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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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Hybrid nanoparticles combining plasmonic and catalytic components have recently gained interest for their potential use in sunlight‐to‐chemical energy conversion. However, a deep understanding of the structure–performance that maximizes the use of the incoming energy remains elusive. Here, a suite of Au and Pd based nanostructures in core–shell and core‐satellites configurations are designed and their photocatalytic activity for Hydrogen (H2) generation under sunlight illumination is tested. Formic acid is employed as H2 source. Core‐satellite systems show a higher enhancement of the reaction upon illumination, compared to core–shell ones. Electromagnetic simulations reveal that a key difference between both configurations is the excitation of highly localized and asymmetric electric fields in the gap between both materials. In this scheme, the core Au particle acts as an antenna, efficiently capturing visible light via the excitation of localized plasmon resonances, while the surrounding Pd satellites transduce the locally‐enhanced electric field into catalytic activity. These findings advance the understanding of plasmon‐driven photocatalysis, and provide an important benchmark to guide the design of the next generation of plasmonic bimetallic nanostructures.

The optical properties of nanoparticle clusters vary with the spatial arrangement of the constituent particles, but also the overall orientation of the cluster with respect to the incident light. This is particularly important in the context of nanoscale chirality and associated chiroptical responses, such as circular dichroism or differential scattering of circularly polarised light in the far-field, or local degree of optical chirality in the near-field. We explore the angular dependence of such quantities for a few archetypal geometries: a dimer of gold nanorods, a helix of gold nanospheres, and a linear chain of silicon particles. The examples serve to illustrate the possible variation of chiroptical responses with the direction of light incidence, but also, consequently, the importance of a robust orientation-averaging procedure when modelling general clusters of particles in random orientation. Our results are obtained with the rigorous superposition T-matrix method, which provides exact analytical formulas for fixed and orientation-averaged properties.

The T-matrix framework offers accurate and efficient modelling of electromagnetic scattering by nonspherical particles in a wide variety of applications ranging from nano-optics to atmospheric science. Its analytical setting, in contrast to purely numerical methods, also provides a fertile ground for further theoretical developments. Perhaps the main purported limitation of the method, when extended to systems of multiple particles, is the often-stated requirement that the smallest circumscribed spheres of neighbouring scatterers not overlap. We consider here such a scenario with two adjacent spheroids whose aspect ratio we vary to control the overlap of the smallest circumscribed spheres, and compute far-field cross-sections and near-field intensities using the superposition T-matrix method. The results correctly converge far beyond the no-overlap condition, and although numerical instabilities appear for the most extreme cases of overlap, requiring high multipole orders, convergence can still be obtained by switching to quadruple precision. Local fields converge wherever the Rayleigh hypothesis is valid for each single scatterer and, remarkably, even in parts of the overlap region. Our results are validated against finite-element calculations, and the agreement demonstrates that the superposition T-matrix method is more robust and broadly applicable than generally assumed.

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum‐chemical simulations and the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time‐dependent Hartree‐Fock theory simulation data of a single chiral molecule to compute the T‐matrix of a cross‐like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum‐mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T‐matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T‐matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T‐matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T‐matrix‐based formulas for computing traditional chiro‐optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light‐matter interactions of arbitrarily‐high multipolar orders.

Self-assembled metamaterials attract considerable interest as they promise to make isotropic bulk metamaterials available at low costs. The optical response of self-assembled metamaterials is derived predominantly from the response of its individual constituents, i.e., the meta-atoms. Beyond effective properties, primary experimentally observable quantities, such as specific cross-sections, are at the focus of interest as they are frequently considered when exploiting metamaterials in specific applications. This posses the challenge of predicting these observable quantities for a diluted ensemble of randomly oriented meta-atoms. Thus far, this has been achieved by either averaging the optical response of the meta-atom across all possible incident fields or by restricting the consideration to only an electric and magnetic dipolar response. This, however, is either time-consuming or imposes an unnecessary limitation. Here, we solve this problem by deriving and presenting explicit expressions for experimentally observable quantities of metamaterials made from randomly arranged and oriented meta-atoms characterized by their T-matrix.

Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers.

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter, we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of the most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious.

We provide a detailed user guide for smarties a suite of Matlab codes for the calculation of the optical properties of oblate and prolate spheroidal particles, with comparable capabilities and ease-of-use as Mie theory for spheres. smarties is a Matlab implementation of an improved T-matrix algorithm for the theoretical modelling of electromagnetic scattering by particles of spheroidal shape. The theory behind the improvements in numerical accuracy and convergence is briefly summarised, with reference to the original publications. Instructions of use, and a detailed description of the code structure, its range of applicability, as well as guidelines for further developments by advanced users are discussed in separate sections of this user guide. The code may be useful to researchers seeking a fast, accurate and reliable tool to simulate the near-field and far-field optical properties of elongated particles, but will also appeal to other developers of light-scattering software seeking a reliable benchmark for non-spherical particles with a challenging aspect ratio and/or refractive index contrast.

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as “laws of nature” by practitioners of numerical computing:
1. High-level dynamic programs have to be slow,
2. One must prototype in one language and then rewrite in another language for speed or deploy- ment, and
3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts.
We introduce the Julia programming language and its design — a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming.
Julia shows that one can have machine performance without sacrificing human convenience.

A generalized mathematical formulation is presented for the scattering
and absorption of electromagnetic time harmonic waves by multiple
spherical particles. A central element of this formulation is the
addition theorem for vector wave functions, which allows a scattered
field from one sphere to be represented as an exciting field about
another sphere. A simplified derivation of the addition theorem, and
important characteristics of where it can and can not be used, are
developed. The Mie solution, coupled with the addition theorem, results
in a system of linear interaction equations for the multipole
coefficients that describe the scattered field from each sphere in the
system. In this regard, the multiple sphere formulation results in an
implicit, rather than explicit, solution for the scattered field;
numerical methods (i.e., linear equation solvers) must be applied to
obtain numerical results. The calculation of the T matrix of the
multiple sphere system, from which orientation averaged scattering and
absorption properties can be obtained, is described. The presentation
ends with a discussion on the application of the multiple sphere
formulation to describing the propagation of electromagnetic waves in
discretely inhomogeneous media.

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input–output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.

For systems of multiple spheres, we investigate in detail the ‘individual’ and aggregate electromagnetic scattering matrices, and their relations with conservation laws, reciprocity and the optical theorem. In order for these relations to adopt their simplest form, care is taken to completely extract both incoming and outgoing phase factors in the definitions. We illustrate that the ‘individual’ cross-sections in an aggregate are defined only in terms of part of the total field, and consequently do not individually obey conservation laws or reciprocity; these relations should be satisfied for the scattering by the entire aggregate. We demonstrate that for scatterer centred transfer matrices, the conservation laws and reciprocity are automatically satisfied regardless of whether or not sufficient multipolarities were retained in the description of individual scatterers. Derivations and results are worked out in a particularly compact and transparent formalism, including magnetic permeability contrast, and the possibility of complex polarizations.

We report values of pseudodielectric functions 〈ε〉=〈ε1〉+i〈ε2〉 measured by spectroscopic ellipsometry and refractive indices ñ=n+ik, reflectivities R, and absorption coefficients α calculated from these data. Rather than correct ellipsometric results for the presence of overlayers, we have removed these layers as far as possible using the real-time capability of the spectroscopic ellipsometer to assess surface quality during cleaning. Our results are compared with previous data. In general, there is good agreement among optical parameters measured on smooth, clean, and undamaged samples maintained in an inert atmosphere regardless of the technique used to obtain the data. Differences among our data and previous results can generally be understood in terms of inadequate sample preparation, although results obtained by Kramers-Kronig analysis of reflectance measurements often show effects due to improper extrapolations. The present results illustrate the importance of proper sample preparation and of the capability of separately determining both ε1 and ε2 in optical measurements.

