Abstract

We study the interaction of an electromagnetic field with a nonabsorbing or absorbing dispersive sphere in the framework of complex angular momentum techniques. We assume that the dielectric function of the sphere presents a Drude-like behavior or an ionic crystal behavior modelling metallic and semiconducting materials. We more particularly emphasize and interpret the modifications induced in the resonance spectrum by absorption. We prove that “resonant surface-polariton modes” are generated by a unique surface wave, i.e., a surface- (plasmon or phonon) polariton, propagating close to the sphere surface. This surface polariton corresponds to a particular Regge pole of the electric part (TM) of the S matrix of the sphere. From the associated Regge trajectory, we can construct semiclassically the spectrum of the complex frequencies of the resonant surface polariton modes, which can be considered as Breit–Wigner-type resonances. Furthermore, by taking into account the Stokes phenomenon, we derive an asymptotic expression for the position in the complex angular momentum plane of the surface polariton Regge pole. We then describe semiclassically the surface polariton and provide analytical expressions for its dispersion relation and its damping in the nonabsorbing and absorbing cases. In these analytic expressions, we more particularly exhibit well-isolated terms directly linked to absorption. Finally, we explain why the photon-sphere system can be considered as an artificial atom (a “plasmonic atom” or “phononic atom”), and we briefly discuss the implication of our results in the context of the Casimir effect.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
    [CrossRef]
  2. R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319-330 (1968).
    [CrossRef]
  3. R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: I,” J. Phys. C 1, 614-629 (1968).
    [CrossRef]
  4. R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630-643 (1968).
    [CrossRef]
  5. R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: III,” J. Phys. C 1, 1515-1531 (1968).
    [CrossRef]
  6. R. Ruppin, in Electromagnetic Surface Modes, A.D.Boardman, ed. (Wiley, 1982).
  7. S. S. Martinos, “Surface electromagnetic modes in metal spheres,” Phys. Rev. B 31, 2029-2032 (1985).
    [CrossRef]
  8. R. Ruppin, “Electromagnetic energy in dispersive spheres,” J. Opt. Soc. Am. A 15, 524-527 (1998).
    [CrossRef]
  9. B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag, 2001).
    [CrossRef]
  10. H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
    [CrossRef]
  11. J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
    [CrossRef]
  12. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
    [CrossRef]
  13. H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56-63 (2007).
    [CrossRef] [PubMed]
  14. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982),
  15. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, 1992).
    [CrossRef]
  16. J. W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge U. Press, 2000).
    [CrossRef]
  17. R. D. Dingle, Asymptotic Expansions: Their Derivation and Interpretation (Academic, 1973).
  18. M. V. Berry, “Uniform asymptotic smoothing of stokes's discontinuities,” Proc. R. Soc. London, Ser. A 422, 7-21 (1989).
    [CrossRef]
  19. M. V. Berry and C. J. Howls, “Hyperasymptotics,” Proc. R. Soc. London A 430, 653-667 (1990).
  20. H. Segur, S. Tanveer, and H. Levine, Asymptotics Beyond All Orders (Plenum, 1991).
  21. S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
    [CrossRef]
  22. S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
    [CrossRef]
  23. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).
  24. M. Fox, Optical Properties of Solids (Oxford University Press, 2001).
  25. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
  27. M. V. Berry, “Attenuation and focusing of electromagnetic surface waves rounding gentle bends,” J. Phys. A 8, 1952-1971 (1975).
    [CrossRef]
  28. G. N. Watson, Theory of Bessel Functions (Cambridge U. Press, 1995), 2nd ed.
  29. H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23-95 (1965).
    [CrossRef]
  30. H. Raether, Surface Plasmons Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, 1988).
  31. T. Ito and K. Sakoda, “Photonic bands of metallic systems II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
    [CrossRef]
  32. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).
  33. D. V. Guzatov and V. V. Klimov, Plasmonic Atoms and Plasmonic Molecules (arXiv:physics/0703251).
  34. S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6to6 μm, range,” Phys. Rev. Lett. 78, 5-8 (1997).
    [CrossRef]
  35. M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
    [CrossRef]
  36. A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
    [CrossRef]
  37. C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).
  38. C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
    [CrossRef]

2007 (3)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56-63 (2007).
[CrossRef] [PubMed]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

2006 (1)

A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
[CrossRef]

2005 (1)

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

2004 (4)

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
[CrossRef]

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

2001 (3)

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
[CrossRef]

