Abstract

We study the interaction of focused radially-polarized light with metal nanospheres. By expanding the electromagnetic field in terms of multipoles, we gain insight on the excitation of localized surface plasmon-polariton resonances in the nanoparticle. We show that focused radially-polarized beams offer more opportunities than a focused plane wave or a Gaussian beam for tuning the near- and far-field system response. These results find applications in nano-optics, optical tweezers, and optical data storage.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).
  2. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett.  91, 233901(4) (2003).
    [CrossRef] [PubMed]
  3. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
    [CrossRef] [PubMed]
  4. S. J. van Enk, "Atoms, dipole waves, and strongly focused light beams," Phys. Rev. A 69, 043813(8) (2004).
    [CrossRef]
  5. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004).
    [CrossRef] [PubMed]
  6. A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
    [CrossRef] [PubMed]
  7. A. V. Failla, S. Jager, T. Zuchner, M. Steiner, and A. J. Meixner, "Topology measurements of metal nanoparticles with 1 nm accuracy by Confocal Interference Scattering Microscopy," Opt. Express 15, 8532-8542 (2007).
    [CrossRef] [PubMed]
  8. T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
    [CrossRef]
  9. K. Sendur, W. Challener, and O. Mryasov, "Interaction of spherical nanoparticles with highly focused beam of light," Opt. Express 16, 2874-2886 (2008).
    [CrossRef] [PubMed]
  10. A. S. van de Nes and P. Torok, "Rigorous analysis of spheres in Gauss-Laguerre beams," Opt. Express 15, 13360-13374 (2007).
    [CrossRef] [PubMed]
  11. N. J. Moore and M. A. Alonso, "Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams," Opt. Express 16, 5926-5933 (2008).
    [CrossRef] [PubMed]
  12. J. Lerme, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, "Optical response of metal or dielectric nano-objects in strongly convergent light beams," Phys. Rev. B 77, 245406-13 (2008).
    [CrossRef]
  13. N. M. Mojarad, V. Sandoghdar, and M. Agio, "Plasmon spectra of nanospheres under a tightly focused beam," J. Opt. Soc. Am. B 25, 651-658 (2008).
    [CrossRef]
  14. C. J. R. Sheppard and P. T¨or¨ok, "Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion," J. Mod. Opt. 44, 803-818 (1997).
    [CrossRef]
  15. J. A. Lock, J. T. Hodges, and G. Gouesbet, "Failure of the optical theorem for Gaussian-beam scattering by a spherical particle," J. Opt. Soc. Am. A 12, 2708-2715 (1995).
    [CrossRef]
  16. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
    [CrossRef]
  17. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
    [CrossRef]
  18. K. S. Youngworth and T. G. Brown "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  19. R. Borghi, M. Santarsiero, and M. A. Alonso, "Highly focused spirally polarized beams," J. Opt. Soc. Am. A 22, 1420-1431 (2005).
    [CrossRef]
  20. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).
  21. G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, "Perfect reflection of light by an oscillating dipole," Phys. Rev. Lett. 101, 180404(4) (2008) and supplementary material.
    [CrossRef] [PubMed]
  22. S. A. Maier and H. A. Atwater, "Plasmonic: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101(10) (2005).
    [CrossRef]
  23. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  24. B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
    [CrossRef]
  25. Wolfram Research, Inc., MATHEMATICA, Version 5.1, Champaign, IL (2004).
  26. M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
    [CrossRef]
  27. V. Giannini and J. A. S’anchez-Gil, "Excitation and emission enhancement of single molecule fluorescence through multiple surface-plasmon resonances on metal trimer nanoantennas," Opt. Lett. 33, 899-901 (2008).
    [CrossRef] [PubMed]

2008 (5)

2007 (3)

2006 (1)

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2001 (3)

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

2000 (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1995 (1)

1981 (1)

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Agio, M.

Alonso, M. A.

Barber, P. W.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Borghi, R.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Challener, W.

Chang, R. K.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Failla, A. V.

T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
[CrossRef]

A. V. Failla, S. Jager, T. Zuchner, M. Steiner, and A. J. Meixner, "Topology measurements of metal nanoparticles with 1 nm accuracy by Confocal Interference Scattering Microscopy," Opt. Express 15, 8532-8542 (2007).
[CrossRef] [PubMed]

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Giannini, V.

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Gouesbet, G.

Hartschuh, A.

