Abstract

Near-field polarization distribution of a plasmonic prolate nanospheroid in an incident electromagnetic field versus its polarization and the spheroid’s aspect ratio is studied in detail. Polarization of the near-field is described with the help of the 3D generalized Stokes parameters, allowing simple visualization. It is shown that this distribution has a complex structure, which drastically depends on the incident field polarization and parameters of the plasmon resonance of the nanoparticle. Received analytical solutions cover the whole set of particles with shape varying from spherical to the nanoneedles and nanorods by changing the aspect ratio of the spheroid. An experiment for visualization of the vectorial near-field around a plasmonic nanoparticle is proposed.

© 2014 Optical Society of America

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  2. Alternatively, one can study the dependence of the vectorial near-field of the prolate nanospheroid at fixed value of its aspect ratio versus the polarization and frequency of the incident field.
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    [CrossRef] [PubMed]
  7. J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
    [CrossRef] [PubMed]
  8. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
    [CrossRef] [PubMed]
  9. T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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    [CrossRef] [PubMed]
  28. P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  33. J. Perez-Juste, L. M. Liz-Marzan, S. Carnie, D. Y. C. Chan, and P. Mulvaney, “Electric-field-directed growth for gold nanorods in aqueous surfactant solutions,” Adv. Funct. Mater. 14, 571–579 (2004).
    [CrossRef]
  34. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
    [CrossRef]
  35. G. Hass and L. Hadley, Optical Properties of Metals (American Institute of Physics Handbook) ed. by D. E. Gray, ed. (McGraw-Hill, 1963).
  36. M. S. Agranovich, B. Z. Katsenelenbaum, A. N. Sivov, and N. N. Voitovich, Generalized Method of Eigenoscillation in Diffraction Theory (Wiley, 1999).
  37. V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom placed near a prolate nanospheroid,” Eur. Phys. J. D 20, 133–148 (2002).
    [CrossRef]
  38. A. F. Stevenson, “Electromagnetic scattering by an ellipsoid in the third approximation,” Appl. Phys. 24, 1143–1151 (1953).
    [CrossRef]
  39. It is worth to note here that the degree of polarization we introduced in the paper does not reflect the fluctuations of the incident field vector. In order to take these fluctuations into account one has to use different definition of the degree of polarization via the Stokes parameters, which for the plane wave has the form: P*=(S12+S22+S32)0.5/S0. Without fluctuations, this polarization degree is always equal to 1.
  40. P. J. S. Smith, I. Davis, C. G. Galbraith, and A. Stemmer, “Special issue on high-resolution optical imaging,” J. Opt. 15(9), 090201 (2013).
    [CrossRef]

2013

A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovskii, and Yu. S. Kivshar, “Optical nanoantennas,” Phys. Usp. 56, 539–564 (2013).
[CrossRef]

I. Liberal, I. Ederra, R. Gonzalo, and R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 063807 (2013).
[CrossRef]

B. S. Luk’yanchuk, A. E. Miroshnichenko, and Yu. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt. 15, 073001 (2013).
[CrossRef]

M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
[CrossRef] [PubMed]

P. J. S. Smith, I. Davis, C. G. Galbraith, and A. Stemmer, “Special issue on high-resolution optical imaging,” J. Opt. 15(9), 090201 (2013).
[CrossRef]

2012

D. S. Kim and Z. H. Kim, “Role of in-plane polarizability of the tip in scattering near-field microscopy of a plasmonic nanoparticle,” Opt. Express 8, 8689–8699 (2012).
[CrossRef]

Yu. V. Vladimirova, V. V. Klimov, V. M. Pastukhov, and V. N. Zadkov, “Modification of two-level-atom resonance fluorescence near a plasmonic nanostructure,” Phys. Rev. A 85, 053408 (2012).
[CrossRef]

2011

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[CrossRef]

2010

V. Mizeikis, E. Kowalska, B. Ohtani, and S. Juodkazis, “Frequency- and polarization-dependent optical response of asymmetric spheroidal silver nanoparticles on dielectric substrate,” Phys. Status Solidi RRL 4, 268–270 (2010).
[CrossRef]

2009

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[CrossRef] [PubMed]

P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
[CrossRef]

2008

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[CrossRef] [PubMed]

2007

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[CrossRef] [PubMed]

T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
[CrossRef] [PubMed]

M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007).
[CrossRef]

2006

S. Kühn, U. Hàkanson, L. Rogobeand, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

2005

J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

2004

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93, 200801 (2004).
[CrossRef] [PubMed]

