Abstract

Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma by using a general, unifying procedure based on the equation of motion of the polarization and the electromagnetic potentials. Known results are reproduced in a much more direct manner, and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in this plasma is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved, and the reflected and refracted fields are computed, as well as the reflection coefficient. Generalized Fresnel relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon–polariton modes are identified. As is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).

© 2009 Optical Society of America

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References

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  1. R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
    [CrossRef]
  2. E. A. Stern and R. A. Ferrell, “Surface plasma oscillations of a degenerate electron gas,” Phys. Rev. 120, 130-136 (1960).
    [CrossRef]
  3. A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14, 1347-1361 (1976).
    [CrossRef]
  4. S. DasSarma and J. J. Quinn, “Hydrodynamic model of linear response for a jellium surface: non-retarded limit,” Phys. Rev. B 20, 4872-4882 (1979).
    [CrossRef]
  5. N. E. Glass and A. A. Maradudin, “Surface plasmons on a large-amplitude grating,” Phys. Rev. B 24, 595-602 (1981).
    [CrossRef]
  6. S. DasSarma and J. J. Quinn, “Collective excitations in semiconductor superlattices,” Phys. Rev. B 25, 7603-7618 (1982).
    [CrossRef]
  7. W. L. Schaich and J. F. Dobson, “Excitation modes of neutral jellium slabs,” Phys. Rev. B 49, 14700-14707 (1994).
    [CrossRef]
  8. G. Link and R. v. Baltz, “Hydrodynamic description of surface plasmons: Nonexistence of the unrestricted half-space solution,” Phys. Rev. B 60, 16157-16163 (1999).
    [CrossRef]
  9. P. A. Fedders, “Some surface effects in an electron gas,” Phys. Rev. 153, 438-443 (1967).
    [CrossRef]
  10. P. A. Fedders, “Indirect coupling of photons to the surface plasmons,” Phys. Rev. 165, 580-587 (1968).
    [CrossRef]
  11. K. L. Kliewer and R. Fuchs, “Collective electronic motion in a metallic slab,” Phys. Rev. 153, 498-512 (1967).
    [CrossRef]
  12. A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B 2, 835-850 (1970).
    [CrossRef]
  13. A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B 7, 2787-2810 (1973).
    [CrossRef]
  14. G. S. Agarwal, “New method in the theory of surface polaritons,” Phys. Rev. B 8, 4768-4779 (1973).
    [CrossRef]
  15. P. J. Feibelman, “Microscopic calculation of the electromagnetic fields in refraction at the jellium-vacuum interface,” Phys. Rev. B 12, 1319-1336 (1975).
    [CrossRef]
  16. P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr. 17, 535-542 (1978).
    [CrossRef]
  17. F. J. Garcia-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163-1166 (1996).
    [CrossRef] [PubMed]
  18. K. Henneberger, “Additional boundary conditions: An historical mistake,” Phys. Rev. Lett. 80, 2889-2892 (1998).
    [CrossRef]
  19. W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
    [CrossRef]
  20. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
    [CrossRef] [PubMed]
  21. F. J. Garcia de Abajo, “Colloquium: Light scattering by particles and hole arrays,” Rev. Mod. Phys. 79, 1267-1290 (2007).
    [CrossRef]
  22. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  23. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  24. M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).
    [CrossRef]
  25. S. Raimes, “The theory of plasma oscillations in metals,” Rep. Prog. Phys. 20, 1-37 (1957).
    [CrossRef]
  26. P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, 1973).
  27. D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817-926 (1974)
    [CrossRef]
  28. G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys. 42, 963-1016 (1979).
    [CrossRef]
  29. Bo E. Sernelius, Surface Modes in Physics (Wiley, 2001).
    [CrossRef]
  30. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000), pp. 714-715, 6.677; 1,2.
  31. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  32. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  33. L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media (Butterworth-Heinemann, 2004).

2007 (1)

F. J. Garcia de Abajo, “Colloquium: Light scattering by particles and hole arrays,” Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

2001 (1)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

2000 (1)

W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[CrossRef]

1999 (1)

G. Link and R. v. Baltz, “Hydrodynamic description of surface plasmons: Nonexistence of the unrestricted half-space solution,” Phys. Rev. B 60, 16157-16163 (1999).
[CrossRef]

1998 (1)

K. Henneberger, “Additional boundary conditions: An historical mistake,” Phys. Rev. Lett. 80, 2889-2892 (1998).
[CrossRef]

1996 (1)

F. J. Garcia-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

1994 (1)

