A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere

Moroz, Alexander

doi:10.1016/j.aop.2004.07.002

Cited by 117 publications

(185 citation statements)

References 97 publications

(424 reference statements)

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“…We shall employ both the mechanical (damped-oscillator) and the energy-transfer models and shall provide a clarification of their equivalence (valid for magnetodielectric material of arbitrary geometry) following the work of Barnett et al, 29 without resorting to explicit calculations as was done in most previous works. 6,11,31 Our work thus generalizes the previous work of Klimov 22,23 to dissipative metamaterials with the calculated decay rates rigorously separated into radiative and nonradiative components, and extends that of Dung et al 24 to the study of molecules at arbitrary positions in the cavity so that the effect due to different molecular orientations can be studied. For simplicity, we shall limit ourselves to linear and isotropic magnetodielectric materials in the following formalism.…”

Section: Introductionsupporting

confidence: 71%

“…For a given molecule-environment configuration, the electromagnetic interaction between them will lead to certain modification of the photonic mode density and hence the molecular transition rate according to Fermi's golden rule. 2 Over the years, this phenomenon has been studied with all kinds of materials including metals and nonmetals as well as different kinds of geometry such as planar, 2,3 spherical, [4][5][6][7][8][9][10][11] and roughened surfaces. 12 In addition, the electromagnetic interaction as well as the molecule-environment system involved in the problem have been studied using different approaches including nonlocal optics 13,14 as well as both classical 3 and quantum mechanical descriptions.…”

Section: Introductionmentioning

confidence: 99%

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Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material

2012

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A comprehensive study is presented on the decay rates of excited molecules in the vicinity of a magnetodielectric material of spherical geometry via electrodynamic modeling. Both the models based on a driven-damped harmonic oscillator and on energy transfers will be applied so that the total decay rates can be rigorously decomposed into the radiative and the nonradiative rates. Clarifications of the equivalence of these two models for arbitrary geometry will be provided. Different possible orientations and locations of the molecule are studied with the molecule being placed near a spherical particle or a cavity. Among other results, TE modes are observed which can be manifested via nonradiative transfer from a tangential dipole within a small range of dissipation parameters set for the spherical particle. In addition, spectral analysis shows that decay rates at such a particle with small absorption are largely dominated by radiative transfer except at multipolar resonances when nonradiative transfer becomes prominent, and relatively unmodified decay is possible when negative refraction takes place.

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Section: Introductionsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material

2012

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“…52 Purcell factors calculated for different filling factors of Si-NCs are shown in the Supporting Information with details of the calculation procedure. 53,54 For comparison, the Purcell factor in methanol (ε methanol = 1.77) is also shown. The Purcell factors in Si-NC solids are larger than those in methanol and increase with increasing the filling factor.…”

mentioning

confidence: 99%

Energy Transfer in Silicon Nanocrystal Solids Made from All-Inorganic Colloidal Silicon Nanocrystals

Furuta

Fujii

Sugimoto

et al. 2015

J. Phys. Chem. Lett.

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Energy transfer between silicon (Si) nanocrystals (NCs) in Si-NC solids was demonstrated by photoluminescence (PL) spectroscopy. Clear differences of PL spectra and the decay rates between solutions and solids of Si-NCs were observed. The change in the PL properties caused by the formation of solids could be explained by the energy transfer from small to large NCs in the size distribution. In order to obtain further evidence of NC-to-NC energy transfer, the size distribution was intentionally modified by mixing solutions of NCs with different size distributions. NC solids made from the mixed solutions exhibited significantly different PL spectral shape and decay rates from those made from unmixed solutions, providing clear evidence of NC-to-NC energy transfer in Si-NC solids.

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“…Yadav et al [6] presented an electromagnetic field analysis for shielded homogeneous and isotropic dielectric spheres applicable to both the microwave and optical frequencies. Chew [7] and Moroz [8] developed recursive transfer matrix solutions for a dipole radiating both within and outside a stratified dielectric sphere.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis of a multilayer dielectric microsphere in a free-space ambient medium

LaComb

Casey

2015

J. Opt. Soc. Am. A

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An analysis of the eigenmodes associated with a dielectric sphere embedded within one or more spherical layers of varying permittivity is presented. A matrix formulation is applied to the general multilayer problem, and the solution is validated by comparison to the complex transcendental equations derived for the homogeneous dielectric spherical resonator and a single-layer spherical dielectric resonator. Although only lossless cases are considered for simplicity, the formulation presented is applicable to resonators (with loss or gain) via the replacement of real permittivities with complex permittivities. The matrix formulation presented for the multilayer dielectric sphere follows a previously published development with the inclusion of some significant corrections. A Wronskian filter effective index approximation is developed for the estimation of Bessel functions of large order (expanding the functionality of the models to evaluation of whispering gallery modes), which is easily integrated into the presented models. Numerical simulations are generated utilizing MATLAB to solve for the complex roots of the characteristic equation, amplitude reflection coefficient, surface impedance of the dielectric layers, Q-factor, and field patterns for both TE and TM modes. Results are presented for single-layer and multilayer spherical geometries and compared to previously published results.

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A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere

Cited by 117 publications

References 97 publications

Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material

Decay rates of a molecule in the vicinity of a spherical surface of an isotropic magnetodielectric material

Energy Transfer in Silicon Nanocrystal Solids Made from All-Inorganic Colloidal Silicon Nanocrystals

Modal analysis of a multilayer dielectric microsphere in a free-space ambient medium

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