J. Perez-Juste, L. M. Liz-Marzan, S. Carnie, D. Y. C. Chan, and P. Mulvaney, “Electric-field-directed growth for gold nanorods in aqueous surfactant solutions,” Adv. Funct. Mater. 14, 571–579 (2004).
[CrossRef]

2002

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom placed near a prolate nanospheroid,” Eur. Phys. J. D 20, 133–148 (2002).
[CrossRef]

1999

Z. Q. Qui and S. D. Bader, “Surface magneto-optic Kerr effect (SMOKE),” J. Magn. Magn. Mater. 200, 664–678 (1999).
[CrossRef]

1997

P. Balcou and L. Durtriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851 (1997).
[CrossRef]

Y. Y. Yu, S. S. Chang, C. L. Lee, and C. R. C. Wang, “Gold nanorods: electrochemical synthesis and optical properties,” J. Phys. Chem. B 101, 6661–6664 (1997).
[CrossRef]

1996

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals Force in an Atomic Mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

1993

1977

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced raman scattering,” Science 275, 1102–1106 (1977).
[CrossRef]

1953

A. F. Stevenson, “Electromagnetic scattering by an ellipsoid in the third approximation,” Appl. Phys. 24, 1143–1151 (1953).
[CrossRef]

Agranovich, M. S.

M. S. Agranovich, B. Z. Katsenelenbaum, A. N. Sivov, and N. N. Voitovich, Generalized Method of Eigenoscillation in Diffraction Theory (Wiley, 1999).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[CrossRef] [PubMed]

Aspect, A.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals Force in an Atomic Mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Auzinsh, M.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light–Atom Interactions (Oxford University, 2010).

Azzam, R. M.

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Ligh (Elsevier, 1999).

Bader, S. D.

Z. Q. Qui and S. D. Bader, “Surface magneto-optic Kerr effect (SMOKE),” J. Magn. Magn. Mater. 200, 664–678 (1999).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
[CrossRef]

Balcou, P.

P. Balcou and L. Durtriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851 (1997).
[CrossRef]

Bashara, N. M.

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Ligh (Elsevier, 1999).

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
[CrossRef]

Belov, P. A.

A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovskii, and Yu. S. Kivshar, “Optical nanoantennas,” Phys. Usp. 56, 539–564 (2013).
[CrossRef]

Biagioni, P.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[CrossRef] [PubMed]

P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007).
[CrossRef]

Budker, D.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light–Atom Interactions (Oxford University, 2010).

Carnie, S.

J. Perez-Juste, L. M. Liz-Marzan, S. Carnie, D. Y. C. Chan, and P. Mulvaney, “Electric-field-directed growth for gold nanorods in aqueous surfactant solutions,” Adv. Funct. Mater. 14, 571–579 (2004).
[CrossRef]

Celebrano, M.

M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007).
[CrossRef]

Chan, D. Y. C.

J. Perez-Juste, L. M. Liz-Marzan, S. Carnie, D. Y. C. Chan, and P. Mulvaney, “Electric-field-directed growth for gold nanorods in aqueous surfactant solutions,” Adv. Funct. Mater. 14, 571–579 (2004).
[CrossRef]

Chang, S. S.

Y. Y. Yu, S. S. Chang, C. L. Lee, and C. R. C. Wang, “Gold nanorods: electrochemical synthesis and optical properties,” J. Phys. Chem. B 101, 6661–6664 (1997).
[CrossRef]

Courtois, J. Y.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals Force in an Atomic Mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Davis, I.

P. J. S. Smith, I. Davis, C. G. Galbraith, and A. Stemmer, “Special issue on high-resolution optical imaging,” J. Opt. 15(9), 090201 (2013).
[CrossRef]

Denisyuk, A. I.

A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovskii, and Yu. S. Kivshar, “Optical nanoantennas,” Phys. Usp. 56, 539–564 (2013).
[CrossRef]

Ducloy, M.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom placed near a prolate nanospheroid,” Eur. Phys. J. D 20, 133–148 (2002).
[CrossRef]

Duò, L.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[CrossRef] [PubMed]

P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007).
[CrossRef]

Durtriaux, L.

P. Balcou and L. Durtriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851 (1997).
[CrossRef]

Ederra, I.

I. Liberal, I. Ederra, R. Gonzalo, and R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 063807 (2013).
[CrossRef]

Eisler, H. J.

J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Emory, S. R.

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced raman scattering,” Science 275, 1102–1106 (1977).
[CrossRef]

Esslinger, T.

Farahani, J. N.

J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Felderer, K.

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93, 200801 (2004).
[CrossRef] [PubMed]

Finazzi, M.