The authors consider periodic structures made of spheres embedded in a host material with a different dielectric function. They show how to calculate the reflection and transmission of electromagnetic waves by a slab of the material parallel to a given crystallographic plane. The method of calculation is based on a doubling-layer scheme which obtains the reflection and transmission matrix elements for the multilayer from those of a single layer. The reflection and transmission characteristics of the slab are related to the complex band structure of the photon field associated with the given crystallographic plane of the corresponding infinite crystal, which is introduced in the manner of the low-energy electron diffraction theory. They present numerical results which demonstrate the applicability of the method to real systems of current interest and point out some interesting physics which arose from their calculations. They show in particular that the nondegenerate bands of the photon field at the centre of the surface Brillouin zone do not couple to the incident radiation, leading to total reflection at normal incidence.

We present a method for determination of the random-orientation polarimetric scattering properties of an ar-bitrary, nonsymmetric cluster of spheres. The method is based on calculation of the cluster T matrix, from which the orientation-averaged scattering matrix and total cross sections can be analytically obtained. An efficient numerical method is developed for the T-matrix calculation, which is faster and requires less com-puter memory than the alternative approach based on matrix inversion. The method also allows calculation of the random-orientation scattering properties of a cluster in a fraction of the time required for numerical quadrature. Numerical results for the random-orientation scattering matrix are presented for sphere en-sembles in the form of densely packed clusters and linear chains. © 1996 Optical Society of America.

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

A T-matrix formalism is used to calculate local electric fields around clusters of prolate spheroids in the long-wavelength regime. The calculations are performed as a function of interparticle distance as well as angle of orientation. The observed red shifts in the resonant wavelengths of the characteristic peaks are shown to obey an exponential relationship as a function of interparticle separation and a sinusoidal relationship as a function of angle of rotation of the spheroid. The behavior of the cluster is discussed and the two effects of separation and rotation are compared.

Artificial nanostructures enable fine control of electromagnetic fields at the nanoscale, a possibility that has recently been extended to the interaction between polarised light and chiral matter. The theoretical description of such interactions, and its application to the design of optimised structures for chiroptical spectroscopies, brings new challenges to the common set of tools used in nano-optics. In particular, chiroptical effects often depend crucially on the relative orientation of the scatterer and the incident light, but many experiments are performed with randomly oriented scatterers, dispersed in a solution. We derive new expressions for the orientation-averaged local degree of optical chirality of the electromagnetic field in the presence of a nanoparticle aggregate. This is achieved using the superposition T-matrix framework, ideally suited for the derivation of efficient orientation-averaging formulas in light scattering problems. Our results are applied to a few model examples and illustrate several nonintuitive aspects in the distribution of orientation-averaged degree of chirality around nanostructures. The results will be of significant interest for the study of nanoparticle assemblies designed to enhance chiroptical spectroscopies, and where the numerically efficient computation of the averaged degree of optical chirality enables a more comprehensive exploration of the many possible nanostructures.

This work aims to provide a simple yet complete effective dielectric function for an anisotropic layer of polarizable molecules adsorbed on a metallic surface. This effective medium model considers the important and nontrivial case of nonvacuum embedding media and accounts for orientation effects, coverage dependence through dipole-dipole interactions, and image-dipole effects. To check the model's validity, we focus in particular on the experimentally relevant case of dyes adsorbed on metallic nanospheres. We can then use anisotropic Mie theory, together with the effective dielectric function describing the molecular coating, to calculate their optical properties. We show that this effective medium description is in very good agreement with more elaborate and computationally intensive microscopic calculations based on coupled-dipole models. The effective medium model therefore provides a simple means to investigate orientation effects and coverage dependence, including in more complex systems such as dyes adsorbed on nonspherical or ensembles of nanoparticles. This model can readily be used to further our theoretical understanding of dye-nanoparticle systems, for example in the context of dye-plasmon resonance coupling or surface-enhanced Raman and fluorescence spectroscopy.

