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

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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.