P. Biagioni, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Cross resonant optical antenna,” Phys. Rev. Lett. 102, 256801 (2009).
[CrossRef] [PubMed]

P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
[CrossRef]

M. Finazzi, P. Biagioni, M. Celebrano, and L. Duò, “Selection rules for second-harmonic generation in nanoparticles,” Phys. Rev. B 76, 125414 (2007).
[CrossRef]

Frey, H. G.

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93, 200801 (2004).
[CrossRef] [PubMed]

Friberg, A. T.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Galbraith, C. G.

P. J. S. Smith, I. Davis, C. G. Galbraith, and A. Stemmer, “Special issue on high-resolution optical imaging,” J. Opt. 15(9), 090201 (2013).
[CrossRef]

Giannini, V.

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[CrossRef] [PubMed]

Gómez Rivas, J.

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[CrossRef] [PubMed]

Gonzalo, R.

I. Liberal, I. Ederra, R. Gonzalo, and R. W. Ziolkowski, “Near-field electromagnetic trapping through curl-spin forces,” Phys. Rev. A 87, 063807 (2013).
[CrossRef]

Guckenberger, R.

H. G. Frey, S. Witt, K. Felderer, and R. Guckenberger, “High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip,” Phys. Rev. Lett. 93, 200801 (2004).
[CrossRef] [PubMed]

Hadley, L.

G. Hass and L. Hadley, Optical Properties of Metals (American Institute of Physics Handbook) ed. by D. E. Gray, ed. (McGraw-Hill, 1963).

Hàkanson, U.

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M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
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M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
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A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovskii, and Yu. S. Kivshar, “Optical nanoantennas,” Phys. Usp. 56, 539–564 (2013).
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M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
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B. S. Luk’yanchuk, A. E. Miroshnichenko, and Yu. S. Kivshar, “Fano resonances and topological optics: an interplay of far- and near-field interference phenomena,” J. Opt. 15, 073001 (2013).
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V. Mizeikis, E. Kowalska, B. Ohtani, and S. Juodkazis, “Frequency- and polarization-dependent optical response of asymmetric spheroidal silver nanoparticles on dielectric substrate,” Phys. Status Solidi RRL 4, 268–270 (2010).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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V. Mizeikis, E. Kowalska, B. Ohtani, and S. Juodkazis, “Frequency- and polarization-dependent optical response of asymmetric spheroidal silver nanoparticles on dielectric substrate,” Phys. Status Solidi RRL 4, 268–270 (2010).
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Yu. V. Vladimirova, V. V. Klimov, V. M. Pastukhov, and V. N. Zadkov, “Modification of two-level-atom resonance fluorescence near a plasmonic nanostructure,” Phys. Rev. A 85, 053408 (2012).
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J. Perez-Juste, L. M. Liz-Marzan, S. Carnie, D. Y. C. Chan, and P. Mulvaney, “Electric-field-directed growth for gold nanorods in aqueous surfactant solutions,” Adv. Funct. Mater. 14, 571–579 (2004).
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M. Rahmani, E. Yoxall, B. Hopkins, Y. Sonnefraud, Y. Kivshar, M. Hong, Ch. Phillips, S. Maier, and A. E. Miroshnichenko, “Plasmonic nanoclusters with rotational symmetry: polarization-invariant far-field response vs changing near-field distribution,” ACS Nano 7, 11138–11146 (2013).
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J. N. Farahani, D. W. Pohl, H. J. Eisler, and B. Hecht, “Single quantum dot coupled to a scanning optical antenna: A tunable superemitter,” Phys. Rev. Lett. 95, 017402 (2005).
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S. Kühn, U. Hàkanson, L. Rogobeand, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
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O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
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S. Kühn, U. Hàkanson, L. Rogobeand, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97, 017402 (2006).
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P. Biagioni, M. Savoini, J. S. Huang, L. Duò, M. Finazzi, and B. Hecht, “Near-field polarization shaping by a near-resonant plasmonic cross antenna,” Phys. Rev. B 80, 153409 (2009).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
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T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
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A. E. Krasnok, I. S. Maksymov, A. I. Denisyuk, P. A. Belov, A. E. Miroshnichenko, C. R. Simovskii, and Yu. S. Kivshar, “Optical nanoantennas,” Phys. Usp. 56, 539–564 (2013).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
[CrossRef]

Sundaramurthy, A.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
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L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
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T. H. Taminiau, R. J. Moerland, F. B. Segerink, L. Kuipers, and N. F. van Hulst, “λ/4 resonance of an optical monopole antenna probed by single molecule fluorescence,” Nano Lett. 7, 28–33 (2007).
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A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals Force in an Atomic Mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
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Y. Y. Yu, S. S. Chang, C. L. Lee, and C. R. C. Wang, “Gold nanorods: electrochemical synthesis and optical properties,” J. Phys. Chem. B 101, 6661–6664 (1997).
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A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals Force in an Atomic Mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of spaser-based nanolaser,” Nature (London) 460, 1110–1112 (2009).
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Alternatively, one can study the dependence of the vectorial near-field of the prolate nanospheroid at fixed value of its aspect ratio versus the polarization and frequency of the incident field.

