Influence of structural disorder on plasmonic metasurfaces and their colors—a coupled point dipole approach: tutorial

Abstract

The optical properties of plasmonic metasurfaces are determined not only by the shape and size of the constituting nanostructures, but also by their spatial arrangement. The fast progress in nanofabrication has facilitated the emergence of many advanced metasurface designs that enable controlling the propagation of light on the nanoscale. While simple metasurface designs can be derived from theoretical considerations, it is inevitable to employ computational approaches for complex manipulations of incident light. However, most of the currently available full-wave simulation approaches such as the finite element method (FEM) or finite difference time domain method come with drawbacks that limit the applicability to certain usually simplified or less complex geometries. Within this tutorial, different approaches are outlined for modeling light propagation in complex metasurfaces. We focus on an approach that approximates the nanostructure ensemble as a coupled set of point dipoles and determine their far-field response via the reciprocity theorem. This coupled point dipole approximation (CPDA) model is used to examine randomly distributed, oriented, and scaled nanostructure ensembles. A disorder formalism to introduce the randomness is developed that allows one to progressively perturb periodic arrangements of identical nanostructures and thereby investigate the effects of disorder and correlation. Several disorder metrics are provided that allow one to quantify the disorder, and the relation with the far-field scattering properties is discussed. Spatially and angle resolved hyperspectral datasets are computed for various disordered metasurfaces to assess the capabilities of the CPDA model for different polarization states and incidence angles, among others. The hyperspectral datasets are converted into sRGB color space to deduce the appearances in the image and Fourier planes. Very good agreement of the simulation results with Mie theory, FEM results, and experiments is observed, and possible reasons for the present differences are discussed. The presented CPDA model establishes a highly efficient approach that provides the possibility to rapidly compute the hyperspectral scattering characteristics of metasurfaces with more than 10,000 structures with moderate computational resources, such as state-of-the-art desktop computers with sufficient memory; 16 GB allow for the simulations in this paper, whereas scaling to up to more memory by the factor of N2 allows for the simulation of N times more dipoles. For that reason, the CPDA is a suitable approach for tailoring the bidirectional reflectance distribution function of metasurfaces under consideration of structural perturbations and experimental parameters.