Abstract

We study the modification of the far-field cross sections and the near-field enhancement for gold and silver nanospheres illuminated by a tightly focused beam. Using a multipole-expansion approach we obtain an analytical solution to the scattering problem and provide insight on the effects of focusing on the optical response. Large differences with respect to Mie theory are especially found when the nanoparticle supports quadrupole or higher-order resonances.

© 2008 Optical Society of America

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  2. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).
  3. T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005).
    [CrossRef] [PubMed]
  4. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single molecule fluorescence using a gold nanoparticle as an optical nano-antenna,” Phys. Rev. Lett. 97, 017402 (2006).
    [CrossRef] [PubMed]
  5. P. Anger, P. Bharadway, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
    [CrossRef] [PubMed]
  6. C. Voisin, D. Christofilos, N. Del Fatti, F. Vallée, B. Prével, E. Cottancin, J. Lermé, M. Pellarin, and M. Broyer, “Size-dependent electron-electron interactions in metal nanoparticles,” Phys. Rev. Lett. 85, 2200-2203 (2000).
    [CrossRef] [PubMed]
  7. A. Arbouet, C. Voisin, D. Christofilos, P. Langot, N. Del Fatti, F. Vallée, J. Lermé, G. Celep, E. Cottancin, M. Gaudry, M. Pellarin, M. Broyer, M. Maillard, M. P. Pileni, and M. Treguer, “Electron-phonon scattering in metal clusters,” Phys. Rev. Lett. 90, 177401 (2003).
    [CrossRef] [PubMed]
  8. P. Stoller, V. Jacobsen, and V. Sandoghdar, “Measurement of the complex dielectric constant of a single gold nanoparticle,” Opt. Lett. 31, 2474-2476 (2006).
    [CrossRef] [PubMed]
  9. S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
    [CrossRef] [PubMed]
  10. W. Fritzsche and T. A. Taton, “Metal nanoparticles as labels for heterogeneous, chip-based DNA detection,” Nanotechnology 14, R63-R73 (2003).
    [CrossRef] [PubMed]
  11. J. Seelig, K. Leslie, A. Renn, S. Kühn, V. Jacobsen, M. van de Corput, C. Wyman, and V. Sandoghdar, “Nanoparticle induced fluorescence lifetime modification as nanoscopic ruler: demonstration at the single molecule level,” Nano Lett. 7, 685-689 (2007).
    [CrossRef] [PubMed]
  12. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticles plasmon waveguides,” Nat. Mater. 2, 229-232 (2003).
    [CrossRef] [PubMed]
  13. R. de Waele, A. F. Koenderink, and A. Polman, “Tunable nanoscale localization of energy on plasmon particle arrays,” Nano Lett. 7, 2004-2008 (2007).
    [CrossRef]
  14. C. Sönnichsen, S. Geier, N. E. Hecker, G. von Plessen, J. Feldmann, H. Ditlbacher, B. Lamprecht, J. R. Krenn, F. R. Aussenegg, V. Z.-H. Chan, J. P. Spatz, and M. Möller, “Spectroscopy of single metallic nanoparticles using total internal reflection microscopy,” Appl. Phys. Lett. 77, 2949-2951 (2000).
    [CrossRef]
  15. J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of plasmon resonance spectra from individual nanoparticles,” Nano Lett. 3, 485-491 (2003).
    [CrossRef]
  16. K. Linfords, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticle using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93, 037401 (2004).
    [CrossRef]
  17. S. Berciaud, L. Cognet, G. A. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
    [CrossRef]
  18. M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B 68, 87-92 (1999).
    [CrossRef]
  19. J. R. Arias-González and M. Nieto-Vesperinas, “Resonant near-field eigenmodes of nanocylinders on flat surfaces under both homogeneous and inhomogeneous lightwave excitation,” J. Opt. Soc. Am. A 18, 657-665 (2001).
    [CrossRef]
  20. G. Videen, M. M. Aslan, and M. P. Mengüç, “Characterization of metallic nanoparticles via surface wave scattering: A. Theoretical framework and formulation,” J. Quant. Spectrosc. Radiat. Transf. 93, 195-206 (2005).
    [CrossRef]
  21. M. M. Aslan, M. P. Mengüç, and G. Videen, “Characterization of metallic nanoparticles via surface wave scattering: B. Physical concept and numerical experiments,” J. Quant. Spectrosc. Radiat. Transf. 93, 207-217 (2005).
    [CrossRef]
  22. F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
    [CrossRef] [PubMed]
  23. P. Török, P. D. Higdon, R. Juskaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155, 335-341 (1998).
    [CrossRef]
  24. W. A. Challener, I. K. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11, 3160-3170 (2003).
    [CrossRef] [PubMed]
  25. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377-452 (1908).
    [CrossRef]
  26. N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724-727 (1968).
    [CrossRef]
  27. W.-C. Tsai and R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical objects,” J. Opt. Soc. Am. 65, 1457-1463 (1975).
    [CrossRef]
  28. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632-1639 (1988).
    [CrossRef]
  29. W. G. Tam and R. Corriveau, “Scattering of electromagnetic beams by spherical objects,” J. Opt. Soc. Am. 68, 763-767 (1978).
    [CrossRef]
  30. G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427-1443 (1988).
    [CrossRef]
  31. 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]
  32. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641-1650 (1999).
    [CrossRef]
  33. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
    [CrossRef]
  34. C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt. 44, 803-818 (1997).
    [CrossRef]
  35. G. Gouesbet and G. Grehan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97-103 (1982).
    [CrossRef]
  36. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  37. 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]
  38. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-825 (1985).
    [CrossRef]
  39. Wolfram Research, Inc., MATHEMATICA, Version 5.1, Champaign, Ill. (2004).
  40. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  41. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  42. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  43. J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379-3381 (2000).
    [CrossRef]
  44. E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, “Multipole plasmon resonances in gold nanorods,” J. Phys. Chem. B 110, 2150-2154 (2006).
    [CrossRef] [PubMed]
  45. H. Ditlbacher, J. R. Krenn, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Spectrally coded optical data storage by metal nanoparticles,” Opt. Lett. 15, 563-565 (2000).
    [CrossRef]
  46. 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]
  47. A. J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic particles,” Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
    [CrossRef] [PubMed]