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It is worth to note here that the degree of polarization we introduced in the paper does not reflect the fluctuations of the incident field vector. In order to take these fluctuations into account one has to use different definition of the degree of polarization via the Stokes parameters, which for the plane wave has the form: P*=(S12+S22+S32)0.5/S0. Without fluctuations, this polarization degree is always equal to 1.

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Figures (7)

Fig. 1
Fig. 1

(a) Arrangement of the problem. An incident plane electromagnetic wave interacts with a prolate nanospheroid with c and a being the major and minor semiaxes of the ellipse, respectively, ε is the permittivity of the nanoparticle and εH is the permittivity of the media the nanoparticle is located in. (b) Prolate nanospheroid in an incident linearly polarized plane electromagnetic wave directed at angle θ towards x-axis.

Fig. 2
Fig. 2

Polarization of the near-field of the plasmonic prolate nanospheroid under linearly polarized along the z-axis incident plane electromagnetic wave in the case of the plasmon resonance at α = αres; E0,y = 0 V/m and E0,z = 2000 V/m (about 7 mW/mm2). Left figure shows the distribution of the normalized Stokes parameter S3xz/I. In areas where S3xz takes positive values, the field vector rotates clockwise, whereas in areas with negative values of the Stokes parameter—it rotates anti-clockwise. The right figure shows the distribution of the degree of polarization of the near-field. 3D surface corresponds to the surface at the constant degree of polarization P = 0.8. 2D distributions show respective sections at three planes: xz, yz, and z = 15 nm.

Fig. 3
Fig. 3

The distribution of the degree of polarization of the near-field under the linearly polarized along the z-axis incident field in the case of far away from the plasmon resonance at α = 0.25 < αres (a) and α = 0.41 > αres (b).

Fig. 4
Fig. 4

The distribution of the degree of polarization of the near-field under the linearly polarized along the angle θ = 40° (a) and θ = 70° (b) towards z-axis in the case of the plasmon resonance at α = αres, E0,y = 0 V/m and E0,z = 2000 V/m (about 7 mW/mm2). 3D surface corresponds to the surface at the constant degree of polarization P = 0.8. 2D distributions show respective sections at three planes: xz, yz, and z = 0.

Fig. 5
Fig. 5

The distribution of the degree of polarization of the near-field under the incident field with the left elliptically polarization in the case of the plasmon resonance at α = αres, E0,x = 0 V/m, E0,y = 400i V/m and E0,z = 2000 V/m (about 7 mW/mm2). 3D surface corresponds to the surface at the constant degree of polarization P = 0.8. 2D distributions show respective sections at three planes: xz, yz, and z = 15 nm.

Fig. 6
Fig. 6

Polarization of the near-field of the plasmonic prolate nanospheroid under the incident plane electromagnetic wave of left-handed circular polarization (E0,x = 0 V/m, E0,y = 2000i V/m, E0,z = 2000 V/m) (2000 V/m ≈ 7 mW/mm2) in the case of the plasmon resonance at α = 0.32. Left figure show the distribution of the normalized Stokes parameter S3yz/I versus y, z coordinates. In the light lilac color areas the electric field has left-handed circular polarization, whereas in the red areas—right-handed circular polarization, and in the green areas—the field projections on the axes y and z oscillate with the same phase. Right figure shows the distribution of the degree of polarization of the near-field. 3D surface corresponds to the surface at the constant degree of polarization P = 0.8. 2D distributions show respective sections at three planes: xz, yz, and xy.

Fig. 7
Fig. 7

The distribution of the degree of polarization of the near-field under the incident plane electromagnetic wave of left circular polarization (E0,x = 0 V/m, E0,y = 2000i V/m, E0,z = 2000 V/m) (2000 V/m ≈ 7 mW/mm2) at α = 0.25 < αres (a) and α = 0.42 > αres (b). 3D surface corresponds to the surface at the constant degree of polarization P = 0.8. 2D distributions show respective sections at three planes: xz, yz, and xy.

