二维光子准晶透镜成像的机理研究

Two-dimensional (2D) photonic quasicrystal (PQC) lens has become an important branch and a research hot-spot in the field of the PQC application, due to its properties of array, integration, and perfect imaging. However, the quantitative relationships between the imaging characteristic and the refractive index of the dielectric, the size of the lens, and the relationship of size limits between the thickness limit and the width limit of the lens still need to be established. The mechanism of imaging and the negative refraction effect involved are still controversial. This project is based on a decagonal PQC. The quantitative relationships between the imaging characteristic and the refractive index of the dielectric, the size of the lens will be analyzed by finite-difference time-domain method. The relationship of size limits between the thickness limit and the width limit of the lens will be deduced. The focusing and imaging analysis model to describe the mechanism of 2D PQC flat lens imaging will be proposed. A double-straight-line-track detection method that can be used to detect and analyze the negative refraction effect of the 2D PQC wedge-shaped prism will be studied. The relationship of size limits, the imaging mechanism and the double-straight-line-track detection method will be applied to every fold 2D PQC structure. This project will provide important device parameters, theory reference and methodology for the structural design, performance analysis and wide adoption of applications for the microstructure integrated optical device based on 2D PQC lens and prism.

二维光子准晶透镜因可阵列化与集成化并能完美成像而成为光子准晶应用领域的重要分支及研究热点。然而，其成像特性与电介质折射率及透镜尺寸的定量关系，透镜厚度极限与宽度极限应满足的尺寸极限关系式均尚待确立，其成像机理及所涉负折射效应均尚存争议。本项目拟基于十重光子准晶，采用时域有限差分法分析二维光子准晶平板透镜成像特性与电介质折射率及透镜尺寸的定量关系，导出透镜厚度极限与宽度极限应满足的尺寸极限关系式，建立聚焦成像分析模型以描述其成像机理，提出双直线轨道探测方法以探测分析二维光子准晶楔形棱镜负折射效应，且尺寸极限关系式、成像机理及双直线轨道探测方法将可应用于各重二维光子准晶结构。本项目将为基于二维光子准晶透镜及棱镜的微结构集成光学器件的结构设计、性能分析与应用推广提供重要器件参数、理论依据与方法指导。

二维光子准晶透镜因可阵列化与集成化并能完美成像而成为光子准晶应用领域的重要分支与研究热点。然而，其成像特性与电介质折射率及透镜尺寸的定量关系，透镜厚度极限与宽度极限应满足的尺寸极限关系式均待确立，其成像机理及所涉负折射效应均存争议。本已完成项目基于十重Penrose排列及介质柱型光子准晶，提出了平行扫描方法并分析了二维光子准晶楔形棱镜的折射特性，且发现其折射特性不存在稳定性。分析了二维光子准晶平板透镜成像特性与电介质折射率及透镜尺寸的定量关系，并发现了双聚焦效应及环形光子局域现象。引入了“环形光子流主通道”的概念并给出了严格的定义。建立了二维光子准晶平板透镜的“临界状态宽度分析模型”并得到了透镜可发生稳定聚焦的宽度极限及厚度极限。建立了“双光子流光束干涉聚焦分析模型”并提出了一些重要假设，且由此得到了二维光子准晶透镜宽度极限、厚度极限及聚焦波长三者满足的尺寸极限关系式及成像机理。本已完成项目的研究结果将为基于二维光子准晶透镜及棱镜的微结构集成光学器件的结构设计、性能分析与应用推广提供重要器件参数、理论依据与方法指导。