spin-orbit coupling on the characteristics and evolution of the wave in periodic and quasi-periodic systems.What particularly important is that both these two systems have a strong nonlinear physical mechanism that allows us to reveal the interaction between the nonlinear,spin-orbit coupling,and periodic potential.Our main work and discoveries are listed as below:First,taking Bose-Einstein condensate system with Raman laser as an example,we address the impact of the SOC on the localization properties of waves in Qua-si-periodic optical lattice.Quasi-periodic lattice is a superposition of two lattices with irreducible periodic.It is well known that with the change of relative amplitudes（p₂ p₁）in these two sub-lattices,scalar wave（i.e.,one component waves without SOC）will exhibit localization to delocalization transitions（LDT）at some specific am-plitude ratio.we found that SOC significantly affect the LDT of waves,and under some specific SOC strengths,the LDT corresponding to the value of p₂ p₁ in the SOC system can be much smaller than the system without SOC.A further analysis shows that the reason behind this reduced threshold is lies in the fact that moderate SOC in-duced the band flattening in period systems.An interesting thing happens when SOC strengths is relatively stronger,that is to say SOC drives the system into the state where its evolution becomes similar to the evolution of a one-component system.We also study the effect of nonlinearity on the LDT.Second,taking Lieb lattice introduced in the microcavity of photonic-exciton-coupled semiconductor microcavity system as an example,we adressed the character-istics of linear and nonlinear Waves in the systems of pseudo-spin-orbit coupling（originating from the energy splitting of two kinds of photon modes demonstrated as TE and TM polarization in the cavity）systems.Similar to the generally used honey-comb lattices,we also find edge modes protected by the topological at the edge of the Lieb lattice,and this topological feature exists even when we take the repulsive interac-tion between excitons（self-defocusing nonlinearity）into account,thus we can find a robust,unidirectional propagation of edge dark solitons.Third,we study the influence of Zeeman optical Lattice on the topological proper-ties of Wave in spin-orbit coupled System.In this work,the two components of waves feel the periodic potential with inverted amplitude（here we use the periodic honey-comb potential）.Unlike the traditional external potential,we use inhomogeneous field to simultaneously break time-reversal symmetry and to induce Dirac point in the spec-trum around which edge states appear.We found the edge states supported by two dif-ferent boundaries of the Zeeman optical lattice and this edge state occurs only when spin orbit coupling strength exceeds a certain threshold.Specifically,in compare with polariton system,we find nonlinear edge state with both attactive and repulsive nonlin-earity.Our research on this work,especially in the nonlinear wave,is undering further research,and we look forward to discovering some new features of the topological state in the Zeeman optical lattice.Finally,we introduce one of our work focus on the nonlinear plasmonic waves in chapter five.By introducing chirped characteristics in the metal waveguide array（such as monotonic variations of the distance between neighboring waveguides）to break the symmetry of the electromagnetic waves coupling between adjacent waveguides,we show an adjustable directional motion of the plasmonic lattice soliton and the formation of surface plasmonic solitons.