Equations (25)

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rot h n + i k ε n e n = 0 , rot e n i k h n = 0 .
E ( r , t ) = E 0 ( r ) + n e n ε ( ω ) ε H ε n ε ( ω ) V ( e n , E 0 ) d V V e n 2 d V ,
E = E 0 + n ε ( ω ) ε H ε n ε ( ω ) V ( φ n , E 0 ) d V V φ n 2 d V ( φ n ) ,
φ n m in = Q n ( m ) ( ξ 0 ) P n ( m ) ( η ) P n ( m ) ( ξ ) { cos m ψ sin m ψ }
φ n m out = Q n ( m ) ( ξ ) P n ( m ) ( η ) P n ( m ) ( ξ 0 ) { cos m ψ sin m ψ }
ε n m = P n ( m ) ( ξ 0 ) d d ξ 0 Q n ( m ) ( ξ 0 ) d d ξ 0 P n ( m ) ( ξ 0 ) Q n ( m ) ( ξ 0 ) ε H ,
ξ 0 = c c 2 a 2 = 1 1 α 2
E x ( r , t ) = A x ( r ) cos ( ω t + ϕ x ( r ) ) , E y ( r , t ) = A y ( r ) cos ( ω t + ϕ y ( r ) ) , E z ( r , t ) = A z ( r ) cos ( ω t + ϕ z ( r ) ) ,
P = I max I min I max + I min ,
I ( t ) = ( A x 2 + A y 2 + A z 2 ) + ( A x 2 + A y 2 cos 2 ϕ y + A z 2 cos 2 ϕ z ) cos 2 ω t ( A y 2 sin 2 ϕ y + A z 2 sin 2 ϕ z ) sin 2 ω t .
P = [ ( | A ˜ x | 2 + | A ˜ y | 2 + | A ˜ z | 2 ) 2 4 Im 2 ( A ˜ x * A ˜ y ) 4 Im 2 ( A ˜ x * A ˜ z ) 4 Im 2 ( A ˜ y * A ˜ z ) ] 1 / 2 | A ˜ x | 2 + | A ˜ y | 2 + | A ˜ z | 2 ,
S 3 x y = i ( E x * ( r , ω ) E y ( r , ω ) E x ( r , ω ) E y * ( r , ω ) ) , S 3 x z = i ( E x * ( r , ω ) E z ( r , ω ) E x ( r , ω ) E z * ( r , ω ) ) , S 3 y z = i ( E y * ( r , ω ) E z ( r , ω ) E y ( r , ω ) E z * ( r , ω ) ) ,
P = 1 ( S 3 x y I ) 2 ( S 3 x z I ) 2 ( S 3 y z I ) 2 ,
E = E 0 , z e z + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z P 1 ( η ) Q 1 ( ξ ) .
A ˜ x ( r ) = ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z x P 1 ( η ) Q 1 ( ξ ) ,
A ˜ y ( r ) = ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z y P 1 ( η ) Q 1 ( ξ ) ,
A ˜ z ( r ) = E 0 , z + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z z P 1 ( η ) Q 1 ( ξ ) ,
E = E 0 , x e x + E 0 , z e z + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z P 1 ( η ) Q 1 ( ξ ) + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f E 0 , x P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) cos ψ
A ˜ x ( r ) = E 0 , x + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z x [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f E 0 , x x [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) cos ψ ] ,
A ˜ y ( r ) = ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z y [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f E 0 , x y [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) cos ψ ] ,
A ˜ z ( r ) = E 0 , z + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z z [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f E 0 , x z [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) cos ψ ] .
E = i E 0 , y e y + E 0 , z e z + ε ( ω ) 1 ε 1 , 0 ε ( ω ) P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z P 1 ( η ) Q 1 ( ξ ) + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f i E 0 , y P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) sin ψ ,
A ˜ x ( r ) = ε ( ω ) 1 ε ( ω ) ε 1 , 0 P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z x [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f i E 0 , y x [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) sin ψ ] ,
A ˜ y ( r ) = i E y , 0 + ε ( ω ) 1 ε ( ω ) ε 1 , 0 P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z y [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f i E 0 , y y [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) sin ψ ] ,
A ˜ z ( r ) = E 0 , z + ε ( ω ) 1 ε ( ω ) ε 1 , 0 P 1 ( ξ 0 ) Q 1 ( ξ 0 ) f E 0 , z z [ P 1 ( η ) Q 1 ( ξ ) ] + ε ( ω ) 1 ε 1 , 1 ε ( ω ) P 1 ( 1 ) ( ξ 0 ) Q 1 ( 1 ) ( ξ 0 ) f i E 0 , y z [ P 1 ( 1 ) ( η ) Q 1 ( 1 ) ( ξ ) sin ψ ] .

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