HELIOS: A surface integral equation software for light scattering in homogeneous, periodic, and stratified environments

Abstract

We present HELIOS (HomogEneous and Layered medIa Optical Scattering), an open-source surface integral equation (SIE) software designed for modeling light scattering by particles embedded in homogeneous or layered media and periodic backgrounds. The code implements the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation that has demonstrated exceptional reliability in solving scattering problems with penetrable objects. Domain boundaries are discretized using triangular meshes, upon which the electric and magnetic surface current densities are expanded using the Rao-Wilton-Glisson (RWG) basis functions. For periodic structures, such as photonic crystals and metasurfaces, HELIOS employs Ewald's transformation to efficiently evaluate the infinite series associated with 2D lattices. Regarding stratified media, the code utilizes a matrix-friendly approach for the layered media Green's tensor, computing Sommerfeld integrals and accelerating calculations through a tabulation-interpolation scheme. The source code is implemented in C++, while a Python interface manages the workflow, including simulation setup, solver run, and post-processing. The accuracy and versatility of HELIOS are demonstrated through various examples that cover all its functionalities.

Figures (19)

• Figure 1: Penetrable scatterers in a homogeneous medium. (a) Single particle scenario (domain $\Omega_2$), and (b) multiple attached particles case (domains $\Omega_2$, $\Omega_3$, $\Omega_4$). In both cases the homogeneous background domain is $\Omega_1$.
• Figure 2: Au sphere ($R = 75~\mathrm{nm}$) in free-space. (a) Triangular mesh, and (b) cross-section results comparison between the SIE method and Mie theory for an incident plane wave that propagates towards $+z$ and is $x$-polarized.
• Figure 3: Near-field for (a) an incident plane wave that propagates towards $+z$ and is $x$-polarized, and (b) an in-plane source dipole at ($x = 75~\mathrm{nm},\, z = 75~\mathrm{nm}$) with direction ($\theta = \pi/4,\, \varphi = \pi$). The dipole orientation is defined in the standard spherical coordinates.
• Figure 4: Au-cSi Janus ring in free-space. (a) Triangular mesh, and (b) cross-section results for an incident plane wave that propagates towards $+z$ and is $x$-polarized.
• Figure 5: Near-field for (a) an incident plane wave that propagates towards $+z$ and is $x$-polarized, and (b) a dipole at the origin with direction ($\theta = \pi/2,\, \varphi = 0$).