非线性光学耦合器中的孤子和表面等离子波的安德森局域
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摘要
研究非线性光学耦合器特性的一种有效方法是研究耦合器中存在的孤子对。通过研究孤子对的属性和动力学演变，可以为优化非线性光学耦合器的性能提供参数指导；而与此同时，非线性机制的不同响应特性和耦合器结构的多样性，也为空间光孤子的研究赋予了更丰富的内容和意义。本论文主要目的之一是探讨非局域非线性对耦合器中孤子的影响以及非线性耦合器中表面格子孤子的行为。从光束的衍射抑制这一角度来看，孤子也可以看作是一种光的局域。目前，严格周期阵列中的光孤子和无序波导阵列中的光的安德森局域都是研究的热点。但是,据我们所知无序体系中表面等离子波的安德森局域现象还未有报道。因此，本文的另一个目的是研究无序金属纳米线阵列中的表面等离子波的本征模式分布，期待实现亚波长尺度上的安德森局域。
首先，我们研究了弱非局域非线性和极端非局域非线性条件下的光学双芯耦合器。采用变分法近似(Variational approximation-VA)预测了弱非局域非线性对孤子对称性破缺(Symmetry breaking bifurcation-SBB)和稳定性的影响。同时，采用系统的数值方法研究了系统中存在的三种孤子类型及其对称性破缺，并采用微扰传输法分析了孤子的稳定性。研究结果显示非局域非线性使得孤子的SBB分歧点移动到更高的能量值区域，并且加强了不对称孤子的稳定性，最终使存在于整个区域中的不对称孤子全部稳定，而这一结果与VA方法预测的结果吻合很好。在极端非局域非线性情况下,我们提出了基于Snyder-Mitchell(SM)模型的耦合器模型，并且采用VA方法预测了“线孤子”的对称破缺，结果显示相变导致了“线孤子”相应的两个分量的反对称自发破缺。
表面格子孤子是由系统的离散性和边界截断效应以及非线性共同作用的结果。我们提出了由两个半无限大离散波导阵列组成的耦合器模型，并采用变分法和数值分析法，分析了表面格子孤子的三种类型及其对称性破缺和稳定性。研究发现在耦合常数低于某一临界值时，不对称孤子不再由对称孤子破缺产生，而是独立地存在。
无序体系中的安德森局域是一种普遍的波动现象，因此，我们提出无序金属纳米线阵列中也存在表面等离子波的安德森局域。我们采用耦合模理论和基于第一性原理的有限元方法求解了无序金属纳米线阵列中的安德森局域本征模，并且分析了本征模的特点。研究了金属损耗和介质的增益是否影响安德森局域模式的形成和传输。通过选择合适的激发条件，在尽可能短的距离内激发出安德森局域模式，以保证能够在实验上实现。另外，我们也研究了二维无序金属纳米线阵列中的安德森局域现象。
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.
首先，我们研究了弱非局域非线性和极端非局域非线性条件下的光学双芯耦合器。采用变分法近似(Variational approximation-VA)预测了弱非局域非线性对孤子对称性破缺(Symmetry breaking bifurcation-SBB)和稳定性的影响。同时，采用系统的数值方法研究了系统中存在的三种孤子类型及其对称性破缺，并采用微扰传输法分析了孤子的稳定性。研究结果显示非局域非线性使得孤子的SBB分歧点移动到更高的能量值区域，并且加强了不对称孤子的稳定性，最终使存在于整个区域中的不对称孤子全部稳定，而这一结果与VA方法预测的结果吻合很好。在极端非局域非线性情况下,我们提出了基于Snyder-Mitchell(SM)模型的耦合器模型，并且采用VA方法预测了“线孤子”的对称破缺，结果显示相变导致了“线孤子”相应的两个分量的反对称自发破缺。
表面格子孤子是由系统的离散性和边界截断效应以及非线性共同作用的结果。我们提出了由两个半无限大离散波导阵列组成的耦合器模型，并采用变分法和数值分析法，分析了表面格子孤子的三种类型及其对称性破缺和稳定性。研究发现在耦合常数低于某一临界值时，不对称孤子不再由对称孤子破缺产生，而是独立地存在。
无序体系中的安德森局域是一种普遍的波动现象，因此，我们提出无序金属纳米线阵列中也存在表面等离子波的安德森局域。我们采用耦合模理论和基于第一性原理的有限元方法求解了无序金属纳米线阵列中的安德森局域本征模，并且分析了本征模的特点。研究了金属损耗和介质的增益是否影响安德森局域模式的形成和传输。通过选择合适的激发条件，在尽可能短的距离内激发出安德森局域模式，以保证能够在实验上实现。另外，我们也研究了二维无序金属纳米线阵列中的安德森局域现象。
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.
引文
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