ParticleScattering: Solving and optimizing multiple-scattering problems in Julia

Abstract

SummaryParticleScattering is a Julia (Bezanson et al. 2017) package for computing the electromagnetic fields scattered by a large number of two-dimensional particles, as well as optimizing particle parameters for various applications. Such problems naturally arise in the design and analysis of metamaterials, including photonic crystals (Jahani and Jacob 2016). Unlike most solvers for these problems, ours does not require a periodic structure and is scalable to a large number of particles. In particular, this software is designed for scattering problems involving TM plane waves impinging on a collection of homogeneous dielectric particles with arbitrary smooth shapes. Our code performs especially well when the number of particles is substantially larger than the number of distinct shapes, where particles are considered indistinct if they are identical up to rotation. Solver overviewGiven a scattering problem consisting of a collection of penetrable particles in a homogeneous medium, the software performs the following steps to calculate the total electric field:• For each distinct non-circular shape, a single-and double-layer potential formulation is constructed.• The potential formulations are transformed to a multipole basis of Hankel functions, reducing the degrees of freedom by at least an order of magnitude.• Analytical multipole basis is computed for circular particles.• A multiple-scattering system of equations is constructed, and then solved with the Fast Multipole Method.• Electric field is computed at any point of interest.In addition, ParticleScattering can plot near-and far-field results using the popular framework PyPlot, create publication-level plots with PGFPlots integration, and compute minimum parameters for a desired error level. OptimizationParticleScattering is especially targeted at users who wish to design metamaterials belonging to the class described above. While the large number of variables such metamaterials contain allows for a variety of devices that meet different objectives, it also creates a large search space for choosing them. Therefore, a fast and automated approach can be beneficial for both inventing new designs and improving existing ones. As the results of many ParticleScattering computations can be recycled between optimization iterations, a large

Efficient Computational Design and Optimization of Dielectric Metamaterial Structures

“…The examples in this paper resulted in highly irregular structures, which conforms to observations previously made in [21], where the authors note that aperiodic structures are capable of providing more functionality than their periodic counterparts. We implemented the methods described in this paper for the publicly available open-source software package ParticleScattering.jl [49] in the Julia programming language [44], which also includes the examples presented here.…”

SphericalScattering: A Julia Package for Electromagnetic Scattering from Spherical Objects

“…Other available implementations have a different focus, that is, specific 2D scenarios are addressed (Blankrot & Heitzinger, 2018), T-matrices are employed for general shaped objects (Egel et al, 2017-09;Art Gower & Deakin, 2018;Parker, 2022;Schebarchov et al, 2021), ensemble averaged waves are obtained (Artur Gower, 2020), spontaneous decay rates of a dipole are studied (Rasskazov et al, 2020), light scattering is considered employing only plane waves as excitations (chillin-capybara, 2022;Ladutenko et al, 2017;Leinonen, 2016;Prahl, 2023;Schäfer, 2023;Walter, 2023;Wu, 2023), or only far-field quantities are computed.…”