二维光子晶体板的介电常数分布具有面内的空间周期性，并支持可辐射到自由空间的导模共振。这些辐射到远场的模式可以用动量进行标记，并具有偏振态，因此可以定义动量空间中的偏振场。通过研究不同结构参数和对称性下偏振场的特性以及与外界相互作用的规律，能够为光场操控提供新思路。本文介绍了二维光子晶体板在动量空间中的偏振场的相关特性，并综述了近年来相关的研究和应用。

采用光束传播法对双芯光子晶体光纤中光纤结构参数对纤芯间耦合效率的影响进行分析。首先，根据双芯耦合原理，使用最小二乘法对波导间的耦合系数等参数进行估计，明确孔间距、纤芯折射率差、中央空气孔直径比例、纤芯直径比例、空气孔直径比例和空气孔对称度等参数对双芯光子晶体光纤耦合比及耦合区长度的调节作用，提出一种基于双芯光子晶体光纤的耦合器性能粗调与微调设计方法。然后，根据这一耦合器设计方法，提出一种非对称的双芯光子晶体光纤宽带定向耦合器。该耦合器在1.31~1.55 μm区间实现了50%±5%的耦合比，带宽为240 nm，并具有3 mm的超短耦合长度。本研究成果可为光纤宽带定向耦合器的高效设计提供有意义的参考。

The immunity of topological states against backscattering and structural defects provides them with a unique advantage in the exploration and design of high-precision low-loss optical devices. However, the operating bandwidth of the topological states in certain photonic structures is difficult to actively tune and flexibly reconfigure. In this study, we propose a valley topological photonic crystal (TPC) comprising two inverse honeycomb photonic crystals, consisting of hexagonal silicon and Ge₂Sb₂Te₅ (GST) rods. When GST transitions from the amorphous phase to the crystalline phase, the edge band of the TPC appears as a significant redshift and is inversed from a"∪"to an"∩"shape with topological phase transition, which enables active tuning of the operating bandwidth and propagation direction of topological edge states. Both the topological edge and corner states in a triangular structure constructed using TPCs can be simultaneously adjusted and reconfigured via GST phase transition, along with a change in the group number of corner states. Using the adjustability of topological edge states and electromagnetic coupling between two different topological bearded interfaces, we develop a multichannel optical router with a high tuning degree of freedom, where channels can be actively reconfigured and their on/off states can be freely switched. Our study provides a strategy for the active regulation of topological states and may be beneficial for the development of reconfigurable topological optical devices.

二维光子Moiré超晶格拥有一些常规光子晶体不具备的特性，例如平带特征和不同于安德森局域化的光局域现象。本文利用多光束干涉法构建二维光子Moiré超晶格结构，采用有限元法对其能带结构及光场特性进行研究。通过优化Moiré晶格厚度、空气孔半径对其平带及局域特性的影响，得到了高局域特性的Moiré晶格结构。研究中发现，正方晶格具有不同于六角晶格的准狄拉克锥光局域化效应。本文研究结果对发展高性能微纳结构器件具有重要参考价值。