Incorporation of catalytically active materials into plasmonic metal nanostructures can efficiently merge the reactivity and energy-harvesting abilities of both types of materials for visible light photocatalysis. Herein, we explore the influence of electromagnetic hotspots in the ability of plasmonic core-shell colloidal structures to induce chemical transformations. For this study, we developed a synthetic strategy for the fabrication of Au nanoparticle (NP) trimers in aqueous solution through fine controlled galvanic replacement between Ag nanoprisms and Au precursors. Core-shell [email protected] NP trimers with catalytically active metals (M = Pd, Pt) were subsequently synthesized using Au NP trimers as templates. Our experimental and computational results highlight the synergy of geometry and composition in plasmonic catalysts for plasmon-driven chemical reactions.

In nanophotonics, multipole framework has become an indispensable theoretical tool for analyzing subwavelength meta-atoms and their radiation properties. This work presents higher-order exact dynamic polarizability (alpha) tensors, which can fully represent anisotropic meta-atoms with higher-order multipole transitions. By using the irreducible exact Cartesian multipoles and field components as the basis, the exact alpha-tensor rigorously reflects symmetry information of particles including reciprocity. In addition, the exact alpha-tensor can be obtained from T-matrix simply using basis transformation. Finally, we show that description of meta-atoms using alpha-tensors incorporated with multiple-scattering theory vastly extends the applicability of the multipole framework in nanophotonics, allowing accurate and efficient depiction of complicated, random, multi-scale systems.

Since its inception in the mid-1960s, the T-matrix method has been one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It has been widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This compilation is the ninth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2017. It also includes a few earlier publications that have so far been overlooked.

The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of applicability of the T-matrix method by accounting for the coupling of scattered fields between highly non-spherical particles in close vicinity. This is achieved using an alternative formulation of the translation operator for spherical vector wave functions, based on a plane wave expansion of the particle's scattered electromagnetic field. The accuracy and versatility of the present approach is demonstrated by simulating arbitrarily oriented and densely packed spheroids, for both, dielectric and metallic particles.

A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles.

The validity of the Rayleigh hypothesis (RH) has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nano-optics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the RH, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments.

Surface-Enhanced Raman Scattering (SERS) was discovered in the 1970s and has since grown enormously in breadth, depth, and understanding. One of the major characteristics of SERS is its interdisciplinary nature: it lies at the boundary between physics, chemistry, colloid science, plasmonics, nanotechnology, and biology. By their very nature, it is impossible to find a textbook that will summarize the principles needed for SERS of these rather dissimilar and disconnected topics. Although a basic understanding of these topics is necessary for research projects in SERS with all its many aspects and applications, they are seldom touched upon as a coherent unit during most undergraduate studies in physics or chemistry. This book intends to fill this existing gap in the literature. It provides an overview of the underlying principles of SERS, from the fundamental understanding of the effect to its potential applications. It is aimed primarily at newcomers to the field, graduate student, researcher or scientist, attracted by the many applications of SERS and plasmonics or its basic science. The emphasis is on concepts and background material for SERS, such as Raman spectroscopy, the physics of plasmons, or colloid science, all of them introduced within the context of SERS, and from where the more specialised literature can be followed. * Represents one of very few books fully dedicated to the topic of surface-enhanced Raman spectroscopy (SERS) * Gives a comprehensive summary of the underlying physical concepts around SERS * Provides a detailed analysis of plasmons and plasmonics. "Besides an overview of current promising research topics, this book is a self-contained introduction to Raman spectroscopy and fluorescence that summarises the main concepts and ideas needed for SERS. It is also a self-contained introduction to the physics of plasmon resonances within the broader scope of plasmonics. A detailed presentation of the SERS electromagnetic model and its extension to surface-enhanced fluorescence is included." "Aimed primarily at newcomers to the field, graduate students, and other researchers or scientists attracted by the many possible applications of SERS and plasmonics, or their basic science."--BOOK JACKET.

