Abstract

This paper presents a theoretical analysis of the electromagnetic response of a plasmonic nanoparticle-spacer-plasmonic film system. The physical system consists of a spherical nanoparticle of a plasmonic material such as gold or silver over a plasmonic metal film and separated from the same by a dielectric spacer material. This paper presents a complete analytical solution of the Maxwell’s equations, to determine the optical fields near the gold nanoparticle. It was found that the electromagnetic fields in between the plasmonic nanoparticle and the plasmonic film are extremely sensitive to the spacing between the nanoparticle and the film. This could enable the use of such a system for various sensing applications. The non-local nature of the plasmonic medium was also included in our analysis and it’s effect on the resonances of the system was studied. The analytical solution was compared with an independent numerical method, the Finite Difference Time Domain (FDTD) method, to demonstrate the accuracy of the solution.

© 2014 Optical Society of America

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    [CrossRef]
  35. B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2013 (5)

J. B. Pendry, A. I. Fernandez-Dominguez, Y. Luo, and R. Zhao, “Capturing Photons with transformation optics,” Nature Physics 9, 518–522 (2013).
[CrossRef]

C. Cirací, Y. Urzhumov, and D. R. Smith, “Effects of classical nonlocality on the optical response of three-dimensional plasmonic nanodimers,” J. Opt. Soc. Am. 30(10), 2731–2736 (2013).
[CrossRef]

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
[CrossRef] [PubMed]

C. Cirací, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for Plasmonics: A Macroscopic Approach to a Microscopic Problem,” Chem. Phys. Chem. 14(6), 1109–1116 (2013).
[CrossRef] [PubMed]

A. Moreau, C. Cirací, and D. R. Smith, “Impact of Non-local response on metallodielectric multilayers and optical patch antennas,” Phys. Rev. B 87(4), 045401 (2013).
[CrossRef]

2012 (6)

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. Garca-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-Optics Description of Nonlocal Effects in Plasmonic Nanostructures,” Phys. Rev. Lett. 108(22), 106802 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[CrossRef]

R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
[CrossRef] [PubMed]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
[CrossRef] [PubMed]

2011 (1)

S. Raza, G. Toscano, A. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to non-local response,” Phys. Rev. Lett. 84(12), 121412(R) (2011).

2010 (1)

S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
[CrossRef] [PubMed]

2009 (2)

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
[CrossRef]

V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
[CrossRef]

2008 (2)

A. Dhawan, S. J. Norton, M. D. Gerhold, and T. Vo-Dinh, “Comparison of FDTD numerical computations and analytical multipole expansion method for plasmonics-active nanosphere dimers,” Opt. Express 17(12), 9688– 9697 (2008).
[PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

2007 (3)

V. V. Klimov and D. V. Guzatov, “Optical Properties of an atom in the presence of a two nanosphere cluster,” Quantum Electron. 37(3), 209–230 (2007).
[CrossRef]

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mater. Sci. Eng. C 27(5), 1347–1350 (2007).
[CrossRef]

M. D. Fischbein and M. Drndic, “Sub-10 nm Device Fabrication in a Transmission Electron Microscope,” Nano Lett. 7(5), 13291337 (2007).
[CrossRef]

2005 (1)

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

2003 (2)

K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91(22), 2274021 (2003).
[CrossRef]

J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3(4), 485–491, (2003).
[CrossRef]

2001 (1)

R. Ruppin, “Extinction properties of thin metallic nanowires,” Optics Commun. 190(1), 205–209 (2001).
[CrossRef]

1999 (1)

H. Xu, E. J. Bjereld, M. Kall, and L. Borjesson, “Spectroscopy of single Hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[CrossRef]

1997 (1)

S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

1992 (2)

A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, “Surface-enhanced Raman scattering,” J. Phys: Condensed Matter 4(5), 1143–1212 (1992).