W. L. Schaich and J. F. Dobson, “Excitation modes of neutral jellium slabs,” Phys. Rev. B 49, 14700-14707 (1994).
[CrossRef]

1982 (1)

S. DasSarma and J. J. Quinn, “Collective excitations in semiconductor superlattices,” Phys. Rev. B 25, 7603-7618 (1982).
[CrossRef]

1981 (1)

N. E. Glass and A. A. Maradudin, “Surface plasmons on a large-amplitude grating,” Phys. Rev. B 24, 595-602 (1981).
[CrossRef]

1979 (2)

S. DasSarma and J. J. Quinn, “Hydrodynamic model of linear response for a jellium surface: non-retarded limit,” Phys. Rev. B 20, 4872-4882 (1979).
[CrossRef]

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys. 42, 963-1016 (1979).
[CrossRef]

1978 (1)

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr. 17, 535-542 (1978).
[CrossRef]

1976 (1)

A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14, 1347-1361 (1976).
[CrossRef]

1975 (1)

P. J. Feibelman, “Microscopic calculation of the electromagnetic fields in refraction at the jellium-vacuum interface,” Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

1974 (1)

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817-926 (1974)
[CrossRef]

1973 (2)

A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B 7, 2787-2810 (1973).
[CrossRef]

G. S. Agarwal, “New method in the theory of surface polaritons,” Phys. Rev. B 8, 4768-4779 (1973).
[CrossRef]

1970 (1)

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B 2, 835-850 (1970).
[CrossRef]

1968 (1)

P. A. Fedders, “Indirect coupling of photons to the surface plasmons,” Phys. Rev. 165, 580-587 (1968).
[CrossRef]

1967 (2)

K. L. Kliewer and R. Fuchs, “Collective electronic motion in a metallic slab,” Phys. Rev. 153, 498-512 (1967).
[CrossRef]

P. A. Fedders, “Some surface effects in an electron gas,” Phys. Rev. 153, 438-443 (1967).
[CrossRef]

1960 (1)

E. A. Stern and R. A. Ferrell, “Surface plasma oscillations of a degenerate electron gas,” Phys. Rev. 120, 130-136 (1960).
[CrossRef]

1957 (2)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
[CrossRef]

S. Raimes, “The theory of plasma oscillations in metals,” Rep. Prog. Phys. 20, 1-37 (1957).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “New method in the theory of surface polaritons,” Phys. Rev. B 8, 4768-4779 (1973).
[CrossRef]

Apell, P.

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr. 17, 535-542 (1978).
[CrossRef]

Baltz, R. v.

G. Link and R. v. Baltz, “Hydrodynamic description of surface plasmons: Nonexistence of the unrestricted half-space solution,” Phys. Rev. B 60, 16157-16163 (1999).
[CrossRef]

Barton, G.

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys. 42, 963-1016 (1979).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Brongersma, M. L.

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).
[CrossRef]

Burstein, E.

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817-926 (1974)
[CrossRef]

DasSarma, S.

S. DasSarma and J. J. Quinn, “Collective excitations in semiconductor superlattices,” Phys. Rev. B 25, 7603-7618 (1982).
[CrossRef]

S. DasSarma and J. J. Quinn, “Hydrodynamic model of linear response for a jellium surface: non-retarded limit,” Phys. Rev. B 20, 4872-4882 (1979).
[CrossRef]

Dobson, J. F.

W. L. Schaich and J. F. Dobson, “Excitation modes of neutral jellium slabs,” Phys. Rev. B 49, 14700-14707 (1994).
[CrossRef]

Ebbesen, T. W.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Eguiluz, A.

A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14, 1347-1361 (1976).
[CrossRef]

Fedders, P. A.

P. A. Fedders, “Indirect coupling of photons to the surface plasmons,” Phys. Rev. 165, 580-587 (1968).
[CrossRef]

P. A. Fedders, “Some surface effects in an electron gas,” Phys. Rev. 153, 438-443 (1967).
[CrossRef]

Feibelman, P. J.

P. J. Feibelman, “Microscopic calculation of the electromagnetic fields in refraction at the jellium-vacuum interface,” Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

Ferrell, R. A.

E. A. Stern and R. A. Ferrell, “Surface plasma oscillations of a degenerate electron gas,” Phys. Rev. 120, 130-136 (1960).
[CrossRef]

Fuchs, R.

K. L. Kliewer and R. Fuchs, “Collective electronic motion in a metallic slab,” Phys. Rev. 153, 498-512 (1967).
[CrossRef]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, “Colloquium: Light scattering by particles and hole arrays,” Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

F. J. Garcia-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

Glass, N. E.

