在非线性光学领域，空间光孤子是由光的衍射效应与介质的非线性效应相互平衡而形成的一种横向分布保持不变的稳定光束。由于空间光孤子的稳定传播特性，它可以作为一种信号载体，在光通信领域具有广阔的应用前景。空间光孤子的研究和材料科学与技术的发展息息相关。为了实现纳米尺度的空间光孤子，人们基于表面等离激元(surface plasmon polaritons，SPPs)构建了不同的纳米结构。这类结构通常是由金属和非线性介质构成的周期性光学离散系统，也被称为表面等离激元晶格(plasmonic lattice)。表面等离激元是由光在金属表面激发的电子密度起伏与外部光场耦合而形成的一种表面电磁波。它具有很强的光场局域性，能够增强光与物质之间的相互作用，从而降低介质非线性效应的阈值。因此，表面等离激元晶格中的空间光孤子局域性也会提高，其横向尺度可以达到亚波长量级。由于表面等离激元晶格具有周期性，光在这类结构中的传播类似于固体物理中电子在周期性晶格中的运动，因此合理地设计表面等离激元晶格的光子能带可以有效地控制光的衍射，进而调控光孤子的传播。在表面等离激元晶格结构中形成的空间光孤子被称为表面等离激元晶格孤子(plasmonic lattice solitons，PLSs)，在集成纳米光子器件和光信息处理领域具有重要的理论和应用价值。 在探索新型表面等离激元材料方面，石墨烯这种二维单原子层材料近年来受到了广泛关注。与金属相比，石墨烯的表面等离激元具有更强的局域性以及更低的传播损耗，而且石墨烯本身具有较强的三阶非线性效应，如饱和吸收非线性和光学克尔效应。此外，石墨烯的表面电导率可以通过外加电场或化学掺杂的方式进行调节，从而使基于石墨烯的纳米结构能够更加灵活地调控光的传播。因此，利用石墨烯周期阵列结构取代金属阵列结构产生的表面等离激元晶格孤子，具有更小的横向尺度以及更加灵活的光场调节能力。本文的研究内容包括以下四个方面： (1)研究了单周期石墨烯阵列中形成的表面等离激元晶格孤子。通过基于麦克斯韦方程组的频域有限差分法模拟出石墨烯阵列中表面等离激元晶格孤子的横向分布和传播。讨论了阵列中介质的自聚焦或自散焦非线性与石墨烯的非线性同时对光孤子形成的影响。另外还分析了阵列的周期、石墨烯的化学势以及入射光的强度对孤子横向宽度的影响。研究发现，通过调节石墨烯的化学势可以对表面等离激元晶格孤子的横向宽度进行灵活的调控。 (2)研究了双周期石墨烯阵列中的表面等离激元矢量孤子。单层石墨烯只能支持一种反对称的SPP模式，而由两层石墨烯构成的一组石墨烯对可以支持对称和反对称两种模式。因此，与单周期石墨烯阵列结构相比，双周期石墨烯阵列对应的衍射关系曲线有两条。矢量PLSs的两个光场分量分别对应不同衍射关系曲线中的模式并且具有不同的频率，这样两分量互不相干并通过互自陷效应形成稳定的矢量PLSs。若撤走其中一个光束分量，另一个分量就无法继续稳定传播，而是发生衍射。表面等离激元矢量孤子各分量之间的相互制衡机制有利于人们进一步探索光控光方面的应用。 (3)研究了半无限单周期石墨烯阵列中的表面等离激元界面孤子。在入射光功率相同的情况下，界面孤子比完整单周期阵列中的PLSs具有更强的局域性，而且因其处于阵列边界，也更易于通过外部光场激发。在界面孤子稳定传播的基础上，我们通过调节参数使SPPs的离散衍射效应比非线性效应更强，以致SPPs局域波包以不同的程度向阵列内部逐层扩散，这将有利于发展亚波长尺度下光路由方面的应用。 (4)研究了半无限双周期石墨烯阵列中的表面等离激元界面矢量孤子。结合以上石墨烯阵列中矢量孤子和界面孤子的相关研究，我们在半无限双周期石墨烯阵列中实现了界面矢量孤子。它不仅具有界面孤子的强局域性及易于激发的特点，还具有矢量孤子的光控光特性。这对于构建全光纳米光子器件方面具有重要的应用价值。 关键词：空间光孤子 表面等离激元 石墨烯 光学克尔效应

 In the field of nonlinear optics, optical spatial solitons are stable beams whose transverse distribution remains unchanged due to the balance between light diffraction and nonlinear effect. Because of its stable propagation, optical spatial solitons can be used as a signal carrier and has broad application prospects in the field of optical communication. The study of optical spatial solitons is closely related to the development of materials science and technology. In order to realize nanoscale optical spatial solitons, different types of plasmonic structures have been constructed. These structures are usually periodic optical discrete systems consisting of metal and nonlinear dielectric, which are also known as plasmonic lattices. Surface plasmon polaritons (SPPs) are a type of surface electromagnetic waves formed by the coupling of the electron density fluctuation on the metal surface with the external light field. SPPs exhibit strong localization of optical field, which strengthen the interaction between light and matter, thus reducing the excitation threshold of nonlinear effect. Therefore, the locality of optical spatial solitons will also be improved, and their transverse scales can reach subwavelength scales. Due to the periodicity of plasmonic lattices, the propagation of light in such structures is similar to the motion of electrons in periodic lattices in solid state physics. Therefore, a reasonable design of photonic band sructure for plasmonic lattices can effectively manage the light diffraction, and then control the soliton propagation. Optical spatial solitons formed in plasmonic lattices are called plasmonic lattice solitons (PLSs), which have important theoretical significance and application value in the field