Advances in the field of nanoplasmonics are hindered by the limited capabilities of simulation tools in dealing with realistic systems comprising regions that extend over many light wavelengths. We show that the optical response of unprecedentedly large systems can be accurately calculated by using a combination of surface integral equation (SIE) method of moments (MoM) formulation and an expansion of the electromagnetic fields in a suitable set of spatial wave functions via fast multipole methods. We start with a critical review of volume versus surface integral methods, followed by a short tutorial on the key features that render plasmons useful for sensing (field enhancement and confinement). We then use the SIE-MoM to examine the plasmonic and sensing capabilities of various systems with increasing degrees of complexity, including both individual and interacting gold nanorods and nanostars, as well as large random and periodic arrangements of ∼1000 gold nanorods. We believe that the present results and methodology raise the standard of numerical electromagnetic simulations in the field of nanoplasmonics to a new level, which can be beneficial for the design of advanced nanophotonic devices and optical sensing structures.

Optical and electron-energy-loss data for evaporated-aluminum films have
been critically analyzed and used in an iterative, self-consistent
algorithm that represents a combination of the Kramers-Kronig analysis
and the semiquantum-model application. The novel values of the intrinsic
optical functions of aluminum have been determined in a wide spectral
range from 200 mu m (6.2 meV) to 0.12 nm (10 keV). These functions are
in accordance with recent calculations by Lee and Chang [Phys. Rev. B
49, 2362 (1994)], with dc conductivity measurements, and are in good
agreement with both peak positions and line widths obtained from
electron-energy-loss experiments. The results are examined for internal
consistency by inertial and f-sum rules.

Upon introducing the outgoing spherical (or circular cylinder) partial waves {ψn} as a basis, the equationQT = − Re (Q) is obtained for the transition matrix T describing scattering for general incidence on a smooth object of arbitrary shape. Elements of Q involve integrals over the object surface, e.g. Q mn = ± ( i 2 ) δ mn + ( k 8π ) ∫dσ⋅∇[ Re (ψ m )ψ n ] . where the −, + apply for Dirichlet and Neumann conditions, respectively. For quadric (separable) surfaces, Q is symmetric. Symmetry and unitarity lead to a secular equation defining eigenfunctions for general bodies. Some apparently new closed‐form results are obtained in the low frequency limit, and the transition matrix is computed numerically for the infinite strip.

A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized-approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres. The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.

A method for calculating the extinction, absorption, and scattering cross sections of clusters of neighboring spheres for both fixed and random orientations is developed. The analysis employs the superposition formulation for radiative interactions among spheres, in which the total field from the cluster is expressed as a superposition of vector spherical harmonic expansions about each of the spheres in the cluster. Through the use of addition theorems a matrix equation for the expansion coefficients is obtained. Further application of addition theorems on the inverse of the coefficient matrix is shown to yield analytical expressions for the orientation-averaged total cross sections of the sphere cluster. Calculations of the cross sections of pairs of spheres and fractal aggregates of several spheres are presented. It is found that a dipole representation of the field in each sphere does not adequately predict the absorption cross section of clusters of small-size-parameter spheres when the spheres are highly conducting. For this situation several multipole orders are required for an accurate calculation of the absorption cross section. In addition, the predicted absorption of sphere clusters can be significantly greater than that estimated from the sum of the isolated-sphere cross sections.

An analysis of radiative scattering for an arbitrary configuration of
neighboring spheres is presented. The analysis builds upon the
previously developed superposition solution, in which the scattered
field is expressed as a superposition of vector spherical harmonic
expansions written about each sphere in the ensemble. The addition
theorems for vector spherical harmonics, which transform harmonics from
one coordinate system into another, are rederived, and simple recurrence
relations for the addition coefficients are developed. The relations
allow for a very efficient implementation of the 'order of scattering'
solution technique for determining the scattered field coefficients for
each sphere.