R. Ruppin, “Optical Absorption by a small sphere over a substrate with inclusion of non local effect,” Phys. Rev. B 45(19), 11209–11215 (1992).
[CrossRef]

1987 (1)

B. U. Felderhof and R. B. Jones, “Addition theorems for spherical wave solutions of the vector Helmholtz equation,” J. Math. Phys. 28(4), 836–839 (1987).
[CrossRef]

1983 (1)

P. K. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere plane structure, application to surface enhanced raman spectroscopy,” Surface Science 124, 506–528 (1983).
[CrossRef]

1980 (1)

P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74(2), 301–305 (1980).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of nobel metals,” Phys.Rev.B 6(12), 4370 (1972).

1964 (1)

R. A. Sac, “Three dimensional addition theorems for arbitrary functions involving expansions in Spherical harmonics,” J. Math. Phys. 5, 252 (1964).
[CrossRef]

Acimovic, S. S.

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
[CrossRef]

Akemann, W.

A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, “Surface-enhanced Raman scattering,” J. Phys: Condensed Matter 4(5), 1143–1212 (1992).

Aravind, P. K.

P. K. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere plane structure, application to surface enhanced raman spectroscopy,” Surface Science 124, 506–528 (1983).
[CrossRef]

P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74(2), 301–305 (1980).
[CrossRef]

Auzelyte, V.

V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
[CrossRef]

Bello, V.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mater. Sci. Eng. C 27(5), 1347–1350 (2007).
[CrossRef]

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91(22), 2274021 (2003).
[CrossRef]

Bjereld, E. J.

H. Xu, E. J. Bjereld, M. Kall, and L. Borjesson, “Spectroscopy of single Hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Borjesson, L.

H. Xu, E. J. Bjereld, M. Kall, and L. Borjesson, “Spectroscopy of single Hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
[CrossRef]

Chang, S.

S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
[CrossRef] [PubMed]

Chilkoti, A.

R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
[CrossRef] [PubMed]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of nobel metals,” Phys.Rev.B 6(12), 4370 (1972).

Cirací, C.

A. Moreau, C. Cirací, and D. R. Smith, “Impact of Non-local response on metallodielectric multilayers and optical patch antennas,” Phys. Rev. B 87(4), 045401 (2013).
[CrossRef]

C. Cirací, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for Plasmonics: A Macroscopic Approach to a Microscopic Problem,” Chem. Phys. Chem. 14(6), 1109–1116 (2013).
[CrossRef] [PubMed]

C. Cirací, Y. Urzhumov, and D. R. Smith, “Effects of classical nonlocality on the optical response of three-dimensional plasmonic nanodimers,” J. Opt. Soc. Am. 30(10), 2731–2736 (2013).
[CrossRef]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Dais, C.

V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
[CrossRef]

Degiron, A.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

Dhawan, A.

Drndic, M.

M. D. Fischbein and M. Drndic, “Sub-10 nm Device Fabrication in a Transmission Electron Microscope,” Nano Lett. 7(5), 13291337 (2007).
[CrossRef]

Emory, S. R.

S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

Farquet, P.

V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
[CrossRef]

Felderhof, B. U.

B. U. Felderhof and R. B. Jones, “Addition theorems for spherical wave solutions of the vector Helmholtz equation,” J. Math. Phys. 28(4), 836–839 (1987).
[CrossRef]

Fernandez-Dominguez, A. I.

J. B. Pendry, A. I. Fernandez-Dominguez, Y. Luo, and R. Zhao, “Capturing Photons with transformation optics,” Nature Physics 9, 518–522 (2013).
[CrossRef]

Fernández-Domínguez, A. I.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. Garca-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-Optics Description of Nonlocal Effects in Plasmonic Nanostructures,” Phys. Rev. Lett. 108(22), 106802 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[CrossRef]

Fernndez-Domnguez, A. I.

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Fischbein, M. D.

M. D. Fischbein and M. Drndic, “Sub-10 nm Device Fabrication in a Transmission Electron Microscope,” Nano Lett. 7(5), 13291337 (2007).
[CrossRef]

Garca-Vidal, F. J.

A. I. Fernández-Domínguez, A. Wiener, F. J. Garca-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-Optics Description of Nonlocal Effects in Plasmonic Nanostructures,” Phys. Rev. Lett. 108(22), 106802 (2012).
[CrossRef] [PubMed]

Gates, B. D.