2007

J. Seelig, K. Leslie, A. Renn, S. Kühn, V. Jacobsen, M. van de Corput, C. Wyman, and V. Sandoghdar, “Nanoparticle induced fluorescence lifetime modification as nanoscopic ruler: demonstration at the single molecule level,” Nano Lett. 7, 685-689 (2007).
[CrossRef] [PubMed]

R. de Waele, A. F. Koenderink, and A. Polman, “Tunable nanoscale localization of energy on plasmon particle arrays,” Nano Lett. 7, 2004-2008 (2007).
[CrossRef]

2006

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

P. Anger, P. Bharadway, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, “Multipole plasmon resonances in gold nanorods,” J. Phys. Chem. B 110, 2150-2154 (2006).
[CrossRef] [PubMed]

F. Moreno, F. González, and J. M. Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates,” Opt. Lett. 31, 1902-1904 (2006).
[CrossRef] [PubMed]

P. Stoller, V. Jacobsen, and V. Sandoghdar, “Measurement of the complex dielectric constant of a single gold nanoparticle,” Opt. Lett. 31, 2474-2476 (2006).
[CrossRef] [PubMed]

2005

A. J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic particles,” Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005).
[CrossRef] [PubMed]

G. Videen, M. M. Aslan, and M. P. Mengüç, “Characterization of metallic nanoparticles via surface wave scattering: A. Theoretical framework and formulation,” J. Quant. Spectrosc. Radiat. Transf. 93, 195-206 (2005).
[CrossRef]

M. M. Aslan, M. P. Mengüç, and G. Videen, “Characterization of metallic nanoparticles via surface wave scattering: B. Physical concept and numerical experiments,” J. Quant. Spectrosc. Radiat. Transf. 93, 207-217 (2005).
[CrossRef]

2004

K. Linfords, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticle using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef]

S. Berciaud, L. Cognet, G. A. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

2003

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticles plasmon waveguides,” Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

W. Fritzsche and T. A. Taton, “Metal nanoparticles as labels for heterogeneous, chip-based DNA detection,” Nanotechnology 14, R63-R73 (2003).
[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, 485-491 (2003).
[CrossRef]

