title = {Analysis of {{Radiative Scattering}} for {{Multiple Sphere Configurations}}},
volume = {433},
issn = {1364-5021, 1471-2946},
doi = {10.1098/rspa.1991.0066},
abstract = {An analysis of radiative scattering for an arbitrary configuration of neighbouring 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.},
language = {en},
number = {1889},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
title = {Optical {{Constants}} of the {{Noble Metals}}},
volume = {6},
doi = {10.1103/PhysRevB.6.4370},
abstract = {The optical constants n and k were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 \AA. Three optical measurements were inverted to obtain the film thickness d as well as n and k. The estimated error in d was $\pm$ 2 \AA, and that in n, k was less than 0.02 over most of the spectral range. The results in the film-thickness range 250-500 \AA{} were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.},
title = {Efficient {{Evaluation}} of {{Vector Translation Coefficients}} in {{Multiparticle Light}}-{{Scattering Theories}}},
volume = {139},
issn = {0021-9991},
doi = {10.1006/jcph.1997.5867},
abstract = {Vector addition theorems are a necessary ingredient in the analytical solution of electromagnetic multiparticle-scattering problems. These theorems include a large number of vector addition coefficients. There exist three basic types of analytical expressions for vector translation coefficients: Stein's (Quart. Appl. Math.19, 15 (1961)), Cruzan's (Quart. Appl. Math.20, 33 (1962)), and Xu's (J. Comput. Phys.127, 285 (1996)). Stein's formulation relates vector translation coefficients with scalar translation coefficients. Cruzan's formulas use the Wigner 3jm symbol. Xu's expressions are based on the Gaunt coefficient. Since the scalar translation coefficient can also be expressed in terms of the Gaunt coefficient, the key to the expeditious and reliable calculation of vector translation coefficients is the fast and accurate evaluation of the Wigner 3jm symbol or the Gaunt coefficient. We present highly efficient recursive approaches to accurately evaluating Wigner 3jm symbols and Gaunt coefficients. Armed with these recursive approaches, we discuss several schemes for the calculation of the vector translation coefficients, using the three general types of formulation, respectively. Our systematic test calculations show that the three types of formulas produce generally the same numerical results except that the algorithm of Stein's type is less accurate in some particular cases. These extensive test calculations also show that the scheme using the formulation based on the Gaunt coefficient is the most efficient in practical computations.},
title = {Group {{Theory}}: {{Application}} to the {{Physics}} of {{Condensed Matter}}},
isbn = {978-3-540-32899-5},
abstract = {Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides...},
publisher = {{Springer, Berlin, Heidelberg}},
author = {Dresselhaus, Mildred S. and Dresselhaus, Gene and Jorio, Ado},
title = {International {{Tables}} for {{Crystallography}}, {{Vol}}.{{B}}: {{Reciprocal Space}}},
isbn = {978-0-7923-6592-1},
shorttitle = {International {{Tables}} for {{Crystallography}}, {{Vol}}.{{B}}},
publisher = {{Springer}},
author = {Shmueli, Uri},
year = {2001},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/3WPJZ79F/Shmueli - 2001 - International Tables for Crystallography, Vol.B R.pdf}
}
@book{ITfC:A,
edition = {5th},
series = {IUCr Series. International Tables of Crystallography},
title = {International {{Tables}} for {{Crystallography}}, {{Vol}}.{{A}}: {{Space Group Symmetry}}},
isbn = {978-0-7923-6590-7},
shorttitle = {International {{Tables}} for {{Crystallography}}, {{Vol}}.{{A}}},
publisher = {{Springer, Dordrecht}},
author = {Hahn, Theo},
year = {2002},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/PE7NZCZ8/Hahn - 2002 - International Tables for Crystallography, Vol.A S.pdf}
}
@article{dixon_computing_1970,
title = {Computing Irreducible Representations of Groups},
volume = {24},
issn = {0025-5718, 1088-6842},
doi = {10.1090/S0025-5718-1970-0280611-6},
abstract = {How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers; and there remain practical difficulties even for groups of relatively small orders . The present paper describes three techniques to help solve this problem. These are: the reduction of a reducible unitary representation into its irreducible components; the construction of a complete set of irreducible unitary representations from a single faithful representation; and the calculation of the precise values of a group character from values which have only been computed approximately.},
language = {en-US},
number = {111},
journal = {Math. Comp.},
author = {Dixon, John D.},
year = {1970},
keywords = {computation of characters,Computation of group representations,finite Fourier analysis,irreducible components,iterative processes,reduction of unitary representations,tensor products},
title = {Lattice {{Sums}} for the {{Helmholtz Equation}}},
volume = {52},
issn = {0036-1445},
doi = {10.1137/09075130X},
abstract = {A survey of different representations for lattice sums for the Helmholtz equation is made. These sums arise naturally when dealing with wave scattering by periodic structures. One of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension \$d\_$\backslash$Lambda\$. Lattice sums are related to, and can be calculated from, the quasi-periodic Green's function and this object serves as the starting point of the analysis.},
title = {The Mathematical Theory of Symmetry in Solids; Representation Theory for Point Groups and Space Groups},
isbn = {978-0-19-851920-1},
publisher = {{Clarendon Press, Oxford}},
author = {Bradley, C. J. and Cracknell, A. P.},
year = {1972},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/SB5ZN5WH/C.J. Bradley, A.P. Cracknell - The mathematical theory of symmetry in solids_ representation theory for point groups and space groups (1972, Clarendon Press).djvu}
}
@article{reid_efficient_2015,
archivePrefix = {arXiv},
eprinttype = {arxiv},
eprint = {1307.2966},
title = {Efficient {{Computation}} of {{Power}}, {{Force}}, and {{Torque}} in {{BEM Scattering Calculations}}},
volume = {63},
issn = {0018-926X, 1558-2221},
doi = {10.1109/TAP.2015.2438393},
abstract = {We present concise, computationally efficient formulas for several quantities of interest -- including absorbed and scattered power, optical force (radiation pressure), and torque -- in scattering calculations performed using the boundary-element method (BEM) [also known as the method of moments (MOM)]. Our formulas compute the quantities of interest $\backslash$textit\{directly\} from the BEM surface currents with no need ever to compute the scattered electromagnetic fields. We derive our new formulas and demonstrate their effectiveness by computing power, force, and torque in a number of example geometries. Free, open-source software implementations of our formulas are available for download online.},
number = {8},
journal = {IEEE Transactions on Antennas and Propagation},
author = {Reid, M. T. Homer and Johnson, Steven G.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/I2DXTKUF/Reid ja Johnson - 2015 - Efficient Computation of Power, Force, and Torque .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/LG7AVZDH/1307.html}