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

Gerhold, M. D.

Gonzlez, M. U.

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
[CrossRef]

Grabhorn, H.

A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, “Surface-enhanced Raman scattering,” J. Phys: Condensed Matter 4(5), 1143–1212 (1992).

Grytzmacher, D.

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V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
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C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
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R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
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J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
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R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
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R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
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S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
[CrossRef]

Lee, S.

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
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S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
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V. Auzelyte, C. Dais, P. Farquet, D. Grytzmacher, L. J. Heyderman, and F. Luo, “Extreme ultraviolet interference lithography at the Paul Scherrer Institut,” J. Micro/Nanolith. MEMS MOEMS 8(2), 021204 (2009).
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Luo, Y.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
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Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
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C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
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S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
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Mock, J. J.

R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
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C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
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J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3(4), 485–491, (2003).
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A. Moreau, C. Cirací, and D. R. Smith, “Impact of Non-local response on metallodielectric multilayers and optical patch antennas,” Phys. Rev. B 87(4), 045401 (2013).
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Mortensen, N. A.

S. Raza, G. Toscano, A. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to non-local response,” Phys. Rev. Lett. 84(12), 121412(R) (2011).

Moskovits, M.

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
[CrossRef] [PubMed]

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
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S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
[CrossRef] [PubMed]

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
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A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, “Surface-enhanced Raman scattering,” J. Phys: Condensed Matter 4(5), 1143–1212 (1992).

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E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

Pedano, M. L.

S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
[CrossRef] [PubMed]

Pellegrini, G.

G. Pellegrini, G. Mattei, V. Bello, and P. Mazzoldi, “Interacting metal nanoparticles: Optical properties from nanoparticle dimers to core-satellite systems,” Mater. Sci. Eng. C 27(5), 1347–1350 (2007).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. I. Fernandez-Dominguez, Y. Luo, and R. Zhao, “Capturing Photons with transformation optics,” Nature Physics 9, 518–522 (2013).
[CrossRef]

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
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C. Cirací, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for Plasmonics: A Macroscopic Approach to a Microscopic Problem,” Chem. Phys. Chem. 14(6), 1109–1116 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. Garca-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-Optics Description of Nonlocal Effects in Plasmonic Nanostructures,” Phys. Rev. Lett. 108(22), 106802 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, “Transformation optics description of touching metal nanospheres,” Phys. Rev. B 85(16), 165148 (2012).
[CrossRef]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
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Quidant, R.

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
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S. Raza, G. Toscano, A. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to non-local response,” Phys. Rev. Lett. 84(12), 121412(R) (2011).

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S. Li, M. L. Pedano, S. Chang, C. A. Mirkin, and G. C. Schatz, “Gap Structure Effects on Surface-Enhanced Raman Scattering Intensities for Gold Gapped Rods,” Nano Lett. 10(5) 1722–1727 (2010).
[CrossRef] [PubMed]

Schultz, S.

J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3(4), 485–491, (2003).
[CrossRef]

Smith, D. R.

C. Cirací, Y. Urzhumov, and D. R. Smith, “Effects of classical nonlocality on the optical response of three-dimensional plasmonic nanodimers,” J. Opt. Soc. Am. 30(10), 2731–2736 (2013).
[CrossRef]

C. Cirací, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for Plasmonics: A Macroscopic Approach to a Microscopic Problem,” Chem. Phys. Chem. 14(6), 1109–1116 (2013).
[CrossRef] [PubMed]

A. Moreau, C. Cirací, and D. R. Smith, “Impact of Non-local response on metallodielectric multilayers and optical patch antennas,” Phys. Rev. B 87(4), 045401 (2013).
[CrossRef]

R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
[CrossRef] [PubMed]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3(4), 485–491, (2003).
[CrossRef]

Stewart, M.

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

Stockman, M. I.

K. Li, M. I. Stockman, and D. J. Bergman, “Self-similar chain of metal nanospheres as an efficient nanolens,” Phys. Rev. Lett. 91(22), 2274021 (2003).
[CrossRef]

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A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. (Artech, Boston, MA, 2000).

