title = {Canonical Quantization of Macroscopic Electromagnetism},
volume = {12},
issn = {1367-2630},
abstract = {Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers\textendash{}Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/MHJA3DSX/Philbin_2010_Canonical quantization of macroscopic electromagnetism.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/R5AHRZRR/123008.html}
}
@article{huttner_quantization_1992,
title = {Quantization of the Electromagnetic Field in Dielectrics},
volume = {46},
abstract = {We present a fully canonical quantization scheme for the electromagnetic field in dispersive and lossy linear dielectrics. This scheme is based on a microscopic model, in which the medium is represented by a collection of interacting matter fields. We calculate the exact eigenoperators for the coupled system and express the electromagnetic field operators in terms of them. The dielectric constant of the medium is explicitly derived and is shown to satisfy the Kramers-Kronig relations. We apply these results to treat the propagation of light in dielectrics and obtain simple expressions for the electromagnetic field in the medium in terms of space-dependent creation and annihilation operators. These operators satisfy a set of equal-space commutation relations and obey spatial Langevin equations of evolution. This justifies the use of such operators in phenomenological models in quantum optics. We also obtain two interesting relationships between the group and the phase velocity in dielectrics.},
author = {Huttner, Bruno and Barnett, Stephen M.},
month = oct,
year = {1992},
keywords = {_tablet},
pages = {4306-4322},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/EQ6HCUDJ/Huttner_Barnett_1992_Quantization of the electromagnetic field in dielectrics.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/VP7HX7MC/PhysRevA.46.html}
}
@article{mandelstam_quantum_1962,
title = {Quantum Electrodynamics without Potentials},
volume = {19},
issn = {0003-4916},
abstract = {A scheme is proposed for quantizing electrodynamics in terms of the electromagnetic fields without the introduction of potentials. The equations are relativistically covariant and do not require the introduction of unphysical states and an indefinite metric. Calculations carried out according to current quantization methods in the Coulomb or Lorentz gauges are justified in the new formalism. The theory exhibits an analogy between phases of operators and electromagnetic fields on the one hand, and coordinate systems and space curvature on the other. It is suggested that this analogy may be useful in quantizing the gravitational field.},
title = {Theory of the {{Spontaneous Optical Emission}} of {{Nanosize Photonic}} and {{Plasmon Resonators}}},
volume = {110},
abstract = {We provide a self-consistent electromagnetic theory of the coupling between dipole emitters and dissipative nanoresonators. The theory that relies on the concept of quasinormal modes with complex frequencies provides an accurate closed-form expression for the electromagnetic local density of states of any photonic or plasmonic resonator with strong radiation leakage, absorption, and material dispersion. It represents a powerful tool to calculate and conceptualize the electromagnetic response of systems that are governed by a small number of resonance modes. We use the formalism to revisit Purcell's factor. The new formula substantially differs from the usual one; in particular, it predicts that a spectral detuning between the emitter and the resonance does not necessarily result in a Lorentzian response in the presence of dissipation. Comparisons with fully vectorial numerical calculations for plasmonic nanoresonators made of gold nanorods evidence the high accuracy of the predictions achieved by our semianalytical treatment.},
title = {Plasmon-Mediated Superradiance near Metal Nanostructures},
volume = {82},
abstract = {We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nanometers from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.},
title = {Canonical {{Quantization}} of {{Light}} in a {{Linear Dielectric}}},
volume = {16},
issn = {0295-5075},
abstract = {Quantization of the macroscopic electromagnetic field via effective susceptibilities leads to inconsistencies if the medium is dispersive. A canonical quantization scheme has to take explicit account of the matter field. By introducing a simple model for the matter, we are able to resolve some of the difficulties highlighted in the recent literature. We demonstrate the fundamental significance of the electromagnetic energy flux (rather than the density) and justify the use of temporal modes of the field. Our analysis leads to an apparently unknown relationship between the group and phase velocity in a linear dielectric medium.},
author = {Huttner, B. and Baumberg, J. J. and Barnett, S. M.},
month = sep,
year = {1991},
pages = {177},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/5FJP7FZI/Huttner et al. - 1991 - Canonical Quantization of Light in a Linear Dielec.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/CCZPG7NS/010.html}
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HES6WJTP/(Wiley science paperback series) Craig F. Bohren, Donald R. Huffman-Absorption and scattering of light by small particles-Wiley-VCH (1998).djvu}
title = {Multipole {{Translation Theory}} for the {{Three}}-{{Dimensional Laplace}} and {{Helmholtz Equations}}},
volume = {16},
issn = {1064-8275},
abstract = {The mathematical theory of multipole translation operators for the three-dimensional Laplace and Helmholtz equations is summarized and extended. New results for the Laplace equation include an elementary proof of the inner-to-inner translation theorem, from which follows the definition of a far-field signature function analogous to that of the Helmholtz equation. The theory for the Helmholtz equation is developed in terms of a new convolutional form of the translation operator, which is connected to Rokhlin's diagonal form by means of Wigner 3-j symbols., The mathematical theory of multipole translation operators for the three-dimensional Laplace and Helmholtz equations is summarized and extended. New results for the Laplace equation include an elementary proof of the inner-to-inner translation theorem, from which follows the definition of a far-field signature function analogous to that of the Helmholtz equation. The theory for the Helmholtz equation is developed in terms of a new convolutional form of the translation operator, which is connected to Rokhlin's diagonal form by means of Wigner 3-j symbols.},
title = {The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription},
volume = {35},
issn = {1045-9243},
shorttitle = {The Fast Multipole Method for the Wave Equation},
abstract = {A practical and complete, but not rigorous, exposition of the fact multiple method (FMM) is provided. The FMM provides an efficient mechanism for the numerical convolution of the Green's function for the Helmholtz equation with a source distribution and can be used to radically accelerate the iterative solution of boundary-integral equations. In the simple single-stage form presented here, it reduces the computational complexity of the convolution from O(N/sup 2/) to O(N/sup 3/2/), where N is the dimensionality of the problem's discretization.{$<>$}},
number = {3},
journal = {IEEE Antennas and Propagation Magazine},
doi = {10.1109/74.250128},
author = {Coifman, R. and Rokhlin, V. and Wandzura, S.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/9Z8788XV/Coifman et al. - 1993 - The fast multipole method for the wave equation a.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/KN5GUPCG/abs_all.html}
title = {Analysis of {{Radiative Scattering}} for {{Multiple Sphere Configurations}}},
volume = {433},
issn = {1364-5021, 1471-2946},
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.},
title = {Fast, {{Exact}}, and {{Stable Computation}} of {{Multipole Translation}} and {{Rotation Coefficients}} for the 3-{{D Helmholtz Equation}}},
abstract = {We develop exact expressions for translations and rotations of local and
multipole fundamental solutions of the Helmholtz equation in spherical
coordinates. These expressions are based on recurrence relations that we
develop, and to our knowledge are presented here for the first time. The
symmetry and other properties of the coefficients are also examined, and
based on these efficient procedures for calculating them are presented. Our
expressions are direct, and do not use the Clebsch-Gordan coefficients or
the Wigner 3-j symbols, though we compare our results with methods that use
these, to prove their accuracy. We test our expressions on a number of
simple calculations, and show their accuracy. For evaluating a \$N\_t\$ term
truncation of the translation (involving \$O(N\_t\^2)\$ multipoles), compared to
previous exact expressions that rely on the Clebsch-Gordan coefficients or
the Wigner \$3-j\$ symbol that require \$O(N\_t\^5)\$ operations, our expressions require \$O(N\_t\^4)\$) evaluations, with a small constant multiplying the order
term.