H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
[CrossRef]

T. Ito and K. Sakoda, “Photonic bands of metallic systems II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

1998 (1)

1997 (1)

S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6to6 μm, range,” Phys. Rev. Lett. 78, 5-8 (1997).
[CrossRef]

1990 (1)

M. V. Berry and C. J. Howls, “Hyperasymptotics,” Proc. R. Soc. London A 430, 653-667 (1990).

1989 (1)

M. V. Berry, “Uniform asymptotic smoothing of stokes's discontinuities,” Proc. R. Soc. London, Ser. A 422, 7-21 (1989).
[CrossRef]

1985 (1)

S. S. Martinos, “Surface electromagnetic modes in metal spheres,” Phys. Rev. B 31, 2029-2032 (1985).
[CrossRef]

1975 (1)

M. V. Berry, “Attenuation and focusing of electromagnetic surface waves rounding gentle bends,” J. Phys. A 8, 1952-1971 (1975).
[CrossRef]

1968 (4)

R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319-330 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: I,” J. Phys. C 1, 614-629 (1968).
[CrossRef]

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630-643 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: III,” J. Phys. C 1, 1515-1531 (1968).
[CrossRef]

1965 (1)

H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23-95 (1965).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Ancey, S.

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56-63 (2007).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry and C. J. Howls, “Hyperasymptotics,” Proc. R. Soc. London A 430, 653-667 (1990).

M. V. Berry, “Uniform asymptotic smoothing of stokes's discontinuities,” Proc. R. Soc. London, Ser. A 422, 7-21 (1989).
[CrossRef]

M. V. Berry, “Attenuation and focusing of electromagnetic surface waves rounding gentle bends,” J. Phys. A 8, 1952-1971 (1975).
[CrossRef]

Bordag, M.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
[CrossRef]

Bulgac, A.

A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

Décanini, Y.

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

Dingle, R. D.

R. D. Dingle, Asymptotic Expansions: Their Derivation and Interpretation (Academic, 1973).

Dung, H. T.

H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
[CrossRef]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

Englman, R.

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630-643 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: III,” J. Phys. C 1, 1515-1531 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: I,” J. Phys. C 1, 614-629 (1968).
[CrossRef]

Folacci, A.

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

Fox, M.

M. Fox, Optical Properties of Solids (Oxford University Press, 2001).

Fuchs, R.

Gabrielli, P.

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

Genet, C.

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

Grandy, J. W. T.

J. W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge U. Press, 2000).
[CrossRef]

Greffet, J.-J.

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

Guzatov, D. V.

D. V. Guzatov and V. V. Klimov, Plasmonic Atoms and Plasmonic Molecules (arXiv:physics/0703251).

Henkel, C.

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

Howls, C. J.

M. V. Berry and C. J. Howls, “Hyperasymptotics,” Proc. R. Soc. London A 430, 653-667 (1990).

Inglesfield, J. E.

J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
[CrossRef]

Intravaia, F.

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

Ito, T.

T. Ito and K. Sakoda, “Photonic bands of metallic systems II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

Joulain, K.

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

Kemp, R.

J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
[CrossRef]

Kliewer, K. L.

Klimov, V. V.

D. V. Guzatov and V. V. Klimov, Plasmonic Atoms and Plasmonic Molecules (arXiv:physics/0703251).

Knöll, L.

H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
[CrossRef]

Lambrecht, A.

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

Lamoreaux, S. K.

S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6to6 μm, range,” Phys. Rev. Lett. 78, 5-8 (1997).
[CrossRef]

Levine, H.

H. Segur, S. Tanveer, and H. Levine, Asymptotics Beyond All Orders (Plenum, 1991).

Magierski, P.

A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
[CrossRef]

Martinos, S. S.

S. S. Martinos, “Surface electromagnetic modes in metal spheres,” Phys. Rev. B 31, 2029-2032 (1985).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).

Mohideen, U.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
[CrossRef]

Mostepanenko, V. M.

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
[CrossRef]

Mulet, J.-P.

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982),

Nussenzveig, H. M.

H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23-95 (1965).
[CrossRef]

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, 1992).
[CrossRef]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, 1988).

Reynaud, S.

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

Ruppin, R.