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S. Raza, G. Toscano, A. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to non-local response,” Phys. Rev. Lett. 84(12), 121412(R) (2011).

Urzhumov, Y.

C. Cirací, Y. Urzhumov, and D. R. Smith, “Effects of classical nonlocality on the optical response of three-dimensional plasmonic nanodimers,” J. Opt. Soc. Am. 30(10), 2731–2736 (2013).
[CrossRef]

C. Cirací, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
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Whitesides, G. M.

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

Wiener, A.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett 111(9), 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. Garca-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-Optics Description of Nonlocal Effects in Plasmonic Nanostructures,” Phys. Rev. Lett. 108(22), 106802 (2012).
[CrossRef] [PubMed]

Willson, C. G.

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
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R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
[CrossRef] [PubMed]

Wubs, M.

S. Raza, G. Toscano, A. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to non-local response,” Phys. Rev. Lett. 84(12), 121412(R) (2011).

Xu, H.

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
[CrossRef] [PubMed]

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
[CrossRef] [PubMed]

H. Xu, E. J. Bjereld, M. Kall, and L. Borjesson, “Spectroscopy of single Hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83(21), 4357–4360 (1999).
[CrossRef]

Xu, Q.

B. D. Gates, Q. Xu, M. Stewart, D. Ryan, C. G. Willson, and G. M. Whitesides, “New approaches to nanofabrication: molding, printing, and other yechniques,” Chem. Rev. 105(4), 1171–1196 (2005).
[CrossRef] [PubMed]

Zauscher, S.

J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8(8), 2245–2252 (2008).
[CrossRef] [PubMed]

Zhang, S.

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic Properties of Gold Nanoparticles Separated from a Gold Mirror by an Ultra-thin Oxide,” Nano Lett. 12(4), 2088–2094, (2012).
[CrossRef] [PubMed]

S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold Mirror by an ultrathin oxide,” Nano Lett. 12, 2088 (2012).
[CrossRef] [PubMed]

Zhao, R.

J. B. Pendry, A. I. Fernandez-Dominguez, Y. Luo, and R. Zhao, “Capturing Photons with transformation optics,” Nature Physics 9, 518–522 (2013).
[CrossRef]

ACS Nano (2)

R. T. Hill, J. J. Mock, A. Hucknall, S. D. Wolter, N. M. Jokerst, D. R. Smith, and A. Chilkoti, “Plasmon Ruler with Angstrom Length Resolution,” ACS Nano 6(10), 9237–9246 (2012).
[CrossRef] [PubMed]

S. S. Acimovic, M. P. Kreuzer, M. U. Gonzlez, and R. Quidant, “Plasmon Near-Field Coupling in Metal Dimers as a Step toward Single-Molecule Sensing,” ACS Nano 3(5), 12311237 (2009).
[CrossRef]

Chem. Phys. Chem. (1)

C. Cirací, J. B. Pendry, and D. R. Smith, “Hydrodynamic model for Plasmonics: A Macroscopic Approach to a Microscopic Problem,” Chem. Phys. Chem. 14(6), 1109–1116 (2013).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

P. K. Aravind and H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74(2), 301–305 (1980).
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Figures (10)

Fig. 1
Fig. 1

Plasmonic nanostructure consisting of a gold nanoparticle over a gold film seperated by a spacer material. This system is excited by an incident plane electromagnetic wave and responds to this excitation by emitting it’s own scattered field.

Fig. 2
Fig. 2

(a) Schematic figure showing the plasmonic nanostructure being excited by a plane wave of wave vector ki. The plasmonic material has a permittivity function εP(ω) and the nanoparticle is separated from the substrate of the same material by a spacer of permittivity εs. (b) Schematic figure showing the choice of coordinates in the solution.

Fig. 3
Fig. 3

Analytical calculation of the effect of t on the field enhancement η in the spacer material (a) η vs λ for a = 30 nm, silica spacer ns = 1.5, α = 60° and t lying in the range 1 nm – 10 nm. (b) η vs λ for a = 30 nm, silica spacer ns = 1.5, α = 60° and t lying in the range 0.1 nm – 0.9 nm.