N. E. Glass and A. A. Maradudin, “Surface plasmons on a large-amplitude grating,” Phys. Rev. B 24, 595-602 (1981).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000), pp. 714-715, 6.677; 1,2.

Harrison, M. J.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B 2, 835-850 (1970).
[CrossRef]

Henneberger, K.

K. Henneberger, “Additional boundary conditions: An historical mistake,” Phys. Rev. Lett. 80, 2889-2892 (1998).
[CrossRef]

Kik, P. G.

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).
[CrossRef]

Kliewer, K. L.

K. L. Kliewer and R. Fuchs, “Collective electronic motion in a metallic slab,” Phys. Rev. 153, 498-512 (1967).
[CrossRef]

Landau, L.

L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media (Butterworth-Heinemann, 2004).

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Lifshitz, E.

L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media (Butterworth-Heinemann, 2004).

Link, G.

G. Link and R. v. Baltz, “Hydrodynamic description of surface plasmons: Nonexistence of the unrestricted half-space solution,” Phys. Rev. B 60, 16157-16163 (1999).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maradudin, A. A.

N. E. Glass and A. A. Maradudin, “Surface plasmons on a large-amplitude grating,” Phys. Rev. B 24, 595-602 (1981).
[CrossRef]

A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B 7, 2787-2810 (1973).
[CrossRef]

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Melnyk, A. R.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B 2, 835-850 (1970).
[CrossRef]

Mills, D. L.

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817-926 (1974)
[CrossRef]

A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B 7, 2787-2810 (1973).
[CrossRef]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

F. J. Garcia-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

Platzman, P. M.

P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, 1973).

Preist, T. W.

W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[CrossRef]

Quinn, J. J.

S. DasSarma and J. J. Quinn, “Collective excitations in semiconductor superlattices,” Phys. Rev. B 25, 7603-7618 (1982).
[CrossRef]

S. DasSarma and J. J. Quinn, “Hydrodynamic model of linear response for a jellium surface: non-retarded limit,” Phys. Rev. B 20, 4872-4882 (1979).
[CrossRef]

A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14, 1347-1361 (1976).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Raimes, S.

S. Raimes, “The theory of plasma oscillations in metals,” Rep. Prog. Phys. 20, 1-37 (1957).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000), pp. 714-715, 6.677; 1,2.

Sambles, R. J.

W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[CrossRef]

Schaich, W. L.

W. L. Schaich and J. F. Dobson, “Excitation modes of neutral jellium slabs,” Phys. Rev. B 49, 14700-14707 (1994).
[CrossRef]

Sernelius, Bo E.

Bo E. Sernelius, Surface Modes in Physics (Wiley, 2001).
[CrossRef]

Stern, E. A.

E. A. Stern and R. A. Ferrell, “Surface plasma oscillations of a degenerate electron gas,” Phys. Rev. 120, 130-136 (1960).
[CrossRef]

Stratton, J. A.

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

Tan, W.-C.

W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[CrossRef]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wolff, P. A.

P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, 1973).

Phys. Rev. (5)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874-881 (1957).
[CrossRef]

E. A. Stern and R. A. Ferrell, “Surface plasma oscillations of a degenerate electron gas,” Phys. Rev. 120, 130-136 (1960).
[CrossRef]

P. A. Fedders, “Some surface effects in an electron gas,” Phys. Rev. 153, 438-443 (1967).
[CrossRef]

P. A. Fedders, “Indirect coupling of photons to the surface plasmons,” Phys. Rev. 165, 580-587 (1968).
[CrossRef]

K. L. Kliewer and R. Fuchs, “Collective electronic motion in a metallic slab,” Phys. Rev. 153, 498-512 (1967).
[CrossRef]

Phys. Rev. B (11)

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B 2, 835-850 (1970).
[CrossRef]

A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B 7, 2787-2810 (1973).
[CrossRef]

G. S. Agarwal, “New method in the theory of surface polaritons,” Phys. Rev. B 8, 4768-4779 (1973).
[CrossRef]

P. J. Feibelman, “Microscopic calculation of the electromagnetic fields in refraction at the jellium-vacuum interface,” Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

A. Eguiluz and J. J. Quinn, “Hydrodynamic model for surface plasmons in metals and degenerate semiconductors,” Phys. Rev. B 14, 1347-1361 (1976).
[CrossRef]

S. DasSarma and J. J. Quinn, “Hydrodynamic model of linear response for a jellium surface: non-retarded limit,” Phys. Rev. B 20, 4872-4882 (1979).
[CrossRef]