R. Ruppin, “Electromagnetic energy in dispersive spheres,” J. Opt. Soc. Am. A 15, 524-527 (1998).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: III,” J. Phys. C 1, 1515-1531 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: I,” J. Phys. C 1, 614-629 (1968).
[CrossRef]

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630-643 (1968).
[CrossRef]

R. Ruppin, in Electromagnetic Surface Modes, A.D.Boardman, ed. (Wiley, 1982).

Sakoda, K.

T. Ito and K. Sakoda, “Photonic bands of metallic systems II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

Segur, H.

H. Segur, S. Tanveer, and H. Levine, Asymptotics Beyond All Orders (Plenum, 1991).

Sernelius, B. E.

B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag, 2001).
[CrossRef]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Tanveer, S.

H. Segur, S. Tanveer, and H. Levine, Asymptotics Beyond All Orders (Plenum, 1991).

Watson, G. N.

G. N. Watson, Theory of Bessel Functions (Cambridge U. Press, 1995), 2nd ed.

Welsch, D.-G.

H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
[CrossRef]

Wirzba, A.

A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
[CrossRef]

Ann. Fond. Louis Broglie (1)

C. Genet, F. Intravaia, A. Lambrecht, and S. Reynaud, “Electromagnetic vacuum fluctuations, Casimir and van der Waals forces,” Ann. Fond. Louis Broglie 29, 331-348 (2004).

Ann. Phys. (N.Y.) (1)

H. M. Nussenzveig, “High-frequency scattering by an impenetrable sphere,” Ann. Phys. (N.Y.) 34, 23-95 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. A (1)

M. V. Berry, “Attenuation and focusing of electromagnetic surface waves rounding gentle bends,” J. Phys. A 8, 1952-1971 (1975).
[CrossRef]

J. Phys. C (3)

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: I,” J. Phys. C 1, 614-629 (1968).
[CrossRef]

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630-643 (1968).
[CrossRef]

R. Englman and R. Ruppin, “Optical lattice vibrations in finite ionic crystals: III,” J. Phys. C 1, 1515-1531 (1968).
[CrossRef]

Phys. Rep. (1)

M. Bordag, U. Mohideen, and V. M. Mostepanenko, “New developments in the Casimir effect,” Phys. Rep. 353, 1-205 (2001).
[CrossRef]

Phys. Rev. A (2)

H. T. Dung, L. Knöll, and D.-G. Welsch, “Decay of an excited atom near an absorbing microsphere,” Phys. Rev. A 64, 013804 (2001).
[CrossRef]

C. Henkel, K. Joulain, J.-P. Mulet, and J.-J. Greffet, “Coupled surface polaritons and the Casimir force,” Phys. Rev. A 69, 023808 (2004).
[CrossRef]

Phys. Rev. B (6)

J. E. Inglesfield, J. M. Pitarke, and R. Kemp, “Plasmon bands in metallic nanostructures,” Phys. Rev. B 69, 233103 (2004).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on metallic and semiconducting cylinders: A complex angular momentum analysis,” Phys. Rev. B 70, 245406 (2004).
[CrossRef]

S. S. Martinos, “Surface electromagnetic modes in metal spheres,” Phys. Rev. B 31, 2029-2032 (1985).
[CrossRef]

T. Ito and K. Sakoda, “Photonic bands of metallic systems II. Features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed cylinders: a complex angular momentum analysis,” Phys. Rev. B 72, 085458 (2005).
[CrossRef]

S. Ancey, Y. Décanini, A. Folacci, and P. Gabrielli, “Surface polaritons on left-handed spheres,” Phys. Rev. B 76, 195413 (2007).
[CrossRef]

Phys. Rev. D (1)

A. Bulgac, P. Magierski, and A. Wirzba, “Scalar Casimir effect between Dirichlet spheres or a plate and a sphere,” Phys. Rev. D 73, 025007 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6to6 μm, range,” Phys. Rev. Lett. 78, 5-8 (1997).
[CrossRef]

Proc. R. Soc. London (1)

M. V. Berry and C. J. Howls, “Hyperasymptotics,” Proc. R. Soc. London A 430, 653-667 (1990).

Proc. R. Soc. London, Ser. A (1)

M. V. Berry, “Uniform asymptotic smoothing of stokes's discontinuities,” Proc. R. Soc. London, Ser. A 422, 7-21 (1989).
[CrossRef]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007).
[CrossRef]

Sci. Am. (1)

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56-63 (2007).
[CrossRef] [PubMed]

Other (15)

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, 1982),

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, 1992).
[CrossRef]