Fig. 4
Fig. 4

Analytical calculations for (a) λres (for the first two modes) vs log(t/t0) for a = 30 nm, silica spacer ns = 1.5, α = 60°. (b) log(ηres0) (for the first two modes) vs log(t/t0) for a = 30 nm, silica spacer ns = 1.5, α = 60°. In both the figures t0 = 0.1 nm and η0 =20.

Fig. 5
Fig. 5

Analytical calculation of the effect of a on the field enhancement η in the spacer material. η vs λ for t = 5 nm, silica spacer ns = 1.5, α = 60° and a lying in the range 30 nm – 90 nm.

Fig. 6
Fig. 6

Comparison of FDTD results (solid) and analytical calculations (dotted) for (a) a = 30 nm, α = 60°, ns = 1.5 and t = 3, 5 and 10 nm (b) t = 5 nm, α = 60°, ns = 1.5 and a = 30, 35 and 40 nm.

Fig. 7
Fig. 7

Analytical calculation of the effect of spacer refractive index on the fields inside the spacer material. η vs λ for t = 5 nm, α = 60°, a = 50 nm and ns lying in the range 1 – 1.78.

Fig. 8
Fig. 8

Analytical calculation of the effect of angle on the field enhancement inside the spacer material for a particular wavelength of incident light. η vs α at λ = 633 nm, t = 5 nm, a = 30 nm, ns = 1.5

Fig. 9
Fig. 9

Analytical calculation of the effect of non-locality (i.e. effect of β) on the primary resonant wavelength of the system. λres (for the first mode) vs log(t/t0) for a = 30 nm, silica spacer ns = 1.5, α = 60° and different β. In this plot t0 = 0.1 nm

Fig. 10
Fig. 10

Analytical calculation of the effect of non-locality (i.e. β) on the maximum enhancement of the optical fields in the spacer material. log(ηres0) (for the first mode) vs log(t/t0) for a = 30 nm, silica spacer ns = 1.5, α = 60° and different β. In this plot η0 =20.

Equations (36)