A. Arbouet, C. Voisin, D. Christofilos, P. Langot, N. Del Fatti, F. Vallée, J. Lermé, G. Celep, E. Cottancin, M. Gaudry, M. Pellarin, M. Broyer, M. Maillard, M. P. Pileni, and M. Treguer, “Electron-phonon scattering in metal clusters,” Phys. Rev. Lett. 90, 177401 (2003).
[CrossRef] [PubMed]

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

W. A. Challener, I. K. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11, 3160-3170 (2003).
[CrossRef] [PubMed]

2001

J. R. Arias-González and M. Nieto-Vesperinas, “Resonant near-field eigenmodes of nanocylinders on flat surfaces under both homogeneous and inhomogeneous lightwave excitation,” J. Opt. Soc. Am. A 18, 657-665 (2001).
[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]

2000

H. Ditlbacher, J. R. Krenn, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Spectrally coded optical data storage by metal nanoparticles,” Opt. Lett. 15, 563-565 (2000).
[CrossRef]

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379-3381 (2000).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

C. Voisin, D. Christofilos, N. Del Fatti, F. Vallée, B. Prével, E. Cottancin, J. Lermé, M. Pellarin, and M. Broyer, “Size-dependent electron-electron interactions in metal nanoparticles,” Phys. Rev. Lett. 85, 2200-2203 (2000).
[CrossRef] [PubMed]

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

C. Sönnichsen, S. Geier, N. E. Hecker, G. von Plessen, J. Feldmann, H. Ditlbacher, B. Lamprecht, J. R. Krenn, F. R. Aussenegg, V. Z.-H. Chan, J. P. Spatz, and M. Möller, “Spectroscopy of single metallic nanoparticles using total internal reflection microscopy,” Appl. Phys. Lett. 77, 2949-2951 (2000).
[CrossRef]

1999

M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B 68, 87-92 (1999).
[CrossRef]

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641-1650 (1999).
[CrossRef]

1998

P. Török, P. D. Higdon, R. Juskaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155, 335-341 (1998).
[CrossRef]

1997

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

1995

1988

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427-1443 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

1985

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-825 (1985).
[CrossRef]

1982

G. Gouesbet and G. Grehan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97-103 (1982).
[CrossRef]

1981

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]

1978

1975

1972

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

1968

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724-727 (1968).
[CrossRef]

1959

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

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377-452 (1908).
[CrossRef]

Ann. Phys.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377-452 (1908).
[CrossRef]

Appl. Phys. B

M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B 68, 87-92 (1999).
[CrossRef]

Appl. Phys. Lett.

C. Sönnichsen, S. Geier, N. E. Hecker, G. von Plessen, J. Feldmann, H. Ditlbacher, B. Lamprecht, J. R. Krenn, F. R. Aussenegg, V. Z.-H. Chan, J. P. Spatz, and M. Möller, “Spectroscopy of single metallic nanoparticles using total internal reflection microscopy,” Appl. Phys. Lett. 77, 2949-2951 (2000).
[CrossRef]

J. R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F. R. Aussenegg, and J. C. Weeber, “Design of multipolar plasmon excitations in silver nanoparticles,” Appl. Phys. Lett. 77, 3379-3381 (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]

IEEE Trans. Antennas Propag.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724-727 (1968).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632-1639 (1988).
[CrossRef]

J. Mod. Opt.

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

J. Opt. (Paris)

G. Gouesbet and G. Grehan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97-103 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Chem. B

E. K. Payne, K. L. Shuford, S. Park, G. C. Schatz, and C. A. Mirkin, “Multipole plasmon resonances in gold nanorods,” J. Phys. Chem. B 110, 2150-2154 (2006).
[CrossRef] [PubMed]

J. Quant. Spectrosc. Radiat. Transf.

G. Videen, M. M. Aslan, and M. P. Mengüç, “Characterization of metallic nanoparticles via surface wave scattering: A. Theoretical framework and formulation,” J. Quant. Spectrosc. Radiat. Transf. 93, 195-206 (2005).
[CrossRef]

M. M. Aslan, M. P. Mengüç, and G. Videen, “Characterization of metallic nanoparticles via surface wave scattering: B. Physical concept and numerical experiments,” J. Quant. Spectrosc. Radiat. Transf. 93, 207-217 (2005).
[CrossRef]

Nano Lett.