of integrated nanophotonic devices and optical information processing. Among new plasmonic materials, graphene, a 2D carbon-atom monolayer structure, has attracted much attention in recent years. Compared with metals, SPPs in graphene have stronger locality and lower propagation loss, and graphene itself possesses stronger third--order nonlinear effects, such as saturable absorption and optical Kerr effect. In addition, the surface conductivity of graphene can be modulated by external electric fields or chemical doping, so that the light propagation in graphene-based nanostructures could be controlled flexibly. Therefore, plasmonic lattice solitons supported by periodic graphene sheet arrays would exhibit smaller transverse scales and more flexible tunability, in comparison with those in metallic arrays. The main work is included as follows: Firstly, we investigate plasmonic lattice solitons in monolayer graphene sheet arrays (GSAs). Plasmonic lattice solitons in GSAs are simulated by using finite-difference frequency-domain method based on Maxwell equations. The influence of both dielectric and graphene nonlinearity on the soliton formation are also discussed. In addition, the effects of the array period, graphene chemical potential and light intensity on the soliton width are analyzed. In the study, we find that the soliton width could be modulated flexibly by tuning graphene chemical potential. Secondly, we investigate vector plasmonic lattice solitons in graphene-pair arrays (GPAs). Single graphene sheet can only support antisymmetric SPP mode, while the graphene pair composed of two graphene sheets can support both symmetric and antisymmetric modes. Therefore, in comparison with single-period GSAs, there are two diffraction-relation curves for GPAs. Two components of vector PLSs correspond to the modes in different diffractionrelation curves and have different frequencies, so they are incoherent to form stable vector PLSs through mutual self-trapping effect. If one light beam is switched off, the other one can not continue propagating stably but diffracts. The interaction between different components of vector PLSs would be useful to explore light-control-light technology. Thirdly, we investigate the surface plasmonic lattice solitons in semi-infinite graphene sheet arrays. In comparison with the bulk PLSs in infinite GSAs, the surface PLSs exhibit stronger locality and are more convenient to excite. On the base of surface PLSs stable propagation, we make light discrete diffraction effect stronger than the nonlinear effect by reducing the incident light intensity or enhancing graphene chemical potential, so that SPPs diffuse into the array layer by layer. This would promote the application in optical routing. Finally, we realize the surface vector PLSs in semi-infinite graphene-pair arrays theoretically. Based on the above researches on vector PLSs and surface PLSs in graphene sheet arrays, we realize surface vector solitons in semi-infinite graphene-pair arrays. Surface vector PLSs have the features of suface solitons including strong locality and being convenient to excite, but also the light-control-light properties of vector solitons. This would have significant applied value in constructing all-optical nanophotonic devices. Keywords: optical spatial solitons; surface plasmon polaritons; graphene; optical Kerr effect