The recent trend in evaluating such translations has been to use approximate
"diagonalizations," that require \$O(N\_t\^3)\$ evaluations with a large
coefficient for the order term. For the Helmholtz equation, these
translations in addition have stabilty problems unless the accuracy of the
truncation and approximate translation are balanced. We derive explicit
exact expressions for achieving "diagonal" translations in \$O(N\_t\^3)\$
operations. Our expressions are based on recursive evaluations of multipole
coefficients for rotations, and are accurate and stable, and have a much
smaller coeffiicient for the order term, resulting practically in much fewer
operations. Future use of the developed methods in computational acoustic
scattering, electromagnetic scattering (radar and microwave), optics and
title = {Radiative Scattering Properties of an Ensemble of Variously Shaped Small Particles},
volume = {67},
abstract = {This paper presents a rigorous solution to the scattering of a monochromatic plane wave by an arbitrary configuration of wavelength-sized small particles that can be of different shape, structure, size, and composition. A T-matrix formulation is developed for the calculation of optical cross sections and the asymmetry parameter of such an ensemble of scatterers in both fixed and random orientations. The solution is based on the T matrix Tjl, that is, the inverse of the coefficient matrix of boundary condition equations. A linear system containing Tjl is derived to efficiently solve the T matrix, which is required in the practical implementation of the solution.},
title = {Calculation of the {{Addition Coefficients}} in {{Electromagnetic Multisphere}}-{{Scattering Theory}}},
volume = {127},
issn = {0021-9991},
abstract = {One of the most intractable problems in electromagnetic multisphere-scattering theory is the formulation and evaluation of vector addition coefficients introduced by the addition theorems for vector spherical harmonics. This paper presents an efficient approach for the calculation of both scalar and vector translational addition coefficients, which is based on fast evaluation of the Gaunt coefficients. The paper also rederives the analytical expressions for the vector translational addition coefficients and discusses the strengths and limitations of other formulations and numerical techniques found in the literature. Numerical results from the formulation derived in this paper agree with those of a previously published recursion scheme that completely avoids the use of the Gaunt coefficients, but the method of direct calculation proposed here reduces the computing time by a factor of 4\textendash{}6.},
title = {Efficient {{Evaluation}} of {{Vector Translation Coefficients}} in {{Multiparticle Light}}-{{Scattering Theories}}},
volume = {139},
issn = {0021-9991},
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 = {Optical {{Binding Phenomena}}: {{Observations}} and {{Mechanisms}}},
isbn = {978-3-642-21195-9},
shorttitle = {Optical {{Binding Phenomena}}},
abstract = {This thesis addresses optical binding - a new area of interest within the field of optical micromanipulation. It presents, for the first time, a rigorous numerical simulation of some of the key results, along with new experimental findings and also physical interpretations of the results. In an optical trap particles are attracted close to areas of high optical intensities and intensity gradients. So, for example, if two lasers are pointed towards each other (a counter propagating trap) then a single particle is trapped in the centre of the two beams \textendash{} the system is analogous to a particle being held by two springs in a potential well. If one increases the number of particles in the trap then naively one would expect all the particles to collect in the centre of the well. However, the effect of optical binding means that the presence of one particle affects the distribution of light experienced by another particle, resulting in extremely complex interactions that can lead to unusual 1D and 2D structures to form within the trap. Optical binding is not only of theoretical interest but also has applications in micromanipulation and assembly.},
language = {en},
publisher = {{Springer Science \& Business Media}},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/7XKKCD9X/(Springer Theses) Jonathan M. Taylor (auth.)-Optical Binding Phenomena_ Observations and Mechanisms -Springer-Verlag Berlin Heidelberg (2011).pdf}
}
@article{pellegrini_interacting_2007,
series = {{{EMRS}} 2006 {{Symposium A}}: {{Current Trends}} in {{Nanoscience}} - from {{Materials}} to {{Applications}}},
title = {Interacting Metal Nanoparticles: {{Optical}} Properties from Nanoparticle Dimers to Core-Satellite Systems},
volume = {27},
issn = {0928-4931},
shorttitle = {Interacting Metal Nanoparticles},
abstract = {Prompted by the growing interest in the optical properties of coupled metal nanoclusters, we implemented a code in the framework of Generalized Multiparticle Mie theory (GMM) to simulate far-field properties of strongly interacting spherical particles. In order to validate the code different case studies, including systems modeled for the first time, have been treated. The extinction properties of noble metal nanocluster dimers, chains and core-satellite structures have been computed. Influence of parameters like interparticle distance, incident field polarization, number of multipolar expansions and chain length has been studied. The code provided reliable results in agreement with previous works and proved to be affordable and robust in any of the treated case.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/77R8E8NQ/Pellegrini et al. - 2007 - Interacting metal nanoparticles Optical propertie.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/IXCSKSFT/S0928493106002657.html}
}
@article{hopfield_theory_1958,
title = {Theory of the {{Contribution}} of {{Excitons}} to the {{Complex Dielectric Constant}} of {{Crystals}}},
volume = {112},
abstract = {It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.},
title = {Photons and {{Atoms}}: {{Introduction}} to {{Quantum Electrodynamics}}},
isbn = {978-0-471-18433-1},
shorttitle = {Photons and {{Atoms}}},
abstract = {Photons and Atoms Photons and Atoms: Introduction to Quantum Electrodynamics provides the necessary background to understand the various physical processes associated with photon-atom interactions. It starts with elementary quantum theory and classical electrodynamics and progresses to more advanced approaches. A critical comparison is made between these different, although equivalent, formulations of quantum electrodynamics. Using this format, the reader is offered a gradual, yet flexible introduction to quantum electrodynamics, avoiding formal discussions and excessive shortcuts. Complementing each chapter are numerous examples and exercises that can be used independently from the rest of the book to extend each chapter in many disciplines depending on the interests and needs of the reader.},
language = {English},
publisher = {{Wiley-VCH}},
author = {{Cohen-Tannoudji}, Claude and {Dupont-Roc}, Jacques and Grynberg, Gilbert},
title = {Atom-{{Photon Interactions}}: {{Basic Processes}} and {{Applications}}},
isbn = {978-0-471-29336-1},
shorttitle = {Atom-{{Photon Interactions}}},
abstract = {Atom-Photon Interactions: Basic Processes and Applications allows the reader to master various aspects of the physics of the interaction between light and matter. It is devoted to the study of the interactions between photons and atoms in atomic and molecular physics, quantum optics, and laser physics. The elementary processes in which photons are emitted, absorbed, scattered, or exchanged between atoms are treated in detail and described using diagrammatic representation. The book presents different theoretical approaches, including: * Perturbative methods * The resolvent method * Use of the master equation * The Langevin equation * The optical Bloch equations * The dressed-atom approach Each method is presented in a self-contained manner so that it may be studied independently. Many applications of these approaches to simple and important physical phenomena are given to illustrate the potential and limitations of each method.},
language = {English},
publisher = {{Wiley-VCH}},
author = {{Cohen-Tannoudji}, Claude and {Dupont-Roc}, Jacques and Grynberg, Gilbert},
month = mar,
year = {1998}
}
@article{gruner_green-function_1996,
title = {Green-Function Approach to the Radiation-Field Quantization for Homogeneous and Inhomogeneous {{Kramers}}-{{Kronig}} Dielectrics},
volume = {53},
abstract = {A quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures. Starting from the phenomenological Maxwell equations, where the properties of the dielectric are described by a permittivity consistent with the Kramers-Kronig relations, an expansion of the field operators is performed that is based on the Green function of the classical Maxwell equations and preserves the equal-time canonical field commutation relations. In particular, in frequency intervals with approximately vanishing absorption the concept of quantization through mode expansion for dispersive dielectrics is recognized. The theory further reveals that weak absorption gives rise to space-dependent mode operators that spatially evolve according to quantum Langevin equations in the space domain. To illustrate the applicability of the theory to inhomogeneous structures, the quantization of the radiation field in a dispersive and absorptive one-interface dielectric is performed. \textcopyright{} 1996 The American Physical Society.},
title = {Classical {{Electrodynamics Third Edition}}},
isbn = {978-0-471-30932-1},
abstract = {A revision of the defining book covering the physics and classical mathematics necessary to understand electromagnetic fields in materials and at surfaces and interfaces. The third edition has been revised to address the changes in emphasis and applications that have occurred in the past twenty years.},
language = {English},
publisher = {{Wiley}},
author = {Jackson, John David},
month = aug,
year = {1998},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/3BWPD4BK/John David Jackson-Classical Electrodynamics-Wiley (1999).djvu}
title = {Heterostructures of Photonic Crystals: Frequency Bands and Transmission Coefficients},
volume = {113},
issn = {0010-4655},
shorttitle = {Heterostructures of Photonic Crystals},
abstract = {We present a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of spherical particles of given periodicity parallel to the surface.},
title = {{{MULTEM}} 2: {{A}} New Version of the Program for Transmission and Band-Structure Calculations of Photonic Crystals},
volume = {132},
issn = {0010-4655},
shorttitle = {{{MULTEM}} 2},
abstract = {We present a new version of a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of non-overlapping spherical particles of given periodicity parallel to the surface. The homogeneous media to the left and right of the slab may be different (have different real and positive dielectric functions and magnetic permeabilities).},
title = {\${{T}}\$ Matrix for Electromagnetic Scattering from an Arbitrary Number of Scatterers with Continuously Varying Electromagnetic Properties},
volume = {10},