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

J. Seelig, K. Leslie, A. Renn, S. Kühn, V. Jacobsen, M. van de Corput, C. Wyman, and V. Sandoghdar, “Nanoparticle induced fluorescence lifetime modification as nanoscopic ruler: demonstration at the single molecule level,” Nano Lett. 7, 685-689 (2007).
[CrossRef] [PubMed]

R. de Waele, A. F. Koenderink, and A. Polman, “Tunable nanoscale localization of energy on plasmon particle arrays,” Nano Lett. 7, 2004-2008 (2007).
[CrossRef]

Nanotechnology

W. Fritzsche and T. A. Taton, “Metal nanoparticles as labels for heterogeneous, chip-based DNA detection,” Nanotechnology 14, R63-R73 (2003).
[CrossRef] [PubMed]

Nat. Mater.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticles plasmon waveguides,” Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Opt. Commun.

P. Török, P. D. Higdon, R. Juskaitis, and T. Wilson, “Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers,” Opt. Commun. 155, 335-341 (1998).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

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]

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

Phys. Rev. Lett.

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

K. Linfords, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, “Detection and spectroscopy of gold nanoparticle using supercontinuum white light confocal microscopy,” Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef]

S. Berciaud, L. Cognet, G. A. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

T. Kalkbrenner, U. Håkanson, A. Schädle, S. Burger, C. Henkel, and V. Sandoghdar, “Optical microscopy via spectral modifications of a nanoantenna,” Phys. Rev. Lett. 95, 200801 (2005).
[CrossRef] [PubMed]

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

P. Anger, P. Bharadway, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

C. Voisin, D. Christofilos, N. Del Fatti, F. Vallée, B. Prével, E. Cottancin, J. Lermé, M. Pellarin, and M. Broyer, “Size-dependent electron-electron interactions in metal nanoparticles,” Phys. Rev. Lett. 85, 2200-2203 (2000).
[CrossRef] [PubMed]

A. Arbouet, C. Voisin, D. Christofilos, P. Langot, N. Del Fatti, F. Vallée, J. Lermé, G. Celep, E. Cottancin, M. Gaudry, M. Pellarin, M. Broyer, M. Maillard, M. P. Pileni, and M. Treguer, “Electron-phonon scattering in metal clusters,” Phys. Rev. Lett. 90, 177401 (2003).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

A. J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic particles,” Proc. Natl. Acad. Sci. U.S.A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A

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

Rev. Mod. Phys.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783-825 (1985).
[CrossRef]

Other

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

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

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

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, 1995).

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Figures (7)

Fig. 1
Fig. 1

Relative strength of the multipole coefficients for the expansion of a PW E l E 1 and a high-NA beam ( α = 60 ° and α = 30 ° ) A l A 1 . Inset, a PW polarized along x and propagating along z is focused by a high-NA lens and scatters on a metal NP positioned at the focus. α is the angular semiaperture of the lens.

Fig. 2
Fig. 2

(a) Scattering and (b) extinction cross sections of a 100 nm gold NP in glass illuminated by a PW and a high-NA beam ( α = 60 ° ) . The inset of (a) shows the incident intensity averaged on the NP according to Eq. (18) and normalized with respect to the intensity at the origin as a function of the angular semiaperture α for λ = 450 and 650 nm . The intensity at the origin is equal to that assumed for PW illumination. The inset of (b) plots the Poynting vector for the high-NA beam ( α = 60 ° ) at λ = 450 nm with the 100 nm gold NP to scale.

Fig. 3
Fig. 3

(a) Scattering and (b) extinction cross sections of a 100 nm silver NP in glass illuminated by a PW and a high-NA beam ( α = 60 ° and 30 ° ).

Fig. 4
Fig. 4

Average radial (solid curves) and tangential (dashed curves) intensity enhancements evaluated at the surface of a 100 nm gold NP in glass illuminated by a PW and high-NA beam ( α = 60 ° ) .

Fig. 5
Fig. 5

Average radial (solid curves) and tangential (dashed curves) intensity enhancements evaluated at the surface of a 100 nm silver NP in glass and air illuminated by a (a) high-NA beam ( α = 60 ° ) and (b) PW.

