Multiple scattering of light in nanoparticle assemblies: user guide for the TERMS program

Abstract

We introduce terms, an open-source Fortran program to simulate near-field and far-field optical properties of clusters of particles. The program solves rigorously the Maxwell equations via the superposition T -matrix method, where incident and scattered fields are decomposed into series of vector spherical waves.terms implements several algorithms to solve the coupled system of multiple scattering equations that describes the electromagnetic interaction between neighbouring scatterers. From this formal solution, the program can compute a number of physically-relevant optical properties, such as far-field cross-sections for extinction, absorption, scattering and their corresponding circular dichroism, as well as local field intensities and degree of optical chirality. By describing the incident and scattered fields in a basis of spherical waves the T -matrix framework lends itself to analytical formulas for orientation-averaged quantities, corresponding to systems of particles in random orientation; terms offers such computations for both far-field and nearfield quantities of interest. This user guide introduces the program, summarises the relevant theory, and is supplemented by a comprehensive suite of stand-alone examples in the website accompanying the code.

Orientation-averaged light scattering by nanoparticle clusters: far-field and near-field benchmarks of numerical cubature methods

“…These examples were chosen for demonstration purposes, but our interest is to approximate the integral of light-scattering quantities, which generally admit no analytical expression. The integrand will be computed numerically with the superposition T -matrix method 13 , and particular configurations can yield very differently-behaved integrands. Typically, we expect that a compact, small-sized cluster (compared to the wavelength) will show a relatively featureless angular pattern, and spherical cubatures of small order will suffice for an accurate orientation averaging process.…”

“…The computational method itself is also subject to other sources of error, such as the fineness of a mesh when the scatterers are discretised in FEM, FDTD or DDA; in the T -matrix method employed here, the key convergence parameter is the maximum multipolar order l max which is used to truncate field expansions 53 . In our implementation, note that l max refers to scatterer-centred expansions 13,22 . Remarkably, we find no interaction between N inc and l max when studying the convergence of orientation-averaged quantities.…”

“…The superposition T -matrix framework is a powerful method for the theoretical description of light scattering by such aggregates [11][12][13] ; it enables fast and accurate computations of far-field crosssections as well as near fields [14][15][16] . A particular strength of the method lies in the prediction of orientation-averaged quantities 11,17,18 : the Tmatrix captures the optical response of a scatterer independently of the incident field, and the properties of vector spherical harmonics used to describe far-field near-field Figure 1: Schematic illustration of the light scattering problem under consideration.…”