abstract = {We consider monochromatic electromagnetic scattering from a fixed configuration of an arbitrary number of separate scatteres which are immersed in a medium with constant electric and magnetic properties. Within the scatterers the electric and magnetic properties are assumed to vary smoothly. By considering the integral equations for the scattering we show that the total T matrix for the configuration of the scatterers can be expressed in terms of the T matrices for the individual scatterers in the same way as was previously found for a similar configuration of scatterers, each having a discontinuity in the electric and magnetic properties at the surface and constant electric and magnetic properties in its interior.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/3GBUR6BJ/Ström - 1974 - $T$ matrix for electromagnetic scattering from an .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/ZTRMRQTG/PhysRevD.10.html}
title = {Scattering of Electromagnetic Waves by Spheroidal Particles: A Novel Approach Exploiting the {{T}} Matrix Computed in Spheroidal Coordinates},
volume = {37},
issn = {0003-6935, 1539-4522},
shorttitle = {Scattering of Electromagnetic Waves by Spheroidal Particles},
author = {R. E. Slusher, B. J. Eggleton (auth.), Richard E. Slusher, Benjamin J. Eggleton (eds.)},
year = {2003},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/IT6C2GJ2/(Springer Series in Photonics 10) R. E. Slusher, B. J. Eggleton (auth.), Richard E. Slusher, Benjamin J. Eggleton (eds.)-Nonlinear Photonic Crystals.pdf}
}
@book{ralf_b._wehrspohn_nanophotonic_2008,
title = {Nanophotonic {{Materials}}: {{Photonic Crystals}}, {{Plasmonics}}, and {{Metamaterials}}},
isbn = {3-527-40858-4 978-3-527-40858-0 978-3-527-62189-7},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/BRK5MPPJ/(Optical science and engineering 102) Kiyotoshi Yasumoto-Electromagnetic Theory and Applications for Photonic Crystals-Taylor & Francis (2006).pdf}
}
@book{sakoda_optical_2005,
edition = {2nd ed},
series = {Springer Series in Optical Sciences, v. 80},
title = {Optical Properties of Photonic Crystals},
isbn = {3-540-20682-5 978-3-540-20682-8 3-540-26965-7 978-3-540-26965-6},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/7BAKUUCB/(Springer series in optical sciences, v. 80) Kazuaki Sakoda-Optical properties of photonic crystals-Springer (2005).pdf}
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/8SMJJUG6/Noda S., Baba T.-Roadmap on Photonic Crystals-Springer (2003).djvu}
}
@book{peter_markos_wave_2008,
edition = {illustrated edition},
title = {Wave {{Propagation}}: {{From Electrons}} to {{Photonic Crystals}} and {{Left}}-{{Handed Materials}}},
title = {Mie Scattering by an Anisotropic Object. {{Part I}}. {{Homogeneous}} Sphere},
volume = {23},
copyright = {\textcopyright{} 2006 Optical Society of America},
issn = {1520-8532},
abstract = {Establishing a vector spherical harmonic expansion of the electromagnetic field propagating inside an arbitrary anisotropic medium, we extend Mie theory to the diffraction by an anisotropic sphere, with or without losses. The particular case of a uniaxial material leads to a simpler analysis. This work opens the way to the construction of a differential theory of diffraction by a three-dimensional object with arbitrary shape, filled by an arbitrary anisotropic material.},
title = {Mie Scattering by an Anisotropic Object. {{Part II}}. {{Arbitrary}}-Shaped Object: Differential Theory},
volume = {23},
copyright = {\textcopyright{} 2006 Optical Society of America},
issn = {1520-8532},
shorttitle = {Mie Scattering by an Anisotropic Object. {{Part II}}. {{Arbitrary}}-Shaped Object},
abstract = {The differential theory of diffraction by an arbitrary-shaped body made of arbitrary anisotropic material is developed. The electromagnetic field is expanded on the basis of vector spherical harmonics, and the Maxwell equations in spherical coordinates are reduced to a first-order differential set. When discontinuities of permittivity exist, we apply the fast numerical factorization to find the link between the electric field vector and the vector of electric induction, developed in a truncated basis. The diffraction problem is reduced to a boundary-value problem by using a shooting method combined with the S-matrix propagation algorithm, formulated for the field components instead of the amplitudes.},
title = {{\emph{T}} Matrix of the Homogeneous Anisotropic Sphere: Applications to Orientation-Averaged Resonant Scattering},
volume = {24},
copyright = {\textcopyright{} 2007 Optical Society of America},
issn = {1520-8532},
shorttitle = {{\emph{T}} Matrix of the Homogeneous Anisotropic Sphere},
abstract = {We illustrate some numerical applications of a recently derived semianalytic method for calculating the T matrix of a sphere composed of an arbitrary anisotropic medium with or without losses. This theory is essentially an extension of Mie theory of the diffraction by an isotropic sphere. We use this theory to verify a long-standing conjecture by Bohren and Huffman that the extinction cross section of an orientation-averaged anisotropic sphere is not simply the average of the extinction cross sections of three isotropic spheres, each having a refractive index equal to that of one of the principal axes.},
title = {T-Matrix Computations of Light Scattering by Large Spheroidal Particles},
volume = {109},
issn = {0030-4018},
abstract = {It is well known that T-matrix computations of light scattering by nonspherical particles may suffer from the ill-conditionality of the process of matrix inversion, which has precluded calculations for particle size parameters larger than about 25. It is demonstrated that calculating the T-matrix using extended-precision instead of double-precision floating-point variables is an effective approach for suppressing the numerical instability in computations for spheroids and allows one to increase the maximum particle size parameter for which T-matrix computations converge by as significant a factor as 2\textendash{}2.7. Yet this approach requires only a negligibly small extra memory, an affordable increase in CPU time consumption, and practically no additional programming effort. As a result, the range of particle size parameters, for which rigorous T-matrix computations of spheroidal scattering can be performed, now covers a substantial fraction of the gap between the domains of applicability of the Rayleigh and geometrical optics approximations.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {T-Matrix Computations of Light Scattering by Nonspherical Particles: {{A}} Review},
volume = {55},
issn = {0022-4073},
shorttitle = {T-Matrix Computations of Light Scattering by Nonspherical Particles},
abstract = {We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanied by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.},
author = {Mishchenko, Michael I. and Travis, Larry D. and Mackowski, Daniel W.},
month = may,
year = {1996},
pages = {535-575},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/8EA7QMDG/Mishchenko et al. - 1996 - T-matrix computations of light scattering by nonsp.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HNWF8F6R/0022407396000027.html}
}
@article{asano_light_1975,
title = {Light {{Scattering}} by a {{Spheroidal Particle}}},
volume = {14},
copyright = {\textcopyright{} 1975 Optical Society of America},
issn = {1539-4522},
abstract = {The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.},
abstract = {We further test our electromagnetic multisphere-scattering solution developed earlier by comparing theoretical predictions from the theory with a set of laboratory measurements of microwave analog to light scattering by aggregated spheres. This solution is an extension of Mie theory to the multisphere case, generally applicable to an arbitrary aggregate of spherical and/or nonspherical particles. It is demonstrated once again that the theory is in a uniform agreement with experiment, convincingly confirming the veracity of the multiparticle-scattering formulation. The computer code for the calculation of the scattering by an aggregate of spheres in a fixed orientation and the experimental data havebeen made publically available.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Light Scattering Computational Methods for Particles on Substrates},
volume = {70},
issn = {0022-4073},
abstract = {Four theoretical and computational methods to describe the scattering from simple particles on substrates are presented and discussed. These methods are based on the extinction theorem, image theory, the double-interaction model, and geometrical optics (ray-tracing). We compare the four methods with measurements of scattered light from gold metallic cylinders resting on a gold metallic substrate. In particular, we analyze the co-polarized (s and p polarization) full-scan and back-scattering intensities in the far field within the plane of incidence. Advantages and disadvantages of each method as a computational and reliable tool are discussed.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Discrete Sources Method for Light Scattering Analysis from {{3D}} Asymmetrical Features on a Substrate},
volume = {70},
issn = {0022-4073},
abstract = {The discrete sources method is extended to analyze polarized light scattering by three-dimensional asymmetrical features on a plane penetrable substrate. The strict mathematical model and corresponding numerical scheme are described. Computer simulation results of non-spherical micro-particle scattering show that particle shape has a stronger effect on measured response for normal incident scanners.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Light-Scattering by Optically Soft Randomly Oriented Spheroids},
volume = {70},
issn = {0022-4073},
abstract = {In the framework of the Rayleigh\textendash{}Gans\textendash{}Debye approximation and anomalous diffraction approaches, the light scattering characteristics of randomly oriented spheroids have been investigated. It has been proved that the system of randomly oriented spheroids is equivalent to the system of polydisperse spherical particles that have the same values of volume and surface area as nonspherical particles. The power law size distribution meeting these requirements has been obtained.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Calculations of the {{Mie}} Scattering Coefficients for Multilayered Particles with Large Size Parameters},
volume = {70},
issn = {0022-4073},
abstract = {The calculation procedure for the scattering coefficients appearing in the Mie theory is discussed for a case of multilayered particles with a large size parameter. There are two different aspects to the problem. The first aspect concerns a case where the imaginary part of the size parameters remains small. Shown here is the possibility for avoiding the canonical recommendations which prescribe using both upward and downward recursions for different types of Bessel functions. We have justified the procedure based on the upward recursions only where results are as stable as those in the canonical one. The second aspect concerns the case with a large imaginary part of the size parameter. The calculation procedure for a multilayered particle fails in such a case because of 0/0-type uncertainty. However, this problem can be overcome by using the proper asymptotic relations at crucial points. The numerical results are demonstrated for spherical and cylindrical multilayered particles.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Comparisons of the Discrete-Dipole Approximation and Modified Double Interaction Model Methods to Predict Light Scattering from Small Features on Surfaces},
volume = {70},
issn = {0022-4073},