Fig. 6
Fig. 6

Radial intensity enhancement ( log 10 scale) for a 100 nm gold NP in glass illuminated (along z ) by a [(a) and (c)] high-NA beam ( α = 60 ° ) at λ = 645 nm and [(b) and (d)] PW at λ = 642 nm . Cross cuts: [(a) and (b)] x y plane and [(c) and (d)] x z plane. The field is not computed inside the NP.

Fig. 7
Fig. 7

Radial intensity enhancement as a function of θ for ϕ = 0 ° at the surface of a 100 nm gold NP in glass illuminated by a high-NA beam ( α = 60 ° ) at λ = 645 nm and a PW at λ = 642 nm . The contribution from only the scattered field is represented by dashed curves.

Equations (24)

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E i , r = 0 ,
E i , θ = E 0 exp ( i k f ) a ( θ ) cos ϕ ,
E i , ϕ = E 0 exp ( i k f ) a ( θ ) sin ϕ ,
E i ( r , θ , ϕ ) = l [ A l N e 1 l ( r , θ , ϕ ) + B l M o 1 l ( r , θ , ϕ ) ] ,
l i l A l [ P l 1 ( cos θ ) sin θ + d P l 1 ( cos θ ) d θ ] = k f E 0 a ( θ ) ,
A l = ( i ) l E 0 k f 2 l + 1 2 l 2 ( l + 1 ) 2 0 α a ( θ ) [ P l 1 ( cos θ ) sin θ + d P l 1 ( cos θ ) d θ ] sin θ d θ .
E i = l A l ( N e 1 l ( 1 ) i M o 1 l ( 1 ) ) ,
E s = l A l ( a l N e 1 l ( 3 ) + i b l M o 1 l ( 3 ) ) ,
E int = l A l ( d l N e 1 l ( 1 ) i c l M o 1 l ( 1 ) ) ,
a l = m ψ l ( m x ) ψ l ( x ) ψ l ( x ) ψ l ( m x ) m ψ l ( m x ) χ l ( x ) χ l ( x ) ψ l ( m x ) ,
b l = m ψ l ( x ) ψ l ( m x ) ψ l ( m x ) ψ l ( x ) m χ l ( x ) ψ l ( m x ) ψ l ( m x ) χ l ( x ) ,
c l = m χ l ( x ) ψ l ( x ) m ψ l ( x ) χ l ( x ) m χ l ( x ) ψ l ( m x ) ψ l ( m x ) χ l ( x ) ,
d l = m ψ l ( x ) χ l ( x ) m χ l ( x ) ψ l ( x ) m ψ l ( m x ) χ l ( x ) χ l ( x ) ψ l ( m x ) .
W s = 1 2 0 2 π 0 π Re { E s , θ H s , ϕ * E s , ϕ H s , θ * } r 2 sin θ d θ d ϕ ,
W s = π 2 Z k 2 l A l 2 2 l 2 ( l + 1 ) 2 2 l + 1 ( a l 2 + b l 2 ) ,
W e = 1 2 0 2 π 0 π Re { E i , ϕ H s , θ * E i , θ H s , ϕ * E s , θ H i , ϕ * + E s , ϕ H i , θ * } r 2 sin θ d θ d ϕ ,
W e = π 2 Z k 2 l A l 2 2 l 2 ( l + 1 ) 2 2 l + 1 Re { a l + b l } .
I i = 1 2 π a 2 A Re { E i × H i * } z d s .
K = 1 4 π E i ( 0 , 0 , 0 ) 2 0 2 π 0 π E tot ( a , θ , ϕ ) 2 sin θ d θ d ϕ .
K r = 9 16 ( k a ) 4 l A l 2 A 1 2 2 l 3 ( l + 1 ) 3 2 l + 1 [ a l 2 χ l 2 + ψ l 2 2 Re { a l χ l } ψ l ] ,
K t = 9 16 ( k a ) 2 l A l 2 A 1 2 2 l 2 ( l + 1 ) 2 2 l + 1 [ a l 2 χ l 2 + b l 2 χ l 2 + ψ l 2 + ψ l 2 2 Re { a l χ l } ψ l 2 Re { b l χ l } ψ l ] ,
K r = 1 3 [ 4 α 2 + 4 Re { α } + 1 ] ,
K t = 2 3 [ α 2 2 Re { α } + 1 ] ,
α = m 2 1 m 2 + 2 .

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