Solitons In Nonlinear Optical Couplers And Anderson Localization Of Surface Plasmon Polaritons

An effective approach for analyzing the properties of the nonlinear opticalcoupler is to study the soliton pairs in the coupler. Researches on the propertiesand dynamic evolutions of the soliton pairs provide parametric guidance foroptimization of the performance of the nonlinear optical coupler. Meanwhile,different response characteristics of the nonlinear mechanism and structuraldiversity of the couplers enrich the content the soliton and make more sense.One of the purposes of the thesis is to discuss the effect of nonlocal nonlinearityon the solitons in the coupler and the properties of surface lattice solitons. Fromthe perspective of inhibition of diffraction, soliton is an example of lightlocalization. Now, solitons in the strict periodic array and Anderson localizationin disorder waveguide array have attract a lot of interest of researchers, However,as far as we know, there is no reports on the Anderson localization of surfaceplasmon polaritons (SPPs) in the disorder metallic nanowire array. Consequently,another purpose of the thesis is to study the eigenmodes of SPPs in the disordermetallic nanowire array, expecting the realization of sub-wavelength Andersonlocalization.Firstly, we investigate the nonlinear dual-core coupler on the conditions ofweak and ultra nonlocalities. The effects of the weak nonlocality on thesymmetry breaking bifurcation (SBB) and stability of the soliton’s werepredicted through the variational approximation (VA) method. Numericalanalysis method also was adopted to study the three type of solitons and theSBB, while perturbation propagation method was used to analyze stability of solitons. The initial results show that the nonlocal nonlinearity shifts the SBB tohigher power area and makes all the asymmetric solitons stable in the wholeexistence area, which are in good agreement with the predictions by VA. Underthe ultra-nonlocal condition, the coupler model was proposed based on theSnyder-Mitchell(SM) model and SBB of the “access soliton” was analyzed byVA. In that case, the phase transition leads to the spontaneous breaking of theantisymmetry of the corresponding two-component “accessible solitons.”Surface lattice soliton is a result of the combined effect of discrete propertyand truncation of the system and the nonlinearity. We proposed the model of thenonlinear coupler，consisting of two semi-infinite waveguide array and analyzedthe three types of solitons and the SBB through the VA method and numericalanalysis method. We find that below a critical value of the coupling constant,branches of the symmetric and asymmetric modes separate, and accordingly,asymmetric solitons cease to bifurcate from the symmetric ones.Anderson localization in the disorder system is a common wavephenomenon. So, we propose the existence of Anderson localization of surfaceplasmon polaritons (SPPs) in the disorder metallic nanowire array. We calculatethe Anderson eigenmodes and analyze their properties in the disorder metallicnanowire array through the coupler mode theory and finite element method(FEM, based on the first principle). We study the effects of the metal and thegain of the background material on the formation and propagation of theAnderson mode in details. We choose a optimized condition to excite theAnderson mode in a enough short propagation distance， ensuring theexperimental realization. Furthermore, we also study the Anderson localizationof SPPs in two-dimensional metallic nanowire array.