abstract = {Two numerical methods to model light scattering from illuminated features on surfaces are presented. The discrete-dipole approximation (DDA) method is considered, as well as the modified double interaction method (MDIM). The DDA method models electromagnetic scattering of continuous features using discrete dipoles placed on a lattice structure. Sommerfeld integral terms are used to model dipole/surface interaction in the near-field. The MDIM method first computes scattering from the features based in free space using other methods such as Mie theory or other standard light scattering codes (including DDA). The surface interaction is modeled as a first approximation by means of a geometrical shadowing effect and the Fresnel coefficients. Comparisons of the methods will be shown for light scattering from spherical features. The material properties of dielectric and metallic materials will be considered and the feature sizes will be varied. The prediction accuracy and computational requirements of each method will be investigated. For most cases, the studies will show that the DDA method is more accurate than the MDIM method for dielectric materials since the modeling of the feature and surface electromagnetic interaction is more accurate; however, the modified double interaction method may be advantageous over the discrete-dipole approximation method for metallic features because of lesser computational times and memory requirements.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {T-Matrix Method for Electromagnetic Scattering from Scatterers with Complex Structure},
volume = {70},
issn = {0022-4073},
abstract = {We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {An Effective Medium Method for Calculation of the {{T}} Matrix of Aggregated Spheres},
volume = {70},
issn = {0022-4073},
abstract = {An effective medium approach is developed for describing the radiative scattering characteristics of large-scale clusters of spheres. The formulation assumes that the waves exciting each sphere in the cluster can be described by a regular vector harmonic expansion, centered about a common origin of the cluster, and characterized by an effective propagation constant mek. By combining this description with the multiple sphere interaction equations a `homogeneous' T matrix of the cluster is derived, which is analogous to using the effective propagation constant models of the Varadans in conjunction with Waterman's EBCM. However, it is shown that the homogeneous T matrix will not automatically satisfy energy conservation because it cannot account for dependent scattering effects among the spheres. A `discrete' formulation of the T matrix is then developed which retains the effective medium description of the exciting field yet provides for energy conservation. Illustrative calculations show that the effective medium T matrix can provide accurate predictions of the cross sections and scattering matrices of clusters containing a large number of uniformly packed spheres, yet this approximation uses a fraction of the computational time required for an exact solution.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/9E7R7IRX/Mackowski - 2001 - An effective medium method for calculation of the .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/D75CJ78C/S002240730100022X.html}
}
@article{simao_comparative_2001,
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {A Comparative Study in Resonant Light Scattering between Spherical and Cylindrical Dielectric Hosts with a Metallic Inclusion},
volume = {70},
issn = {0022-4073},
abstract = {We show that dielectric spherical and cylindrical particles contaminated with a metallic inclusion have similar spectral resonant behavior. Both geometries show resonance suppression as the position of the inclusion varies. Moreover, it was theoretically observed that the spherical particle suppresses a resonant mode earlier than the cylindrical one. Based on semi-classical arguments, a physical interpretation of this fact is given. In addition, a comment is also made regarding Wiscombe's criteria for estimating the size of the coefficient matrix used to solve the truncated non-homogeneous set of linear equations related to this problem.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {Light-Scattering Properties of Fractal Aggregates: Numerical Calculations by a Superposition Technique and the Discrete-Dipole Approximation},
volume = {70},
issn = {0022-4073},
shorttitle = {Light-Scattering Properties of Fractal Aggregates},
abstract = {Dust particles in space often grow by mutual collisions and appear to be an agglomeration of individual grains, the morphology of which can be described by the concept of fractals. In this paper, we study light scattering by fractal aggregates of identical spheres (monomers) using the superposition technique incorporated into the T-matrix method where the orientationally averaged scattering matrix is analytically obtained. We also apply the discrete-dipole approximation, in which the dipole polarizability of spherical monomers is determined by the first term of the scattering coefficients in the Mie theory. Two cases of the ballistic aggregation process (particle\textendash{}cluster and cluster\textendash{}cluster aggregations) are considered to model fractal aggregates consisting of silicate or carbon material. The dependences of light-scattering properties on the monomer sizes, aggregate structures and material compositions are intensively investigated. The light-scattering properties of the fractal aggregates strongly depend on the size parameters of the monomers. The difference in the scattering function between the particle\textendash{}cluster and cluster\textendash{}cluster aggregates can be seen in the case of monomers much smaller than the wavelength of incident radiation. When the size parameter of monomers exceeds unity, the material composition of the monomers influences the light-scattering properties of the aggregates, but different morphologies result in similar scattering and polarization patterns. We show that silicate aggregates consisting of submicron-sized monomers, irrespective of the aggregate size and morphology, produce a backscattering enhancement and a negative polarization observed for dust in the solar system.},
series = {Light {{Scattering}} by {{Non}}-{{Spherical Particles}}},
title = {A Study of the Absorption and Extinction Properties of Hexagonal Ice Columns and Plates in Random and Preferred Orientation, Using Exact {{T}}-Matrix Theory and Aircraft Observations of Cirrus},
volume = {70},
issn = {0022-4073},
abstract = {Absorption and extinction properties of the finite hexagonal ice column and hexagonal ice plate in random and preferred orientation are studied at the wavelength of 80 {$\mu$}m using a new implementation of exact T-matrix theory. For the case of random orientation at size parameters around two, it is shown that the hexagonal ice column and hexagonal ice plate absorption resonances are diminished relative to Mie theory, and the same behaviour is also noted for an aggregate particle consisting of eight hexagonal elements. The absorption properties of the aggregate particle have been calculated using the finite-difference time-domain method. It is also shown that extinction and absorption solutions for the hexagonal ice column and hexagonal ice plate can differ significantly if incidence occurs perpendicular or parallel to the cylindrical axis of the hexagon. For the case of perpendicular incidence on the edge of the hexagon, absorption solutions can exceed those of Mie theory, and for the case of parallel incidence, behaviour of the extinction solutions for hexagonal ice columns and hexagonal ice plates is shown to be similar to previously published work based on the prolate and oblate spheroid. Interference structure, associated with surface waves, is resolved on the hexagonal column extinction solution and the hexagonal plate absorption solution, thereby demonstrating that surface waves can exist on a non-axisymmetric geometry. The usefulness of assuming the hexagonal ice column in retrieval of ice crystal effective size is also investigated using aircraft based radiometric observations of semi-transparent cirrus at the wavelengths of 8.5 and 11 {$\mu$}m.},
author = {Baran, Anthony J. and Francis, Peter N. and Havemann, Stephan and Yang, Ping},
month = aug,
year = {2001},
pages = {505-518},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/QA86H7C3/Baran ym. - 2001 - A study of the absorption and extinction propertie.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/C6E9VZIB/S0022407301000255.html}
}
@article{evlyukhin_multipole_2013,
title = {Multipole Analysis of Light Scattering by Arbitrary-Shaped Nanoparticles on a Plane Surface},
volume = {30},
copyright = {\textcopyright{} 2013 Optical Society of America},
issn = {1520-8540},
abstract = {A theoretical approach, based on the discrete dipole approximation, for multipole analysis of light scattering by arbitrary-shaped nanoparticles located near or on a plane surface is presented. The obtained equations include the first multipoles up to the magnetic quadrupole and electric octupole moments. It is discussed how the suggested approach can be applied to the problem of multipole scattering of surface plasmon polaritons. As an example, the theoretical framework is used for investigation of light scattering by cylindrical Si nanoparticles located on different dielectric substrates, manifesting resonant interaction of these particles with light.},
title = {Multipole Light Scattering by Nonspherical Nanoparticles in the Discrete Dipole Approximation},
volume = {84},
abstract = {In the framework of the discrete dipole approximation we develop a theoretical approach that allows the analysis of the role of multipole modes in the extinction and scattering spectra of arbitrary shaped nanoparticles. The main attention is given to the first multipoles including magnetic dipole and electric quadrupole moments. The role of magnetic quadrupole and electric octupole modes is also discussed. The method is applied to nonspherical Si nanoparticles with resonant multipole responses in the visible optical range, allowing a decomposition of single extinction (scattering) peaks into their constituent multipole contributions. It is shown by numerical simulations that it is possible to design silicon particles for which the electric dipole and magnetic dipole resonances are located at the same wavelength under certain propagation directions of incident light, providing new possibilities in metamaterial developments.},
title = {Optical Response Features of {{Si}}-Nanoparticle Arrays},
volume = {82},
abstract = {Periodic structures of spherical silicon particles are analyzed using the coupled-dipole equations for studying optical response features and local electromagnetic fields. The model takes into account the electric and magnetic dipole moments of the particles embedded in a homogeneous dielectric medium. Particles with radius of 65 nm and larger are considered. It is shown that, due to the large permittivity of silicon, the first two Mie resonances are located in the region of visible light, where the absorption is small and the extinction is basically determined by scattering. The main contribution is given by the induced magnetic and electric dipoles of the particles. Thus, in contrast to metal particle arrays, here is a possibility to combine separately either the electric or magnetic dipole resonances of individual particles with the structural features. As a result, extinction spectra can have additional narrow resonant peaks connected with multiple light scattering by the magnetic dipoles and displaying a Fano-type resonant profile. Reflection and transmission properties of the Si particle arrays are investigated and the conditions of low light reflection and transmission by the particle arrays are discussed, as well as the applicability of the dipole approach. It is shown that the light transmission of finite-size arrays of Si particles can be significantly suppressed at the conditions of the particle magnetic dipole resonance. It is demonstrated that, using resonant conditions, one can separately control the enhancements of local electric and magnetic fields in the structures.},
