基于非线性拓扑绝缘体的新型光场调控

In recently years the physics community has witnessed a hot research interest on a new material named topological insulators. Nevertheless, most of the research endeavors on topological insulators thus far have been limited in the regime of linear physics and linear optics, meanwhile very few attentions have been paid onto the amplitude and phase structures of the topological edge states. Here we propose to investigate the nonlinear photonic topological insulators, and combine topology and nonlinearity to construct novel light fields. We aim to investigate two types of nonlinear topological insulators, the first of which are the ones with a broken time-reversal-symmetry, for which we will use the arrays of helical waveguides as a specific realization to study the impact of the various realistic nonlinear responses on the formation of robustly unidirectionally propagating and meanwhile two-dimensional localized edge state, as well as the formation of two-color topological edge states mediated by the nonlinear wavelength conversion. The second type of topological insulators are the ones with time-reversal-symmetry, and here we will use valley Hall insulators that are readily accessed in photorefractive crystals, to study the nonlinearity-induced localized vortical state and the coupling of orbital angular momentum with valley, as well as the correspondingly enhanced robustness of the edge state, so that the creation of localized vortical state that has a definite propagation direction, a definite orbital angular momentum together with a definite linear momentum. This proposal involves not only theoretical analysis and numerical simulation, but also experimental study. The nonlinear photonic topological insulators have unique application in the construction of novel light field and novel optical functional devices.

近年来，拓扑绝缘体成为光学和物理学研究的热点，然而这方面的研究绝大部分局限在线性范畴，也极少关注拓扑边缘态的振幅和位相结构。本项目提出研究非线性光学拓扑绝缘体，并结合非线性和拓扑构建新型光场。我们拟研究两类非线性拓扑绝缘体，第一类是时间反演对称性破缺的系统，这方面将以实验较易实现的螺旋波导阵列为例，研究各类实际的非线性光学响应对拓扑边缘态的作用以期得到稳定的单向传输且两维局域的边缘态，以及通过非线性波长转换得到双色拓扑边缘态；第二类是保持时间反演对称的系统，这方面将以较易实现的能谷霍尔效应为例， 研究非线性引入的涡旋局域态, 探索轨道角动量和能谷的耦合，以及由此带来的边缘态鲁棒性的增强，得到既有特定传输方向又有特定角动量和线动量的局域的涡旋光场。本课题既涉及理论研究和数值模拟, 又有实验研究。非线性光学拓扑绝缘体在构建新型光场、实现新型光子器件方面具有独特的应用价值。

材料科学的每一次新发展总给非线性光学带来新的机遇和挑战。近年来，一种名叫拓扑绝缘体的材料成为物理学研究的热点，然而，该方面的研究绝大部分局限在线性物理和线性光学的范畴，对光学拓扑绝缘体的非线性特性的研究尚处于起步阶段。本项目通过构建新型光子晶格，研究非线性和拓扑之间的相互作用，关注新形式的光束局域，非线性如何改变拓扑态，以及拓扑如何影响传统的非线性态。通过设计光子莫尔晶格，实现了线性条件下的光波局域和低功率下的空间光孤子；通过非线性效应，展示了拓扑边缘态的两维局域，即拓扑光孤子的存在；通过在非线性晶体中构建打破z-向反演对称性的光子晶格，将索利斯泵浦推进到了非线性范畴，发现了索利斯泵浦的方向和幅度的非线性可调性，揭示了索利斯泵浦的分数阶化和冻结现象的物理机制；在交错型蜂窝状光子晶格中实现了涡旋孤子轨道角动量和能谷之间的耦合效应等。本课题既涉及理论分析和数值模拟, 又有实验研究。这些研究发现对于实现新型光开关、可调光学延时线等新型光子器件具有潜在的应用价值。