On the efficient optimization of optical properties of particulate monolayers by a hybrid finite element approach

Abstract

This article addresses the numerical simulation and optimization of the optical properties of mono-layered nano-particulate films. The particular optical property of interest is the so-called haze factor, for which a model close to an experimental setup is derived. The numerical solution becomes very involved due to the resulting size of computational domain in comparison to the wave length, rendering the direct simulation method infeasible. As a remedy, a hybrid method is suggested, which in essence consistently combines analytical solutions for the far field with finite element-based solutions for the near field. Using a series of algebraic reformulations, a model with an off- and online component is developed, which results in the computational complexity being reduced by several orders of magnitude. Based on the suggested hybrid numerical scheme, which is not limited to the haze factor as objective function, structural optimization problems covering geometrical and topological parametrizations are formulated. These allow the influence of different particle arrangements to be studied. The article is complemented by several numerical experiments underlining the strength of the method.