title = {Nonradiating Anapole Modes in Dielectric Nanoparticles},
volume = {6},
copyright = {2015 Nature Publishing Group},
issn = {2041-1723},
abstract = {{$<$}p{$>$}
The anapole is an intriguing example of a nonradiating source useful in the study of electromagnetic properties in complex phenomena. Here, Miroshnichenko \emph{et al.} demonstrate that a single dielectric nanoparticle can exhibit a radiationless anapole mode at visible\…{$<$}/p{$>$}},
author = {Miroshnichenko, Andrey E. and Evlyukhin, Andrey B. and Yu, Ye Feng and Bakker, Reuben M. and Chipouline, Arkadi and Kuznetsov, Arseniy I. and Luk'yanchuk, Boris and Chichkov, Boris N. and Kivshar, Yuri S.},
title = {Optical Theorem and Multipole Scattering of Light by Arbitrarily Shaped Nanoparticles},
volume = {94},
abstract = {The application of Cartesian multipoles in irreducible representations provides the possibility to get explicit contributions of the toroidal multipole terms in the extinction and scattering power without the introduction of special form factors. In the framework of the Cartesian multipoles, we obtained multipole decomposition (up to the third order) of the induced polarization (current) inside an arbitrarily shaped scatterer (nanoparticle). The third-order decomposition includes the toroidal dipole, magnetic quadrupole, electric octupole terms, and also nonradiating terms. The corresponding multipole decomposition of the scattering cross section, taking into account the electric octupole term, is derived and compared with the multipole decomposition of the extinction cross section obtained using the optical theorem. We show that the role of multipoles in the optical theorem (light extinction) and scattering by arbitrarily shaped nanoparticles can be different. This can result in seemingly paradoxical conclusions with respect to the appearance of multipole contributions in the scattering and extinction cross sections. This fact is especially important for absorptionless nanoparticles, for which the scattering cross section can be calculated using the optical theorem, because in this case extinction is solely determined by scattering. Demonstrative results concerning the role of third-order multipoles in the resonant optical response of high-refractive-index dielectric nanodisks, with and without a through hole at the center, are presented. It is shown that the optical theorem results in a negligible role of the third-order multipoles in the extinction cross sections, whereas these multipoles provide the main contribution in the scattering cross sections.},
title = {Ewald Summations in Systems with Two-Dimensional Periodicity},
volume = {68},
issn = {1097-461X},
abstract = {This study presents formulas for the electrostatic energy of lattices with two-dimensional periodicity, based on Fourier representations and alternatively on the Ewald procedure for convergence acceleration. The work extends the contributions of previous investigators by taking full advantage of plane-group symmetry and by providing analytical formulas for all derivatives of the energy through second order. The derivatives considered include those with respect to the positions of all charges within the unit cell, those with respect to the lattice vectors (cell deformations), and those involving both types of variables.~\textcopyright{} 1998 John Wiley \& Sons, Inc. Int J Quant Chem 68: 385\textendash{}404, 1998},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/JAZ7DZXT/Harris - 1998 - Ewald summations in systems with two-dimensional p.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/KZ577FAF/abstract.html}
}
@article{mazars_lekner_2005,
archivePrefix = {arXiv},
eprinttype = {arxiv},
eprint = {cond-mat/0301161},
title = {Lekner Summations and {{Ewald}} Summations for Quasi-Two Dimensional Systems},
volume = {103},
issn = {0026-8976, 1362-3028},
abstract = {Using the specific model of a bilayer of classical charged particles (bilayer Wigner crystal), we compare the predictions for energies and pair distribution functions obtained by Monte Carlo simulations using three different methods available to treat the long range Coulomb interactions in systems periodic in two directions but bound in the third one. The three methods compared are: the Ewald method for quasi-two dimensional systems [D.E. Parry, Surf. Sci. \$\textbackslash{}bm\{49\}\$, 433 (1975); \textbackslash{}it\{ibid.\}, \$\textbackslash{}bm\{54\}\$, 195 (1976)], the Hautman-Klein method [J. Hautman and M.L. Klein, Mol. Phys. \$\textbackslash{}bm\{75\}\$, 379 (1992)] and the Lekner summations method [J. Lekner, Physica A\$\textbackslash{}bm\{176\}\$, 485 (1991)]. All of the three method studied in this paper may be applied to any quasi-two dimensional systems, including those having not the specific symmetry of slab systems. For the particular system used in this work, the Ewald method for quasi-two dimensional systems is exact and may be implemented with efficiency; results obtained with the other two methods are systematically compared to results found with the Ewald method. General recommendations to implement with accuracy, but not always with efficiency, the Lekner summations technique in Monte Carlo algorithms are given.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/26XXWVMR/Mazars - 2005 - Lekner summations and Ewald summations for quasi-t.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/7TE92NAR/0301161.html}
}
@article{hummer_molecular_1998,
title = {Molecular {{Theories}} and {{Simulation}} of {{Ions}} and {{Polar Molecules}} in {{Water}}},
volume = {102},
issn = {1089-5639},
abstract = {Recent developments in molecular theories and simulation of ions and polar molecules in water are reviewed. The hydration of imidazole and imidazolium is used to exemplify the theoretical issues. The treatment of long-ranged electrostatic interactions in simulations is discussed extensively. It is argued that the Ewald approach is an easy way to get correct hydration free energies corresponding to thermodynamic limit from molecular calculations. Molecular simulations with Ewald interactions and periodic boundary conditions can also be more efficient than many common alternatives. The Ewald treatment permits a conclusive extrapolation to infinite system size. Accurate results for well-defined models have permitted careful testing of simple theories of electrostatic hydration free energies, such as dielectric continuum models. The picture that emerges from such testing is that the most prominent failings of the simplest theories are associated with solvent proton conformations that lead to non-Gaussian fluctuations of electrostatic potentials. Thus, the most favorable cases for second-order perturbation theories are monoatomic positive ions. For polar and anionic solutes, continuum or Gaussian theories are less accurate. The appreciation of the specific deficiencies of those simple models have led to new concepts, multistate Gaussian and quasi-chemical theories, which address the cases for which the simpler theories fail. It is argued that, relative to direct dielectric continuum treatments, the quasi-chemical theories provide a better theoretical organization for the computational study of the electronic structure of solution species.},
author = {Hummer, Gerhard and Pratt, Lawrence R. and Garc{\'i}a, Angel E.},
month = oct,
year = {1998},
pages = {7885-7895},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/WU5N5TMT/Hummer ym. - 1998 - Molecular Theories and Simulation of Ions and Pola.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/I65M7FSZ/jp982195r.html}
}
@incollection{weis_simple_,
series = {Advances in {{Polymer Science}}},
title = {Simple {{Dipolar Fluids}} as {{Generic Models}} for {{Soft Matter}}},
isbn = {978-3-540-26091-2 978-3-540-31581-0},
abstract = {The physical properties, based on simulation results, of model fluids and solids bearing an electric or magnetic point dipole moment are described. Comparison is made with experimental data on ferrofluids and electro- or magneto-rheological fluids. The qualitative agreement between experiment and simulation shows the interest of these simple models for the comprehension of physical systems where the dipolar interaction dominates.},
author = {Gao, G. T. and Zeng, X. C. and Wang, Wenchuan},
month = feb,
year = {1997},
pages = {3311-3317},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/P9P9D9CJ/Gao ym. - 1997 - Vapor–liquid coexistence of quasi-two-dimensional .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/M835BVF8/1.html}
}
@article{leeuw_electrostatic_1979,
title = {Electrostatic Lattice Sums for Semi-Infinite Lattices},
volume = {37},
issn = {0026-8976},
abstract = {The techniques for the rapid computation of energies of three-dimensional neutral periodic assemblies of charged particles are extended to semi-infinite arrays and assemblies of ions in infinite filsm. The results will be useful for simulation of ionic movements in fast-ion conductors and dense colloidal dispersions.},
title = {Efficient {{Methods}} to {{Compute Long}}-{{Range Interactions}} for {{Soft Matter Systems}}},
isbn = {978-3-540-26091-2 978-3-540-31581-0},
abstract = {An extensive introduction to the topic of how to compute long-range interactions efficiently is presented. First, the traditional Ewald sum for 3D Coulomb systems is reviewed, then the P3M method of Hockney and Eastwood is discussed in some detail, and alternative ways of dealing with the Coulomb sum are briefly mentioned. The best strategies to perform the sum under partially periodic boundary conditions are discussed, and two recently developed methods are presented, namely the MMM2D and ELC methods for two-dimensionally periodic boundary conditions, and the MMM1D method for systems with only one periodic coordinate. The dipolar Ewald sum is also reviewed. For some of the methods, error formulas are provided which enable the algorithm to be tuned at a predefined accuracy. Open image in new window},
title = {Rapid Solution of Integral Equations of Classical Potential Theory},
volume = {60},
issn = {0021-9991},
abstract = {An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory. CPU time requirements for previously published algorithms of this type are proportional to n2, where n is the number of nodes in the discretization of the boundary of the region. The CPU time requirements for the algorithm of the present paper are proportional to n, making it considerably more practical for large scale problems.},
title = {Application of the Generalized Shift Operator to the {{Hankel}} Transform},
volume = {3},
issn = {2193-1801},