T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
[CrossRef]

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Hirose, T.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

Hodges, J. T.

Inasawa, S.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

Jager, S.

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Koda, S.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Lock, J. A.

Meixner, A. J.

T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
[CrossRef]

A. V. Failla, S. Jager, T. Zuchner, M. Steiner, and A. J. Meixner, "Topology measurements of metal nanoparticles with 1 nm accuracy by Confocal Interference Scattering Microscopy," Opt. Express 15, 8532-8542 (2007).
[CrossRef] [PubMed]

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

Messinger, B. J.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Mojarad, N. M.

Moore, N. J.

Mryasov, O.

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Omatsu, T.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Qian, H.

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Sandoghdar, V.

Santarsiero, M.

Sendur, K.

Steiner, M.

Sugiyama, M.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

T¨orok, P.

Takami, A.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

van de Nes, A. S.

von Raben, K. U.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Yonekawa, T.

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Zhan, Q.

Zuchner, T.

T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
[CrossRef]

A. V. Failla, S. Jager, T. Zuchner, M. Steiner, and A. J. Meixner, "Topology measurements of metal nanoparticles with 1 nm accuracy by Confocal Interference Scattering Microscopy," Opt. Express 15, 8532-8542 (2007).
[CrossRef] [PubMed]

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Appl. Phys. Lett. (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

M. Sugiyama, S. Inasawa, S. Koda, T. Hirose, T. Yonekawa, T. Omatsu, and A. Takami, "Optical recording media using laser-induced size reduction of Au nanoparticles," Appl. Phys. Lett. 79, 1528-1530 (2001).
[CrossRef]

J. Microsc. (1)

T. Zuchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, "A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy," J. Microsc. 229, 337-343 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, "Orientational imaging of subwavelength Au particles with higher order laser modes," Nano Lett. 6, 1374-1378 (2006).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (3)

J. Lerme, C. Bonnet, M. Broyer, E. Cottancin, S. Marhaba, and M. Pellarin, "Optical response of metal or dielectric nano-objects in strongly convergent light beams," Phys. Rev. B 77, 245406-13 (2008).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
[CrossRef]

Other (7)

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).

G. Zumofen, N. M. Mojarad, V. Sandoghdar, and M. Agio, "Perfect reflection of light by an oscillating dipole," Phys. Rev. Lett. 101, 180404(4) (2008) and supplementary material.
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, "Plasmonic: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101(10) (2005).
[CrossRef]

S. J. van Enk, "Atoms, dipole waves, and strongly focused light beams," Phys. Rev. A 69, 043813(8) (2004).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett.  91, 233901(4) (2003).
[CrossRef] [PubMed]

Wolfram Research, Inc., MATHEMATICA, Version 5.1, Champaign, IL (2004).

C. J. R. Sheppard and P. T¨or¨ok, "Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion," J. Mod. Opt. 44, 803-818 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Relative strength |Bl /B 1| of the multipoles in the incident field. The result for a FPW is also shown for comparison [13]. The inset sketches a radially-polarized beam focused onto a NP. The red curve is the beam intensity profile before the lens, f is the focal length, α the angular semi-aperture, wo the beam waist and a = f/wo .

Fig. 2.
Fig. 2.

Extinction efficiency ��e of a 100 nm silver NP in glass illuminated by three different FRBs and a FPW. D, Q and O respectively label the dipole, quadrupole and octupole resonances. Inset: electric field intensity (contours) and Poynting vector (arrows) in the focal region for α= 90°, a = 1.5, and λ = 520 nm.

Fig. 3.
Fig. 3.

Radial and tangential (inset) average intensity enhancement for a 100 nm silver NP in glass illuminated by three different FRBs and a FPW. D, Q and O respectively label the dipole, quadrupole and octupole resonances.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Einc=l=1BlNe0l(1),
Bl=2l+12l(l+1)2kfilexp(ikf)0αE(a,θ)dPl(cosθ)dθsinθdθ,
Es=l=1alBlNe0l(3),Ei=l=1dlBlNe0l(1),
Ws=πZk2l=1Bl2al22l(l+1)2l+1,We=πZk2l=1Bl2Re{al}2l(l+1)2l+1,
Kr=916(kR)4lBlB12l2(l+1)22l+1[ψl2+al2χl2+2Re{al*χl*}ψl],
Kt=916(kR)2lBlB12l(l+1)22l+1[ψl2+al2χl2+2Re{al*χl*}ψl],

Metrics