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E i = E 0 exp ( i k i . r ) H i = k i × E 0 ω μ 0 exp ( i k i . r )
k i = k 0 ( z ^ cos α + x ^ sin α ) E 0 = E p ( x ^ cos α z ^ sin α ) + E s y ^
E = 0 , H = 0 , × E = i ω μ 0 H and × H = i ε ω E
2 H + k 2 H = 0 and 2 E + k 2 E = 0
2 ψ + k 2 ψ = 0
2 v + k 2 v = 0
v = i ψ i + ψ i × r + × ( ψ i × r )
E = × ( Π e × r ) k + Π m × r H = k i ω μ 0 ( × ( Π m × r ) k + Π e × r )
ψ ( r ) = l = 0 m = l l ( a l m j l ( k r ) + b l m h l ( 1 ) ( k r ) ) Y l m ( θ , ϕ )
Π e ( r ) = l = 0 m = l l ( a l m j l ( k r ) + b l m h l ( 1 ) ( k r ) ) Y l m ( θ , ϕ ) Π m ( r ) = l = 0 m = l l ( c l m j l ( k r ) + d l m h l ( 1 ) ( k r ) ) Y l m ( θ , ϕ )
Π e inc = l = 0 m = l l A l m j l ( k 0 r ) Y l m ( θ , ϕ ) Π m inc = l = 0 m = l l B l m j l ( k 0 r ) Y l m ( θ , ϕ )
A l m = i l 1 4 π ( 2 l + 1 ) ( l m ) ! ( l + m ) ! [ E p ( 1 + ( 1 ) l + m Γ ( α ) ) d P l m ( cos α ) d α im E s sin α ( 1 + ( 1 ) l + m Γ ( α ) ) P l m ( cos α ) ]
B l m = i l 1 4 π ( 2 l + 1 ) ( l m ) ! ( l + m ) ! [ E s ( 1 + ( 1 ) l + m Γ ( α ) ) d P l m ( cos α ) d α im E p sin α ( 1 + ( 1 ) l + m Γ ( α ) ) P l m ( cos α ) ]
Π e sca = Π e radn + Π e refln
Π m sca = Π m radn + Π m refln
Π e radn = l = 0 m = l l S l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ )
Π e refln = Γ av l = 0 m = l l S l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ )
Π e sca = l = 0 m = l l S l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ ) + Γ av l = 0 m = l l S l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ )
Π m sca = l = 0 m = l l G l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ ) + Γ a v l = 0 m = l l G l m h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ )
Π e in = l = 0 m = l l ρ l m j l ( k P r ) Y l m ( θ , ϕ ) Π m in = l = 0 m = l l σ l m h l ( 1 ) ( k P r ) Y l m ( θ , ϕ )
E θ sca + E θ inc = E θ in , E ϕ sca + E ϕ inc = E ϕ in and ε 0 ( E r sca + E r inc ) = ε P ( ω ) E r in H θ sca + H θ inc = H θ in , H ϕ sca + H ϕ inc = H ϕ in and H r sca + H r inc = H r in
h l ( 1 ) ( k 0 r ) Y l m ( θ , ϕ ) = q = | m | ζ q l m j q ( k 0 r ) Y l m ( θ , ϕ ) for r < 2 d
ζ q l m = n = | m | i l n q ( 1 ) n + q ( 2 n + 1 ) 3 ( 2 q + 1 ) h n ( 1 ) ( k 0 d ) [ n q n 0 0 0 ] [ n q n m m 0 ]
S l m = Q l [ q = | m | Γ a v ζ l m q S q m + A l m ] G l m = f l [ q = | m | Γ a v ζ l m q G q m + B l m ]
Q l = k P 2 d d a ( a j l ( k 0 a ) ) j l ( k P a ) k 0 2 d d a ( a j l ( k P a ) ) j l ( k 0 a ) k 0 2 d d a ( a j l ( k P a ) ) h l ( 1 ) ( k 0 a ) k P 2 d d a ( a h l ( 1 ) ( k 0 a ) ) j l ( k P a )
f l = d d a ( a j l ( k 0 a ) ) j l ( k P a ) d d a ( a j l ( k P a ) ) j l ( k 0 a ) d d a ( a j l ( k P a ) ) h l ( 1 ) ( k 0 a ) d d a ( a h l ( 1 ) ( k 0 a ) ) j l ( k P a )
ε P T ( ω ) ε 0 = 1 ω P 2 ω 2 + i γ ω
ε P L ( k , ω ) ε 0 = 1 ω P 2 ω 2 + i γ ω β 2 k 2
× ( × E ) = μ 0 ω 2 D
( k P T ) 2 = μ 0 ε P T ( ω ) ω 2 and ε P L ( k P L , ω ) = 0 or ( k P L ) 2 = ω 2 ω P 2 + i γ ω β 2
E = × ( Π e × r ) k P T + Π m × r × Π L
H = k P T i ω μ 0 ( × ( Π m × r ) k P T + Π e × r )
Π L in = l = 0 m = l l c l m j l ( k P L r ) Y l m ( θ , ϕ )
S l m = g l [ q = | m | Γ a v ζ l m q S q m + A l m ]
g l = ( k P T ) 2 d d a ( a j l ( k 0 a ) ) j l ( k P T a ) k 0 2 d d a ( a j l ( k P T a ) ) j l ( k 0 a ) δ l j l ( k 0 a ) k 0 2 d d a ( a j l ( k P T a ) ) h l ( 1 ) ( k 0 a ) ( k P T ) 2 d d a ( a h l ( 1 ) ( k 0 a ) ) j l ( k P T a ) + δ l h l ( 1 ) ( k 0 a )
δ l = ( k P T ) 2 l ( l + 1 ) a d d a ( j l ( k P L a ) ) ( k P T ) 2 k 0 2 k P T k 0 j l ( k P L a ) j l ( k P T a )

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