J. W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge U. Press, 2000).
[CrossRef]

R. D. Dingle, Asymptotic Expansions: Their Derivation and Interpretation (Academic, 1973).

B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag, 2001).
[CrossRef]

R. Ruppin, in Electromagnetic Surface Modes, A.D.Boardman, ed. (Wiley, 1982).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

D. V. Guzatov and V. V. Klimov, Plasmonic Atoms and Plasmonic Molecules (arXiv:physics/0703251).

H. Raether, Surface Plasmons Vol. 111 of Springer Tracts in Modern Physics (Springer-Verlag, 1988).

H. Segur, S. Tanveer, and H. Levine, Asymptotics Beyond All Orders (Plenum, 1991).

G. N. Watson, Theory of Bessel Functions (Cambridge U. Press, 1995), 2nd ed.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).

M. Fox, Optical Properties of Solids (Oxford University Press, 2001).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

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 (12)

Fig. 1
Fig. 1

(a) Scattering cross section σ sca . (b) Scattering resonances in the complex ω a c -plane. We consider a nonabsorbing sphere: ε c ( ω ) has the Drude-type behavior with ε = 1 , ω p a c = 2 π , and γ = 0 while ε h = 1 . Dots (⋅) correspond to poles of S E ( ω ) while plus (+) correspond to poles of S M ( ω ) .

Fig. 2
Fig. 2

(a) Absorption cross section σ abs . (b) Scattering resonances in the complex ω a c -plane. We consider an absorbing sphere: ε c ( ω ) has the Drude-type behavior with ε = 1 , ω p a c = 2 π , and γ = 1 100 while ε h = 1 . Dots (⋅) correspond to poles of S E ( ω ) while plus (+) correspond to poles of S M ( ω ) .

Fig. 3
Fig. 3

(a) Scattering cross section σ sca . (b) Scattering resonances in the complex ω a c -plane. We consider a nonabsorbing sphere: ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , ω L a c = 3 π , and γ = 0 while ε h = 1 . Dots (⋅) correspond to poles of S E ( ω ) while plus (+) correspond to poles of S M ( ω ) .

Fig. 4
Fig. 4

(a) Absorption cross section σ abs . (b) Scattering resonances in the complex ω a c -plane. We consider an absorbing sphere: ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , ω L a c = 3 π , and γ = 1 100 while ε h = 1 . Dots (⋅) correspond to poles of S E ( ω ) while plus (+) correspond to poles of S M ( ω ) .

Fig. 5
Fig. 5

Regge poles in the complex angular momentum plane. ε c ( ω ) has the Drude-type behavior with ε = 1 and ω p a c = 2 π while ε h = 1 . The distribution corresponds to ω a c = 4 , and we have ε c ( ω ) < 0 . Dots (⋅) and crosses (×) correspond, respectively, to Regge poles for γ = 0 and for γ = 1 100 .

Fig. 6
Fig. 6

Regge poles in the complex angular momentum plane. ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , and ω L a c = 3 π while ε h = 1 . The distribution corresponds to ω a c = 8.3 , and we have ε c ( ω ) < 0 . Dots (⋅) and crosses (×) correspond, respectively, to Regge poles for γ = 0 and for γ = 1 100 .

Fig. 7
Fig. 7

Regge trajectory for the SP Regge pole: comparison between a nonabsorbing and an absorbing sphere. ε c ( ω ) has the Drude-type behavior with ε = 1 and ω p a c = 2 π while ε h = 1 . As ω a c ω s a c , the real part of the SP Regge pole always increases indefinitely while its imaginary part vanishes for γ = 0 and increases indefinitely for γ 0 .

Fig. 8
Fig. 8

Regge trajectory for the SP Regge pole: comparison between a nonabsorbing and an absorbing sphere. ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , and ω L a c = 3 π while ε h = 1 . As ω a c ω s a c , the real part of the SP Regge pole increases indefinitely while its imaginary part vanishes for γ = 0 and increases indefinitely for γ 0 .

Fig. 9
Fig. 9

Regge trajectory for the SP Regge pole: comparison between exact and asymptotic theories. ε c ( ω ) has the Drude-type behavior with ε = 1 , ω p a c = 2 π , and γ = 0 while ε h = 1 .

Fig. 10
Fig. 10

Regge trajectory for the SP Regge pole: comparison between exact and asymptotic theories. ε c ( ω ) has the Drude-type behavior with ε = 1 , ω p a c = 2 π , and γ = 1 100 while ε h = 1 .

