Optical properties of three-dimensional plasmonic structures: Advanced methods and chirality

二维(2D)和三维(3D)金属光子晶体和超材料的光学性质提供了诸如带隙、负折射率、手性和偏振效应等特征，这些特征可以导致许多应用。这些设备包括传感器、隐身设备和超级透镜。目前，对这些结构的理论描述还不够全面。它基于简单的模型和数值方法，如时域有限差分(FDTD)、有限元方法(FE)、多极多极子方法(MMP)、边界元方法(BEM)和傅立叶模态法(FMM)。虽然实验设计已经变得相当复杂，但到目前为止，数值方法往往局限于更简单的几何形状。复杂程度较高的结构的模拟常常会遇到收敛问题。在这个项目中，我们的目标是改进傅立叶模态法和散射矩阵(S矩阵)相结合的方法[1，2]的收敛性能，通过使用一些数值方法，如自适应空间分辨率[3]、因式分解规则[4]和匹配坐标[7]来模拟二维和三维结构的光学性质。后一种匹配坐标的方法提供了以高精度计算平面结构的光学性质的可能性，即使它们不能用笛卡尔网格来描述。到目前为止，这项技术已经被应用于由单层组成的特定结构。这个方案的具体目标是：(A)将该方法扩展到三维层叠，(B)研究手性结构的光学性质，以及(C)使用文献[2，6]中描述的方法来推导这些结构的光学本征模，该方法必须适应匹配的坐标。

The optical properties of two-dimensional (2D) and three-dimensional (3D) metallic photonic crystals and metamaterials provide features such as band gaps, negative refractive indices, chirality, and polarization effects that can lead to a number of applications. These include sensors, cloaking devices, and superlenses. Nowadays, the theoretical description of these structures is insufficient and incomplete. It is based on simple models as well as numerical methods such as Finite Difference Time Domain (FDTD), Finite Element Method (FEM), Multipole Multipole Method (MMP), Boundary Element Method (BEM), and Fourier Modal Method (FMM). While the experimental designs already become quite complex, the numerical methods until now are often restricted to simpler geometries. Simulations of structures with higher complexity often suffer under problems in convergence. In this project we are aiming to improve the convergence of the Fourier modal method in combination with a scattering matrix (S-matrix) approach [1, 2] for simulations of optical properties of 2D and 3D structures by using a number of numerical methods such as adaptive spatial resolution [3] (ASR), factorization rules [4], and matched coordinates [7]. The latter method of matched coordinates provides the possibility to calculate the optical properties of planar structures with a high accuracy even if they cannot be described in a Cartesian grid. Up to now, this technique has been applied to specific structures consisting of single layers. Detailed goals of this proposal are: (a) extending this method to three-dimensional stacks of layers, (b) studying the optical properties of chiral structures, and (c) deriving the optical eigenmodes of these structures using the approach described in [2, 6], which has to be adapted for matched coordinates.