Nonlinear Photonic Topological Insulators

这一提议的目的是通过使用耦合光波导系统来促进对无序光子拓扑材料中新的物理现象的理解。特别是，我们的理论和实验研究将涉及(1)拓扑非线性模式的研究；(2)新型晶格结构的研究，特别是Lieb和Kagome几何结构；(3)具有PT对称晶格结构的拓扑介质中的非线性波动动力学研究。除了揭示新的基本科学知识，这是基于我们使用高度可控的光学系统(即渐变耦合波导阵列)的复杂方法，我们的结果将具有直接的技术意义，因为它们可以用于远程通信和光子数据处理。我们将利用我们卓越的制造技术，允许单独解决许多物理问题。我们将把实验工作与理论分析相结合，以便更全面地解释我们的结果，并优化器件性能。本论文的目标是：(1)我们将首次在任何物理系统中演示拓扑非线性边缘模和拓扑孤子；(2)我们将从理论和实验上研究几何对线性和非线性拓扑模形成的影响；(3)我们将从理论和实验上分析PT对称光子介质中孤子和非线性拓扑边缘模的形成。我们将确定这种孤子的存在范围，确定它们的稳定性和动力学性质。

The aim of this proposal is to promote the understanding of new physical phenomena in disordered photonic topological materials, by using coupled optical waveguide systems. In particular, our theoretical and experimental research will address (1) Studies of topological nonlinear modes; (2) studies of novel lattice structures, in particular Lieb and Kagome geometries; (3) Studies of nonlinear wave dynamics in topological media with PT-symmetric lattice structure. Apart from revealing new and fundamental scientific knowledge, which is based on our sophisticated approach of using a highly controllable optical system (i.e., arrays of evanescently coupled waveguides), our results will have immediate technological significance, as they can be used in tele-communication and photonic data processing. We will take advantage of our superior fabrication technology that allows the individual addressing of numerous physical questions. We will combine the experimental work with theoretical analysis, in order to explain our results thoroughly and optimize device performance.The objectives of the proposed work are: (1) We will demonstrate, for the first time in any physical system, topological nonlinear edge modes and a topological soliton; (2) We will investigate, theoretically and experimentally, the impact of geometry on the formation of linear and nonlinear topological modes; (3) We will analyze the formation of solitons ad nonlinear topological edge modes in PT-symmetric photonic media, in theory and experiment. We will determine the regime of existence of such solitons, determine their stability and dynamical properties.