Fig. 11
Fig. 11

Regge trajectory for the SP Regge pole: comparison between exact and asymptotic theories. ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , ω L a c = 3 π , and γ = 0 while ε h = 1 .

Fig. 12
Fig. 12

Regge trajectory for the SP Regge pole: comparison between exact and asymptotic theories. ε c ( ω ) has the ionic crystal behavior with ε = 2 , ω T a c = 2 π , ω L a c = 3 π , and γ = 1 100 while ε h = 1 .

Tables (4)

Tables Icon

Table 1 First Complex Frequencies of RSPMs (TM Polarization) a

Tables Icon

Table 2 First Complex Frequencies of RSPMs (TM Polarization) a

Tables Icon

Table 3 Some Complex Frequencies of RSPMs (TM Polarization) a

Tables Icon

Table 4 Some Complex Frequencies of RSPMs (TM Polarization) a

Equations (49)

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

k I ( ω ) = ( ω c ) ε h and k II ( ω ) = ( ω c ) ε c ( ω )
ε c ( ω ) = ε ( 1 ω p 2 ω 2 + i γ ω p ω ) ,
ε c ( ω ) = ε ( ω L 2 ω 2 i γ ω T ω ω T 2 ω 2 i γ ω T ω ) .
ε c ( ω ) = ε c ( ω ) + i ε c ( ω )
ε c ( ω ) = ε [ 1 ω p 2 ω 2 + ( γ ω p ) 2 ] ,
ε c ( ω ) = ε [ γ ω p 2 ( ω p ω ) ω 2 + ( γ ω p ) 2 ]
ε c ( ω ) = ε [ ( ω L 2 ω 2 ) ( ω T 2 ω 2 ) + ( γ ω T ω ) 2 ( ω T 2 ω 2 ) 2 + ( γ ω T ω ) 2 ] ,
ε c ( ω ) = ε [ γ ω T ω ( ω L 2 ω T 2 ) ( ω T 2 ω 2 ) 2 + ( γ ω T ω ) 2 ]
S l E ( ω ) = 1 2 a l E ( ω )
a l E ( ω ) = C l E ( ω ) D l E ( ω ) ,
C l E ( ω ) = k II ( ω ) ψ l [ k II ( ω ) a ] ψ l [ k I ( ω ) a ] k I ( ω ) ψ l [ k I ( ω ) a ] ψ l [ k II ( ω ) a ] ,
D l E ( ω ) = k II ( ω ) ψ l [ k II ( ω ) a ] ζ l ( 1 ) [ k I ( ω ) a ] k I ( ω ) ζ l ( 1 ) [ k I ( ω ) a ] ψ l [ k II ( ω ) a ] ,
S l M ( ω ) = 1 2 a l M ( ω )
a l M ( ω ) = C l M ( ω ) D l M ( ω ) ,
C l M ( ω ) = k II ( ω ) ψ l [ k I ( ω ) a ] ψ l [ k II ( ω ) a ] k I ( ω ) ψ l [ k II ( ω ) a ] ψ l [ k I ( ω ) a ] ,
D l M ( ω ) = k II ( ω ) ζ l ( 1 ) [ k I ( ω ) a ] ψ l [ k II ( ω ) a ] k I ( ω ) ψ l [ k II ( ω ) a ] ζ l ( 1 ) [ k I ( ω ) a ] .
σ sca ( ω ) = 2 π [ k I ( ω ) ] 2 l = 1 ( 2 l + 1 ) [ a l E ( ω ) 2 + a l M ( ω ) 2 ]
σ abs ( ω ) = 2 π [ k I ( ω ) ] 2 l = 1 ( 2 l + 1 ) { [ Re a l E ( ω ) a l E ( ω ) 2 ] + [ Re a l M ( ω ) a l M ( ω ) 2 ] } .
D l E , M ( ω ) = 0 for l = 1 , 2 , 3 ,
Γ l p 2 ω ω l p ( 0 ) + i Γ l p 2 .
