On the efficient optimization of optical properties of particulate monolayers by a hybrid finite element approach
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RESEARCH PAPER
On the efficient optimization of optical properties of particulate monolayers by a hybrid finite element approach Johannes Semmler1 · Michael Stingl1 Received: 11 February 2020 / Revised: 8 September 2020 / Accepted: 28 September 2020 © The Author(s) 2020
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. Keywords Maxwell’s equation · Finite element method · Vector spherical harmonics · Particle scattering · Haze factor · Gradient-based optimization Mathematics Subject Classification (2010) 35Q61 · 35Q93 · 49M05 · 90C30
1 Introduction In this paper, we focus on the numerical simulation of light scattering of particle monolayers that consist of nonspherical and inhomogeneous particles. Furthermore, the haze factor is used to characterize the design of such thin films (Preston et al. 2013). It should be noted that experiments show (see Bley et al. 2018) that design motifs corresponding to a low or high haze factor of a particulate monolayer can be transferred to the design of a transparent and conductive thin film. Such films play an important role
Responsible Editor: Hyunsun Alicia Kim Michael Stingl
[email protected] 1
Lehrstuhl f¨ur Angewandte Mathematik (Kontinuierliche Optimierung), Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg (FAU), Cauerstraße 11, 91058 Erlangen, Germany
in many photonic applications, such as OLEDs (Hecht et al. 2011), touch screens (Layani et al. 2014) and solar panels (Atwater and Polman 2010). In terms of numerical simulation, the challenge is that the haze factor is calculated by evaluating the scattered electromagnetic field on a hemisphere that is larger than the wavelength of the visible light by several orders of magnitude. Hence, a classical numerical scheme based, e.g., on the finite element method (FEM) (Monk 2003), would result in a huge demand on computational resources or may even be out of reach. Alternative n
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