N. E. Glass and A. A. Maradudin, “Surface plasmons on a large-amplitude grating,” Phys. Rev. B 24, 595-602 (1981).
[CrossRef]

S. DasSarma and J. J. Quinn, “Collective excitations in semiconductor superlattices,” Phys. Rev. B 25, 7603-7618 (1982).
[CrossRef]

W. L. Schaich and J. F. Dobson, “Excitation modes of neutral jellium slabs,” Phys. Rev. B 49, 14700-14707 (1994).
[CrossRef]

G. Link and R. v. Baltz, “Hydrodynamic description of surface plasmons: Nonexistence of the unrestricted half-space solution,” Phys. Rev. B 60, 16157-16163 (1999).
[CrossRef]

W.-C. Tan, T. W. Preist and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134-11138 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

F. J. Garcia-Vidal and J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

K. Henneberger, “Additional boundary conditions: An historical mistake,” Phys. Rev. Lett. 80, 2889-2892 (1998).
[CrossRef]

Phys. Scr. (1)

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr. 17, 535-542 (1978).
[CrossRef]

Rep. Prog. Phys. (3)

S. Raimes, “The theory of plasma oscillations in metals,” Rep. Prog. Phys. 20, 1-37 (1957).
[CrossRef]

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817-926 (1974)
[CrossRef]

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys. 42, 963-1016 (1979).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. Garcia de Abajo, “Colloquium: Light scattering by particles and hole arrays,” Rev. Mod. Phys. 79, 1267-1290 (2007).
[CrossRef]

Other (9)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).
[CrossRef]

P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, 1973).

Bo E. Sernelius, Surface Modes in Physics (Wiley, 2001).
[CrossRef]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 2000), pp. 714-715, 6.677; 1,2.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

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

L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media (Butterworth-Heinemann, 2004).

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Figures (1)

Fig. 1
Fig. 1

Reflection coefficient for a semi-infinite plasma for β = π 6 and various incidence angles α. One can see the shoulder occurring at the transparency edge ω p cos α and the zero occurring at ω 2 = ω p 2 ( 1 tan 2 α ) for α = β = π 6 ( R 2 = 0 , ϕ = 0 ).

Equations (50)