abstract = {It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that under this generalized definition of shift, both convolution and shift theorems now apply to the Hankel transform. The operation of a generalized shift is compared to that of a simple shift via example.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/IXG9H85Q/Baddour - 2014 - Application of the generalized shift operator to t.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/IJ3X5XXC/2193-1801-3-246.html}
}
@article{adkins_three-dimensional_2013,
archivePrefix = {arXiv},
eprinttype = {arxiv},
eprint = {1302.1830},
primaryClass = {math-ph},
title = {Three-Dimensional {{Fourier}} Transforms, Integrals of Spherical {{Bessel}} Functions, and Novel Delta Function Identities},
abstract = {We present a general approach for evaluating a large variety of three-dimensional Fourier transforms. The transforms considered include the useful cases of the Coulomb and dipole potentials, and include situations where the transforms are singular and involve terms proportional to the Dirac delta function. Our approach makes use of the Rayleigh expansion of exp(i p.r) in terms of spherical Bessel functions, and we study a number of integrals, including singular integrals, involving a power of the independent variable times a spherical Bessel function. We work through several examples of three-dimensional Fourier transforms using our approach and show how to derive a number of identities involving multiple derivatives of 1/r, 1/r\^2, and delta(\textbackslash{}vec r).},
title = {Operational and Convolution Properties of Three-Dimensional {{Fourier}} Transforms in Spherical Polar Coordinates},
volume = {27},
copyright = {\textcopyright{} 2010 Optical Society of America},
issn = {1520-8532},
abstract = {For functions that are best described with spherical coordinates, the three-dimensional Fourier transform can be written in spherical coordinates as a combination of spherical Hankel transforms and spherical harmonic series. However, to be as useful as its Cartesian counterpart, a spherical version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the spherical version of the standard Fourier operation toolset. In particular, convolution in various forms is discussed in detail as this has important consequences for filtering. It is shown that standard multiplication and convolution rules do apply as long as the correct definition of convolution is applied.},
author = {Wang, Qing and Ronneberger, Olaf and Burkhardt, Hans},
year = {2008},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/I36FI8XD/Wang et al. - 2008 - Fourier Analysis in Polar and Spherical Coordinate.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/62QT93PD/WRB08.html}
}
@article{bloomfield_indefinite_2017,
archivePrefix = {arXiv},
eprinttype = {arxiv},
eprint = {1703.06428},
primaryClass = {math},
title = {Indefinite {{Integrals}} of {{Spherical Bessel Functions}}},
abstract = {Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in \$x\$ multiplying one or two spherical Bessel functions of the first kind \$j\_l(x)\$ with integer order \$l\$. Closed-form solutions are presented where possible, and recursion relations are developed that are guaranteed to reduce all integrals in this class to closed-form solutions. These results allow for definite integrals over spherical Bessel functions to be computed quickly and accurately. For completeness, we also present our results in terms of ordinary Bessel functions, but in general, the recursion relations do not terminate.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/253VUGDB/Bloomfield et al. - 2017 - Indefinite Integrals of Spherical Bessel Functions.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/UQ4RZDZ2/1703.html}
}
@article{sheppard_hankel_2015,
title = {The {{Hankel Transform}} in N-Dimensions and {{Its Applications}} in {{Optical Propagation}} and {{Imaging}}},
volume = {188},
issn = {1076-5670},
abstract = {Wave propagation is considered in multidimensional reciprocal space. For the first Rayleigh-Sommerfeld diffraction integral, the propagating field can be represented by homogeneous and inhomogeneous components. These add up to give a propagating component on a hemispherical surface in reciprocal space, and an evanescent component that lies totally outside the corresponding sphere. If evanescent waves can be neglected, the 3D angular spectrum method, entailing inverse Fourier transformation of the weighted hemisphere, can be used to calculate efficiently the propagated field. This basic concept is applied in spaces of different dimensionality. For functions displaying hyperspherical symmetry in nD space, the corresponding Hankel transformation leads to Hankel-transform pairs. Tables of functions relevant in wave propagation, diffraction, and information optics are presented. The two-dimensional (2D) case is particularly important as it can be applied to propagation in planar wave guides, surface plasmonics, and cross sections of propagationally invariant fields, as well as to fringe analysis and image processing in two dimensions.},
title = {Combinatorial {{Identities}} for {{Stirling Numbers}}},
abstract = {This book is a unique work which provides an in-depth exploration into the mathematical expertise, philosophy, and knowledge of H W Gould. It is written in a style that is accessible to the reader with basic mathematical knowledge, and yet contains material that will be of interest to the specialist in enumerative combinatorics. This book begins with exposition on the combinatorial and algebraic techniques that Professor Gould uses for proving binomial identities. These techniques are then applied to develop formulas which relate Stirling numbers of the second kind to Stirling numbers of the first kind. Professor Gould's techniques also provide connections between both types of Stirling numbers and Bernoulli numbers. Professor Gould believes his research success comes from his intuition on how to discover combinatorial identities. This book will appeal to a wide audience and may be used either as lecture notes for a beginning graduate level combinatorics class, or as a research supplement for the specialist in enumerative combinatorics. Sample Chapter(s)Foreword (94 KB)Chapter 1: Basic Properties of Series (183 KB) Contents: Basic Properties of Series The Binomial Theorem Iterative Series Two of Professor Gould's Favorite Algebraic Techniques Vandermonde Convolution The nth Difference Operator and Euler's Finite Difference Theorem Melzak's Formula Generalized Derivative Formulas Stirling Numbers of the Second Kind S(n; k) Eulerian Numbers Worpitzky Numbers Stirling Numbers of the First Kind s(n; k) Explicit Formulas for s(n; n \textemdash{} k) Number Theoretic Definitions of Stirling Numbers Bernoulli Numbers Appendix A: Newton-Gregory Expansions Appendix B: Generalized Bernoulli and Euler Polynomials Readership: Undergraduates, graduates and researchers interested in combinatorial and algebraic techniques.},
author = {\cyrchar\CYRA.\cyrchar\CYRP, \cyrchar\CYRP\cyrchar\cyrr\cyrchar\cyru\cyrchar\cyrd\cyrchar\cyrn\cyrchar\cyri\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRYU.\cyrchar\CYRA, \cyrchar\CYRB\cyrchar\cyrr\cyrchar\cyrery\cyrchar\cyrch\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRO.\cyrchar\CYRI, \cyrchar\CYRM\cyrchar\cyra\cyrchar\cyrr\cyrchar\cyri\cyrchar\cyrch\cyrchar\cyre\cyrchar\cyrv{}},
author = {\cyrchar\CYRA.\cyrchar\CYRP, \cyrchar\CYRP\cyrchar\cyrr\cyrchar\cyru\cyrchar\cyrd\cyrchar\cyrn\cyrchar\cyri\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRYU.\cyrchar\CYRA, \cyrchar\CYRB\cyrchar\cyrr\cyrchar\cyrery\cyrchar\cyrch\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRO.\cyrchar\CYRI, \cyrchar\CYRM\cyrchar\cyra\cyrchar\cyrr\cyrchar\cyri\cyrchar\cyrch\cyrchar\cyre\cyrchar\cyrv{}},
author = {\cyrchar\CYRA.\cyrchar\CYRP, \cyrchar\CYRP\cyrchar\cyrr\cyrchar\cyru\cyrchar\cyrd\cyrchar\cyrn\cyrchar\cyri\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRYU.\cyrchar\CYRA, \cyrchar\CYRB\cyrchar\cyrr\cyrchar\cyrery\cyrchar\cyrch\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{} and \cyrchar\CYRO.\cyrchar\CYRI, \cyrchar\CYRM\cyrchar\cyra\cyrchar\cyrr\cyrchar\cyri\cyrchar\cyrch\cyrchar\cyre\cyrchar\cyrv{}},
author = {\cyrchar\CYRV.\cyrchar\CYRA, \cyrchar\CYRD\cyrchar\cyri\cyrchar\cyrt\cyrchar\cyrk\cyrchar\cyri\cyrchar\cyrn{} and \cyrchar\CYRA.\cyrchar\CYRP, \cyrchar\CYRP\cyrchar\cyrr\cyrchar\cyru\cyrchar\cyrd\cyrchar\cyrn\cyrchar\cyri\cyrchar\cyrk\cyrchar\cyro\cyrchar\cyrv{}},
year = {1962}
}
@article{wu_accurate_1993,
title = {An {{Accurate Computation}} of the {{Hypergeometric Distribution Function}}},
volume = {19},
issn = {0098-3500},
abstract = {The computation of the cumulative hypergeometric distribution function is of interest to many researchers who are working in the computational sciences and related areas. Presented here is a new method for computing this function that applies prime number factorization to the factorials. We also apply cancellation to the numerator and denominator to reduce the computational complexity of the initial, the tail end, or weighted probabilities to achieve maximum accuracy. The new method includes two algorithms, one using recursion and the other using iteration. These two algorithms are machine independent; precision is arbitrary, subject to storage limitation. The development of the algorithms is discussed, and some test results and the comparison of these two algorithms are given. To implement both algorithms, we use the Ada programming language that is an American National Standard Institute standardized language. The language has special features such as exception handling and tasks. Exception handling is used to make programming easier and to prevent overflow or underflow conditions during the execution of the program. Tasks are used to compute the numerator and denominator concurrently, and to maximize the possible number of integer multiplications in the numerator and denominator. All of the computations can be done on currently available machines, and the time consumed by these computations remains reasonably small.},
keywords = {Ada programming language,Peizer approximations,exception handling,hypergeometric distribution function,prime number factorization,tasking},
pages = {33--43},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/CC3GQ79I/Wu - 1993 - An Accurate Computation of the Hypergeometric Dist.pdf}
}
@article{ziv_fast_1991,
title = {Fast {{Evaluation}} of {{Elementary Mathematical Functions}} with {{Correctly Rounded Last Bit}}},
title = {Light Interaction with Photonic and Plasmonic Resonances},
abstract = {In this review, we look at the concepts and state-of-the-art concerning the analysis of micro and nanoresonators from the underlying concept of their natural resonances, also called quasi-normal modes (QNMs). It is these modes with complex frequencies that are responsible for the spectral response and temporal dynamics of the resonators. They are initially excited by the driving near or far-field, then loaded before exponentially decaying in time due to power leakage or absorption. We explore how QNM-expansion formalisms model these basic effects, and how modal interferences give rise to complex Fano-like phenomena in the dynamics. An extensive overview of the historical background and a detailed discussion of more recent relevant theoretical and numerical advances concerning QNMs in electromagnetism is then presented. We further provide a concise description of the role of QNMs with reference to a number of examples involving electromagnetic resonant fields and matter, the modification of the local density of electromagnetic states with resonance, the weak and strong couplings of quantum oscillators with confined fields, the superradiance assisted by nanoresonators, the perturbation of resonance modes, and application of resonant modes in disordered media. We conclude our review with a perspective on the future of QNM concepts.},