D λ 1 2 E , M ( ω ) = 0 for ω > 0 .
ε c ( ω s ) + ε h = 0 .
ω s = ω s + i ω s
ε c ( ω s ) + ε h = 0
ω s = ε c ( ω ) d Re ε c ( ω ) d ω ω = ω s .
ω s ω p 1 + ε h ε ,
ω s γ ω p 2 .
ω s ω L 2 + ( ε h ε ) ω T 2 1 + ε h ε ,
ω s γ ω T 2 .
k SP ( ω ) = Re λ SP ( ω ) a
v p = ω a Re λ SP ( ω ) and v g = d ω a d Re λ SP ( ω ) ,
Re λ SP ( ω l SP ( 0 ) ) = l + 1 2 l = 1 , 2 , ,
Γ l SP 2 = Im λ SP ( ω ) ( d Re λ SP ( ω ) d ω ) ( d Re λ SP ( ω ) d ω ) 2 + ( d Im λ SP ( ω ) d ω ) 2 ω = ω l SP ( 0 )
Γ l SP 2 = Im λ SP ( ω ) d Re λ SP ( ω ) d ω ω = ω l SP ( 0 )
ε c ( ω ) ε h ζ λ SP 1 2 ( 1 ) ( ε h a ω c ) ζ λ SP 1 2 ( 1 ) ( ε h a ω c ) = ψ λ SP 1 2 ( ε c ( ω ) a ω c ) ψ λ SP 1 2 ( ε c ( ω ) a ω c ) .
j λ ( z ) = π 2 z J λ + 1 2 ( z ) and h λ ( 1 ) ( z ) = π 2 z H λ + 1 2 ( 1 ) ( z ) ,
1 ε h H λ SP ( 1 ) ( ε h ω a c ) H λ SP ( 1 ) ( ε h ω a c ) + 1 2 ε h ( c ω a ) = 1 ε c ( ω ) I λ SP ( ε c ( ω ) ω a c ) I λ SP ( ε c ( ω ) ω a c ) + 1 2 ε c ( ω ) ( c ω a ) .
1 ε c ( ω ) I λ SP ( ε c ( ω ) ω a c ) I λ SP ( ε c ( ω ) ω a c ) [ λ SP 2 ε c ( ω ) ( ω a c ) 2 ] 1 2 ε c ( ω ) ( ω a c ) .
1 ε h H λ SP ( 1 ) ( ε h ω a c ) H λ SP ( 1 ) ( ε h ω a c ) [ λ SP 2 ε h ( ω a c ) 2 ] 1 2 ε h ( ω a c ) × ( 1 i e 2 α ( λ SP , ε h ω a c ) )
α ( λ , z ) = ( λ 2 z 2 ) 1 2 λ ln ( λ + ( λ 2 z 2 ) 1 2 z ) .
Re λ SP ( ω ) ( ω a c ) ε h ε c ( ω ) ε h + ε c ( ω ) ( 1 + 1 2 [ ε h + ε c ( ω ) ] ( c ω a ) ) ,
Im λ SP ( ω ) = Im 1 λ SP ( ω ) + Im 2 λ SP ( ω )
Im 1 λ SP ( ω ) [ ε c 2 ( ω ) ε c 2 ( ω ) ε h 2 ] [ Re λ SP ( ω ) ] 2 ε h ( ω a c ) 2 Re λ SP ( ω ) [ 1 ε h ε c ( ω ) 2 [ ε h + ε c ( ω ) ] ( c ω a ) ] × exp { 2 α [ Re λ SP ( ω ) , ε h ω a c ] } ,
Im 2 λ SP ( ω ) ( ω a c ) ε h ε c ( ω ) ε h + ε c ( ω ) ε h ε c ( ω ) 2 ε c ( ω ) [ ε h + ε c ( ω ) ] [ 1 + 1 2 [ ε h + ε c ( ω ) ] ( c ω a ) ] .
k SP ( ω ) ( ω c ) ε h ε c ( ω ) ε h + ε c ( ω ) × [ 1 + 1 2 [ ε h + ε c ( ω ) ] ( c ω a ) ] .
Re λ SP ( ω ) ( ω a c ) ε h ε c ( ω ) ε h + ε c ( ω ) ,
Im λ SP ( ω ) = Im 1 λ SP ( ω ) + Im 2 λ SP ( ω )
Im 1 λ SP ( ω ) [ ε c 2 ( ω ) ε c 2 ( ω ) ε h 2 ] × [ Re λ SP ( ω ) ] 2 ε h ( ω a c ) 2 Re λ SP ( ω ) × exp { 2 α [ Re λ SP ( ω ) , ε h ω a c ] } ,
Im 2 λ SP ( ω ) ( ω a c ) ε h ε c ( ω ) ε h + ε c ( ω ) ε h ε c ( ω ) 2 ε c ( ω ) [ ε h + ε c ( ω ) ] .

Metrics