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L = d r [ 1 2 m n u ̇ 2 1 2 d r U ( r r ) δ n ( r ) δ n ( r ) ] + e d r Φ ( r ) δ n ( r ) ,
m u ̈ = n grad d r U ( r r ) div u ( r ) + e grad Φ ,
div u = ( div v + u 3 z ) θ ( z ) + u 3 ( 0 ) δ ( z ) ,
m u ̈ = n e 2 grad d r d z 1 ( r r ) 2 + ( z z ) 2 [ div v ( r . z ) + u 3 ( r , z ) z ] + n e 2 grad d r 1 ( r r ) 2 + z 2 u 3 ( r , 0 ) + e grad Φ
u ( r , z ; t ) = k d ω u ( k , z ; ω ) e i k r e i ω t
1 r 2 + z 2 = k 2 π k e k z e i k r
ω 2 v = 1 2 k ω p 2 0 d z v e k z z + 1 2 k ω p 2 0 d z v z z e k z z i e k m Φ ,
ω 2 v = ω p 2 v 1 2 ω p 2 v 0 e k z i e k m Φ ,
v = i e k ω p 2 m Φ 0 ( ω 2 ω p 2 ) ( 2 ω 2 ω p 2 ) e k z i e k m Φ ω 2 ω p 2 ,
u 3 = e k ω p 2 m Φ 0 ( ω 2 ω p 2 ) ( 2 ω 2 ω p 2 ) e k z e m Φ ω 2 ω p 2 ,
v ( k , z ) = 2 k v 0 ( k ) e k z + κ 2 k 2 κ 2 + k 2 v ( k , κ ) sin κ z ,
T = n m k v ̇ 0 * ( k ) v ̇ 0 ( k ) + n m k κ v ̇ * ( k , κ ) v ̇ ( k , κ ) ,
U = 2 π n 2 e 2 k v 0 * ( k ) v 0 ( k ) + 4 π n 2 e 2 k κ v * ( k , κ ) v ( k , κ ) ,
E ( k , z ; ω ) = i k ω p 4 Φ ( k , 0 ; ω ) ( ω 2 ω p 2 ) ( 2 ω 2 ω p 2 ) e k z i k ω p 2 Φ ( k , z ; ω ) ω 2 ω p 2 ,
E ( k , z ; ω ) = k ω p 4 Φ ( k , 0 ; ω ) ( ω 2 ω p 2 ) ( 2 ω 2 ω p 2 ) e k z ω p 2 Φ ( k , z ; ω ) ω 2 ω p 2 ,
ω 2 u = e m E + e m E 0 e i κ z ,
A ( r , z ; t ) = 1 c d r d z j ( r , z ; t R c ) R
Φ ( r , z ; t ) = d r d z ρ ( r , z ; t R c ) R ,
j = n e u ̇ θ ( z ) e i k r e i ω t
ρ = n e div u = n e ( i k v + u 3 z ) θ ( z ) e i k r e i ω t + n e u 3 ( 0 ) δ ( z ) e i k r e i ω t
z d x J 0 ( k x 2 z 2 ) e i ω x c = i κ e i κ z ,
E 01 = E 0 cos β cos ϕ , E 02 = E 0 cos β sin ϕ ,
E 03 = E 0 sin β .
E 1 = 2 π i n e κ 0 d z v 1 ( z ) e i κ z z 2 π n e k κ 0 d z u 3 ( z ) z e i κ z z ,
E 2 = 2 π i n e ω 2 c 2 κ 0 d z v 2 ( z ) e i κ z z ,
E 3 = 2 π n e k κ 0 d z v 1 ( z ) z e i κ z z 2 π i n e k 2 κ 0 d z u 3 ( z ) e i κ z z + 4 π n e u 3 ,
z 0 d z f ( z ) z e i κ z z = κ 2 0 d z f ( z ) e i κ z z 2 i κ f ( z )
ω 2 v 1 = i ω p 2 κ 2 0 d z v 1 ( z ) e i κ z z ω p 2 k 2 κ 0 d z u 3 ( z ) z e i κ z z + e m E 01 e i κ z ,
ω 2 v 2 = i ω p 2 ω 2 2 c 2 κ 0 d z v 2 ( z ) e i κ z z + e m E 02 e i κ z ,
ω 2 u 3 = ω p 2 k 2 κ 0 d z v 1 ( z ) z e i κ z z i ω p 2 k 2 2 κ 0 d z u 3 ( z ) e i κ z z + ω p 2 u 3 + e m E 03 e i κ z ,
2 z 2 0 d z v 2 ( z ) e i κ z z = κ 2 0 d z v 2 ( z ) e i κ z z + 2 i κ v 2 .
2 v 2 z 2 + ( κ 2 ω p 2 c 2 ) v 2 = 0 .
v 2 = 2 e E 02 m ω p 2 κ ( κ κ ) K 2 e i κ z ,
κ = κ 2 ω p 2 c 2 = 1 c ω 2 cos 2 α ω p 2 .
sin α sin α = 1 1 ω p 2 ω 2 = 1 ε .
ω 2 = c 2 K 2 = ω p 2 + c 2 K 2 ,
κ 2 u 3 = i k v 1 z .
v 1 = 2 e E 01 m ω p 2 κ ( κ κ ) κ κ + k 2 e i κ z
u 3 = 2 e E 03 m ω p 2 κ ( κ κ ) κ κ + k 2 e i κ z .
ω 2 = 2 ω p 2 c 2 k 2 ω p 2 + 2 c 2 k 2 + ω p 4 + 4 c 4 k 4 .
E 1 = E 01 κ κ κ + κ κ κ k 2 κ κ + k 2 e i κ z ,
E 2 = E 02 κ κ κ + κ e i κ z ,
E 3 = E 03 κ κ κ + κ κ κ k 2 κ κ + k 2 e i κ z .
E 2 refl = cos α ε sin 2 α cos α + ε sin 2 α E 02 e i κ z ,
E 2 refr = 2 cos α cos α + ε sin 2 α E 02 e i κ z .
H 2 refl = ε cos α ε sin 2 α ε cos α + ε sin 2 α H 02 e i κ z ,
H 2 refr = 2 ε cos α ε cos α + ε sin 2 α H 02 e i κ z .
R = R 1 cos 2 β sin 2 ϕ + R 2 ( cos 2 β cos 2 ϕ + sin 2 β ) ,
R 1 = ω cos α ω 2 cos 2 α ω p 2 ω cos α + ω 2 cos 2 α ω p 2 2 = cos α ε sin 2 α cos α + ε sin 2 α 2
R 2 = ( ω 2 ω p 2 ) cos α ω ω 2 cos 2 α ω p 2 ( ω 2 ω p 2 ) cos α + ω ω 2 cos 2 α ω p 2 2 = ε cos α ε sin 2 α ε cos α + ε sin 2 α 2 .

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