title = {Photonic Band Gaps for Arrays of Perfectly Conducting Cylinders},
volume = {52},
abstract = {We study the propagation of electromagnetic waves through arrays of perfectly conducting cylinders for both fundamental polarization cases s and p. We use a generalized Rayleigh identity method and show that for p polarization the fundamental band defines an effective refractive index not in keeping with electrostatics. We exhibit the photonic band structures for very dilute arrays, where they tend towards the expected free-propagation form. We also study them for arrays approaching touching, where very interesting differences between s and p polarization behavior are manifest.},
author = {Nicorovici, N. A. and McPhedran, R. C. and Botten, L. C.},
month = jul,
year = {1995},
pages = {1135-1145},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/44QN6K4W/PhysRevE.52.1135.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/USYDNPNY/Nicorovici ym. - 1995 - Photonic band gaps for arrays of perfectly conduct.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/RTPI6HEA/PhysRevE.52.html}
}
@article{thompson_direct_2018,
title = {A {{Direct Method}} for {{Bloch Wave Excitation}} by {{Scattering}} at the {{Edge}} of a {{Lattice}}. {{Part I}}: {{Point Scatterer Problem}}},
volume = {71},
issn = {0033-5614},
shorttitle = {A {{Direct Method}} for {{Bloch Wave Excitation}} by {{Scattering}} at the {{Edge}} of a {{Lattice}}. {{Part I}}},
abstract = {A new method for determining the reflection and transmission properties of lattices is developed. The method uses multipole expansions, and certain transformations of the algebraic equation systems that appear when boundary conditions are applied. It is more direct, and much simpler, than earlier approaches based on integral transforms and the Wiener\textendash{}Hopf technique. The method is demonstrated for the case of a semi-infinite lattice of sound soft acoustic point scatterers, but can easily be generalised to account for finite size effects, and more general boundary conditions.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/PJY9LEY2/Thompson ja Brougham - 2018 - A Direct Method for Bloch Wave Excitation by Scatt.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/ZLZALEEU/4102358.html}
}
@article{felderhof_addition_1987,
title = {Addition Theorems for Spherical Wave Solutions of the Vector {{Helmholtz}} Equation},
author = {Dufva, Tommi J. and Sarvas, Jukka and Sten, Johan C.-E.},
year = {2008},
pages = {79-99},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/Q4KGEHG4/Dufva et al. - 2008 - Unified Derivation of the Translational Addition T.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/DJ4B9Q6B/pier.html}
}
@book{kokhanovsky_editor_light_2006,
edition = {1},
series = {Springer {{Praxis Books}} / {{Environmental Sciences}}},
title = {Light {{Scattering Reviews}} : {{Single}} and {{Multiple Light Scattering}}},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/N87IKFEK/(Springer Praxis Books) Alexander A. Kokhanovsky (auth.)-Light Scattering Reviews 7_ Radiative Transfer and Optical Properties of Atmosphere and Underlying Surface-Springer-Verlag .pdf}
}
@article{linton_lattice_2010,
title = {Lattice {{Sums}} for the {{Helmholtz Equation}}},
volume = {52},
issn = {0036-1445},
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\_\textbackslash{}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 = {Theory of {{Electron Diffraction}} by {{Crystals}}},
volume = {22},
issn = {1865-7109},
abstract = {A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN'S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD'S method is applied to sum up the series for GREEN'S function.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/VEIUHCCD/Kambe - 2014 - Theory of Electron Diffraction by Crystals.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/WPKCSVZG/Kambe - 2014 - Theory of Electron Diffraction by Crystals.pdf}
}
@article{mcrae_multiplescattering_1966,
title = {Multiple-{{Scattering Treatment}} of {{Low}}-{{Energy Electron}}-{{Diffraction Intensities}}},
title = {Quasi-Periodic {{Green}}'s Functions of the {{Helmholtz}} and {{Laplace}} Equations},
volume = {39},
issn = {0305-4470},
abstract = {A classical problem of free-space Green's function G 0{$\Lambda$} representations of the Helmholtz equation is studied in various quasi-periodic cases, i.e., when an underlying periodicity is imposed in less dimensions than is the dimension of an embedding space. Exponentially convergent series for the free-space quasi-periodic G 0{$\Lambda$} and for the expansion coefficients D L of G 0{$\Lambda$} in the basis of regular (cylindrical in two dimensions and spherical in three dimension (3D)) waves, or lattice sums, are reviewed and new results for the case of a one-dimensional (1D) periodicity in 3D are derived. From a mathematical point of view, a derivation of exponentially convergent representations for Schl{\"o}milch series of cylindrical and spherical Hankel functions of any integer order is accomplished. Exponentially convergent series for G 0{$\Lambda$} and lattice sums D L hold for any value of the Bloch momentum and allow G 0{$\Lambda$} to be efficiently evaluated also in the periodicity plane. The quasi-periodic Green's functions of the Laplace equation are obtained from the corresponding representations of G 0{$\Lambda$} of the Helmholtz equation by taking the limit of the wave vector magnitude going to zero. The derivation of relevant results in the case of a 1D periodicity in 3D highlights the common part which is universally applicable to any of remaining quasi-periodic cases. The results obtained can be useful for the numerical solution of boundary integral equations for potential flows in fluid mechanics, remote sensing of periodic surfaces, periodic gratings, and infinite arrays of resonators coupled to a waveguide, in many contexts of simulating systems of charged particles, in molecular dynamics, for the description of quasi-periodic arrays of point interactions in quantum mechanics, and in various ab initio first-principle multiple-scattering theories for the analysis of diffraction of classical and quantum waves.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/268RXLJ4/Moroz - 2006 - Quasi-periodic Green's functions of the Helmholtz .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/MGA5XR44/dlserr.pdf}
}
@article{wei_broadband_2017,
title = {A {{Broadband ML}}-{{FMA}} for 3-{{D Periodic Green}}'s {{Function}} in 2-{{D Lattice Using Ewald Summation}}},
volume = {65},
issn = {0018-926X},
abstract = {A periodic fast multipole algorithm (P-FMA) is devised for evaluating 3-D periodic Green's function (PGF) for a 2-D lattice which can be used to solve scattering by a structure with 2-D periodicity. The introduction of periodicity in the Green's function formulation produces image sources at each lattice site. Like multilevel FMA (ML-FMA), P-FMA takes advantage of the distance between image sources and observation points to factorize the field using multipoles. By substituting known factorizations of the free-space Green's function into the expression for PGF, one can isolate the summation over the lattice into the translation phase of the FMA. For both plane wave and multipole factorizations, a common term known as lattice constant appears. The lattice constant is an infinite sum over the lattice which does not converge absolutely when expressed as a spatial sum. Using the Ewald summation technique, the lattice constants can be evaluated with exponential convergence and high accuracy. The resulting P-FMA is between O(N) and O(N log N) in memory use and computational complexity, depending on the object size relative to the wavelength.},
number = {6},
journal = {IEEE Transactions on Antennas and Propagation},
doi = {10.1109/TAP.2017.2690533},
author = {Wei, M. and Chew, W. C.},
month = jun,
year = {2017},
keywords = {Convergence,Green's function methods,computational complexity,Geometry,Scattering,periodic structures,2D lattice,2D periodicity,3D periodic Green function,3D PGF evaluation,Broadband antennas,Broadband communication,broadband ML-FMA,Ewald summation,Ewald summation technique,fast multipole method (ML-FMA),FMA translation phase,free-space Green function,lattice constant,lattice sum,Lattices,method of moments (MoM),multilevel,multilevel FMA,multipole factorization,P-FMA,periodic fast multipole algorithm,periodic Green’s function (PGF),periodic scattering,plane wave factorization},
pages = {3134-3145},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/33MFL85V/Wei ja Chew - 2017 - A Broadband ML-FMA for 3-D Periodic Green’s Functi.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/RN9AUGNQ/7891536.html}
}
@article{linton_one-_2009,
title = {One- and Two-Dimensional Lattice Sums for the Three-Dimensional {{Helmholtz}} Equation},
volume = {228},
issn = {0021-9991},
abstract = {The accurate and efficient computation of lattice sums for the three-dimensional Helmholtz equation is considered for the cases where the underlying lattice is one- or two-dimensional. We demonstrate, using careful numerical computations, that the reduction method, in which the sums for a two-dimensional lattice are expressed as a sum of one-dimensional lattice sums leads to an order-of-magnitude improvement in performance over the well-known Ewald method. In the process we clarify and improve on a number of results originally formulated by Twersky in the 1970s.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/YMRZHBY4/Linton ja Thompson - 2009 - One- and two-dimensional lattice sums for the thre.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/Z8CFQ6S9/S0021999108005962.html}
}
@article{waterman_t-matrix_2007,
title = {The {{T}}-Matrix Revisited},
volume = {24},
copyright = {\&\#169; 2007 Optical Society of America},
issn = {1520-8532},
abstract = {We consider electromagnetic scattering from penetrable cylinders of general cross section. After summarizing the basic T-matrix equations the low-frequency case is examined, which leads for nonmagnetic materials to the exact result T=iR-R2 in the Rayleigh limit, satisfying both reciprocity and energy constraints. Here elements of R are given by integrals of regular wave functions over the cylinder surface. A "Rayleigh expansion" is then found that is convergent throughout the Rayleigh region and the lower end of the resonance region and requires no matrix inversion. For bodies of high aspect ratio, there is a problem with significance loss during numerical integration, due to large oscillatory terms. A class of surfaces has now been found for which these terms can be removed, however, enabling us to treat aspect ratios up to 1000:1. These methods are expected to apply also in three dimensions.},
author = {Kristensson, Gerhard and Waterman, P. C.},
month = nov,
year = {1982},
pages = {1612-1625},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/Q7ZEETFQ/Kristensson ja Waterman - 1982 - The T matrix for acoustic and electromagnetic scat.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/XAQLYYR5/1.html}
author = {Enoch, S. and McPhedran, R. C. and Nicorovici, N. A. and Botten, L. C. and Nixon, J. N.},
month = nov,
year = {2001},
pages = {5859-5870},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/GZW5G2AY/Enoch ym. - 2001 - Sums of spherical waves for lattices, layers, and .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/2ZQXY82F/1.html}