We present a new recursive transfer matrix method for calculating local electromagnetic fields in systems of spheres subject to strong dependent scattering. Local field information is often lost or discarded in recursive transfer matrix approaches. In order to preserve the local field information, and to avoid problems associated with the dimensional cut-off of the translation matrices, we calculate the scatterer-centred transfer matrices. Our technique permits systematic studies of local field eiects for all possible incident field directions, and configurations (including orientation averages). Illustrative calculations are presented.

The T-matrix formulation of electromagnetic scattering given previously by Waterman for the case of one scatterer is extended to the case of an arbitrary number of scatterers. The resulting total T matrix is expressed in terms of the individual T matrices by an iterative procedure. The essential tools used in the extension are the expansions associated with a translation of the origin for the spherical-wave solutions of Helmholtz's equation. The connection between these expansions and the unitary irreducible representations and associated local representations of the three-dimensional Euclidean group E(3) is emphasized. Some applications to two spheres are given.

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.

Recently a T-matrix formulation of classical electromagnetic scattering has been given by Waterman for the case of one homogeneous scattere, and this formulation has subsequently been extended to the case of an arbitrary number of homogeneous scatterers by the present authors. In the present article we show that the T-matrix formulation is also well suited for the treatment of electromagnetic scattering from scatterers consisting of an arbitrary number of consecutively enclosing layers with constant electric and magnetic properties. We also show how the earlier results on the T-matrix formulation can be combined with these new results to apply to more general types of multilayered scatterers. Some numerical applications are presented.

Upon defining vector spherical partial waves {Ψn} as a basis, a matrix equation is derived describing scattering for general incidence on objects of arbitrary shape. With no losses present, the scattering matrix is then obtained in the symmetric, unitary form S=-Q̂′*Q̂*, where (perfect conductor) Q̂ is the Schmidt orthogonalization of Qnn′=(k/π)∫dσ·[(∇×ReΨn)×Ψn′], integration extending over the object surface. For quadric (separable) surfaces, Q itself becomes symmetric, effecting considerable simplification. A secular equation is given for constructing eigenfunctions of general objects. Finally, numerical results are presented and compared with experimental measurements.

We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.
[Attached full-text includes a few corrections/notes with respect to the original version]

The conventional vector addition theorem is written in a compact notation. Then a new and succinct derivation of the vector addition theorem is presented that is as close to the derivation of the scalar addition theorem. Newly derived expres-sions in this new derivation are used to diagonalize the vector addition theorem. The diagonal form of the vector addition theorem is important in the design of fast algo-rithms for computational wave physics such as computational electromagnetics and computational acoustics.

Waterman'sT-matrix approach is used to derive a simple analytical expression for the extinction cross-section for randomly-oriented non-spherical grains. Numerical results are presented for randomly-oriented oblate and prolate spheroids and Chebyshev particles composed of astronomical silicate. These results are compared with those for spherical grains, and possible influence of the shape of dust grains on the value of interstellar extinction is considered. The range of validity of the Rayleigh approximation for computing extinction efficiency factors for randomly-oriented non-spherical grains is discussed.

Light Scattering by Systems of Particles comprehensively develops the theory of the null-field method, while covering almost all aspects and current applications. The Null-field Method with Discrete Sources is an extension of the Null-field Method (also called T-Matrix Method) to compute light scattering by arbitrarily shaped dielectric particles. It also incorporates FORTRAN programs and exemplary simulation results that demonstrate all aspects of the latest developments of the method. The FORTRAN source programs included on the enclosed CD exemplify the wide range of application of the T-matrix method. Worked examples of the application of the FORTRAN programs show readers how to adapt or modify the programs for his specific application.

An overview is given over some of the most widely used numerical techniques for solving the electromagnetic scattering problem that start from rigorous electromagnetic theory. In particular, the theoretical foundations of the separation of variables method, the finite-difference time-domain method, the finite-element method, the method of lines, the point matching method, the method of moments, the discrete dipole approximation, and the null-field method (or extended boundary condition method) are reviewed, and the advantages and disadvantages of the different methods are discussed. Aspects concerning the T matrix formulation and the surface Green's function formulation of the electromagnetic scattering problem are addressed.

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.

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.

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.

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.