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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 near-field 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.

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A fast, accurate, and general technique for solving Maxwell’s equations in the presence of a finite cluster of arbitrarily disposed dielectric objects is presented. The electromagnetic field is first decomposed into multipoles with respect to centers close to each of the objects of the cluster and multiple scattering is carried out until convergence is achieved. Radiation scattering cross sections are obtained using this method for clusters formed by homogeneous spheres and coated spheres made of different materials (Al, Si, and SiO2), including magnetic ones. Near- and far-field distributions are offered as well.
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We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modelling arbitrarily shaped microsized objects. The T-matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquet's theorem. A ‘reduced-mode’ T-matrix can also be calculated if the illumination conditions are known.
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The formalism of the quantum theory of angular momentum is used for orientational averaging of the a matrix, the Hermitian tensor T(_sup+)T, and the direct product T(*)_sub_nunu')T_sub|_mumu'. These results are independent of the nature of waves and scatterers. Equations for |<|T> and <T(_sup+)T> are interpreted as specific forms of the generalized Wigner-Eckart theorem for the matrix elements of operators T and T(_sup+)T , which are calculated in terms of symmetrical top eigenfunctions. The averaged values of the ab three types of tensor are used for the analytical calculation of a complete set of incoherent light-scattering observables, i.e., the total scattering and extinction cross sections and the Mueller matrix elements.
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Series expressions for the radially dependent absorption cross section and angle-averaged absorption heat source function within a stratified sphere are presented. A numerically stable and accurate algorithm for computation of the internal radiative properties, as well as the overall scattering and extinction of a stratified sphere having an arbitrary number of layers is developed. The results allow for direct estimation of the degree of penetration and intensity of radiative heating in radially inhomogeneous spherical particles, and also provide an estimate of the thermal emission coefficient of particles having a radial temperature distribution.
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A new method for calculating electromagnetic scattering from an arbitrarily shaped, inhomogeneous, dielectric object is developed. The method is based on an invariant imbedding procedure for computing the T matrix that was originally developed to solve quantum mechanical scattering problems. The final outcome of this approach is a two-term recurrence relation which can be solved numerically for the T matrix. The limiting form of this recurrence relation is a first-order nonlinear differential equation that is identical in form to the quantum mechanical Calogero equation. The results of several test calculations are also presented.