}
@article{linton_schlomilch_2006,
title = {Schl{\"o}milch Series That Arise in Diffraction Theory and Their Efficient Computation},
volume = {39},
issn = {0305-4470},
abstract = {We are concerned with a certain class of Schl{\"o}milch series that arise naturally in the study of diffraction problems when the scatterer is a semi-infinite periodic structure. By combining new results derived from integral representations and the Poisson summation formula with known identities, we obtain expressions which enable the series to be computed accurately and efficiently. Many of the technical details of the derivations are omitted; they can, however, be obtained from Linton 2005 Schl{\"o}milch series that arise in diffraction theory and their efficient computation Technical Report Loughborough University available online at http://www-staff.lboro.ac.uk/ macml1/schlomilch-techreport.pdf.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/CPMW876J/Linton - 2006 - Schlömilch series that arise in diffraction theory.pdf}
}
@article{linton_schlomilch_2006-1,
title = {Schl{\"o}milch Series That Arise in Diffraction Theory and Their Efficient Computation},
volume = {39},
issn = {0305-4470, 1361-6447},
abstract = {We are concerned with a certain class of Schl\textasciidieresis{}omilch series that arise naturally in the study of diffraction problems when the scatterer is a periodic structure. By combining new results derived from integral representations and the Poisson summation formula with known identities, we obtain expressions which enable the series to be computed accurately and efficiently. Most of the technical details of the derivations are omitted; they can, however, be obtained from the technical report [1] available online.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/9NTE39HX/Linton - 2006 - Schlömilch series that arise in diffraction theory.pdf}
}
@article{fruhnert_computing_2017,
title = {Computing the {{T}}-Matrix of a Scattering Object with Multiple Plane Wave Illuminations},
volume = {8},
copyright = {\textcopyright{} 2017 Fruhnert et al.; licensee Beilstein-Institut.},
author = {Fruhnert, Martin and {Fernandez-Corbaton}, Ivan and Yannopapas, Vassilios and Rockstuhl, Carsten},
month = mar,
year = {2017},
pages = {614-626},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/KRUFJDRF/Fruhnert et al. - 2017 - Computing the T-matrix of a scattering object with.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/TMT2EASU/66.html}
}
@book{kristensson_scattering_2016,
address = {{Edison, NJ}},
title = {Scattering of {{Electromagnetic Waves}} by {{Obstacles}}},
isbn = {978-1-61353-221-8},
abstract = {This book is an introduction to some of the most important properties of electromagnetic waves and their interaction with passive materials and scatterers. The main purpose of the book is to give a theoretical treatment of these scattering phenomena, and to illustrate numerical computations of some canonical scattering problems for different geometries and materials. The scattering theory is also important in the theory of passive antennas, and this book gives several examples on this topic. Topics covered include an introduction to the basic equations used in scattering; the Green functions and dyadics; integral representation of fields; introductory scattering theory; scattering in the time domain; approximations and applications; spherical vector waves; scattering by spherical objects; the null-field approach; and propagation in stratified media. The book is organised along two tracks, which can be studied separately or together. Track 1 material is appropriate for a first reading of the textbook, while Track 2 contains more advanced material suited for the second reading and for reference. Exercises are included for each chapter.},
title = {Some a Priori Estimates of Solutions to the {{Maxwell}} Equations},
volume = {38},
copyright = {Copyright \textcopyright{} 2014 John Wiley \& Sons, Ltd.},
issn = {1099-1476},
abstract = {In this paper, we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calder{\'o}n operator for a sphere is investigated and depicted as a function of the frequency. Copyright \textcopyright{} 2014 John Wiley \& Sons, Ltd.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/LHZD4MWL/Kristensson ja Wellander - 2015 - Some a priori estimates of solutions to the Maxwel.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/3XBVHS8V/mma.html}
}
@article{wellander_estimates_2014,
title = {Estimates of Scattered Electromagnetic Fields},
volume = {37},
copyright = {Copyright \textcopyright{} 2013 John Wiley \& Sons, Ltd.},
issn = {1099-1476},
abstract = {AbstractWe present some general estimates of the scattered electromagnetic fields for a general bounded scattering domain {$\Omega$} in the anisotropic materials setting. In particular, it is shown that the - norm and sup norm of the scattered field in an arbitrary finite exterior domain {$\Omega$}s is bounded by the H(curl,{$\Omega$}) norm of the incident field. Moreover, several estimates of the traces of the scattered field on the boundary are presented. These estimates have bearing on estimations on cloaking. Copyright \textcopyright{} 2013 John Wiley \& Sons, Ltd.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/MW57QWH8/Wellander ja Kristensson - 2014 - Estimates of scattered electromagnetic fields.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/VTJNDV5U/mma.html}
}
@article{ganesh_convergence_2012,
title = {Convergence Analysis with Parameter Estimates for a Reduced Basis Acoustic Scattering {{T}}-Matrix Method},
volume = {32},
issn = {0272-4979},
abstract = {Abstract. The celebrated truncated T-matrix method for wave propagation models belongs to a class of the reduced basis methods (RBMs), with the parameters bein},
author = {Ganesh, M. and Hawkins, S. C. and Hiptmair, R.},
month = oct,
year = {2012},
pages = {1348-1374},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/KLKJBTZU/Ganesh ym. - 2012 - Convergence analysis with parameter estimates for .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/N5H8B7SF/654510.html}
}
@article{tao_relation_1998,
title = {Relation of {{Cartesian}} and Spherical Multipole Moments in General Relativity},
volume = {333},
abstract = {The Earth's gravitational field is represented by its multipole moments. Multipole moments have two kinds of equivalent forms, that is, the Cartesian symmetric and trace-free tensors and the spherical harmonic coefficients. The relation between these two forms is interesting and useful for some practical problems. Under Newtonian approximation, there exists a simple relation between the aforesaid two kinds of multipole moments (see Hartmann et al., 1994, for details). But in the 1PN
approximation of general relativity, the relation mentioned above becomes complicated. This paper discusses how to turn the expansion of the 1PN Earth's gravitational potential, which consists of a scalar potential and a vector potential, in terms of BD moments into that in terms of a set of time-slowly-changing, observable multipole moments. Under a specific standard PN gauge, we derive the corresponding
expansion of the potential in terms of spherical harmonics, obtain the relation between the 1PN spherical harmonic coefficients and the
Cartesian multipole moments, and compute the expressions of the lowest order spherical harmonic coefficients including the relation between the 1PN Earth dynamical form-factor J\_2 and the BD mass quadrupole moment of the Earth. As for the 1PN vector potential, we also discuss its
expansion in terms of Cartesian multipole moments under the rigidity approximation. In this paper, we emphasize the choice of the coordinate gauge. Under our ad hoc standard PN gauge, the results have simpler form and clearer physical meaning.},
journal = {Astronomy and Astrophysics},
author = {Tao, Jin-he and Huang, Tianyi},
month = apr,
year = {1998},
pages = {1100-1106},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/23NMKA68/Tao ja Huang - 1998 - Relation of Cartesian and spherical multipole mome.pdf}
}
@article{baryshnikova_optical_nodate,
title = {Optical {{Anapoles}}: {{Concepts}} and {{Applications}}},
abstract = {Interference of electromagnetic modes supported by subwavelength photonic structures is one of the key concepts that underpins the nanoscale control of light in metaoptics. It drives the whole realm of all-dielectric Mie-resonant nanophotonics with many applications for low-loss nanoscale optical antennas, metasurfaces, and metadevices. Specifically, interference of the electric and toroidal dipole moments results in a very peculiar, low-radiating optical state associated with the concept of optical anapole. Here, the physics of multimode interferences and multipolar interplay in nanostructures is uncovered with an intriguing example of the optical anapole. The recently emerged field of anapole electrodynamics is reviewed, explicating its relevance to multipolar nanophotonics, including direct experimental observations, manifestations in nonlinear optics, and rapidly expanding applications in nanoantennas, active photonics, and metamaterials.},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/F984RIWY/Baryshnikova ym. - Optical Anapoles Concepts and Applications.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/5Z2D8YED/adom.html}
}
@article{baryshnikova_optical_2018,
archivePrefix = {arXiv},
eprinttype = {arxiv},
eprint = {1810.02515},
primaryClass = {physics},
title = {Optical Anapoles in Nanophotonics and Meta-Optics},
abstract = {Interference of electromagnetic modes supported by subwavelength photonic structures is one of the key concepts that underpins the subwavelength control of light in meta-optics. It drives the whole realm of all-dielectric Mie-resonant nanophotonics with many applications for low-loss nanoscale optical antennas, metasurfaces, and metadevices. Specifically, interference of the electric and toroidal dipole moments results in a very peculiar, low-radiating optical state associated with the concept of optical anapole. Here, we uncover the physics of multimode interferences and multipolar interplay in nanostructures with an intriguing example of the optical anapole. We review the recently emerged field of anapole electrodynamics explicating its relevance to multipolar nanophotonics, including direct experimental observations, manifestations in nonlinear optics, and rapidly expanding applications in nanoantennas, active photonics, and metamaterials.},
author = {Baryshnikova, Kseniia and Smirnova, Daria and Luk'yanchuk, Boris and Kivshar, Yuri},
month = oct,
year = {2018},
keywords = {Physics - Optics},
file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/QRX8PC6T/Baryshnikova ym. - 2018 - Optical anapoles in nanophotonics and meta-optics.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/S9D252SV/1810.html}
}
@article{nemkov_electromagnetic_2018,
title = {Electromagnetic Sources beyond Common Multipoles},
volume = {98},
abstract = {The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely studied in recent years. Here we inspect more closely the other type of commonly overlooked terms known as the mean-square radii. In particular, we discuss both quantitative and qualitative aspects of the mean-square radii and provide a general geometrical framework for their visualization. We also consider the role of the mean-square radii in expanding the family of nontrivial nonradiating electromagnetic sources.},
