Abstract

The Bloch mode spectrum of surface plasmon polaritons (SPPs) on a finite thickness metal film has been analyzed in the regimes of weak and strong coupling between SPP modes on the opposite film interfaces. The SPP mode dispersion and associated field distributions have been studied. The results have been applied to the description of the light transmission through thick and thin periodically structured metal films at oblique incidence. In contrast to normal incidence, all SPP Bloch modes on a grating structure participate in the resonant photon tunnelling leading to the transmission enhancement. However, at the angle of incidence corresponding to the crossing of different symmetry film SPP Bloch modes, the far-field transmission is suppressed despite the enhanced near-field transmission. The combined SPP mode consisting of the two film SPPs having different symmetries that is achieved at the crossing frequency exhibits no radiative losses on a structured surface.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A.V. Zayats and I.I. Smolyaninov, ???Near-field photonics: surface plasmons polaritons and localized surface plasmons,??? J. Opt. A: Pure Appl. Opt. 5, S16???S50 (2003).
    [CrossRef]
  2. S.I. Bozhevolnyi, J. Erland, K. Leosson, P.M.W. Skovgaard, and J.M. Hvam, ???Waveguiding in surface Plasmon polariton band gap structures,??? Phys. Rev. Lett. 86, 3008???3011 (2001).
    [CrossRef] [PubMed]
  3. W.L. Barnes, T.W. Preist, S.C. Kitson, and J.R. Sambles, ???Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,??? Phys. Rev. B 54, 6227???6244 (1996).
    [CrossRef]
  4. M. Kretschmann and A.A. Maradudin, ???Band structures of two-dimensional surface-plasmon polaritonic crystals,??? Phys. Rev. B 66, 245408 (2002).
    [CrossRef]
  5. I.I. Smolyaninov, A.V. Zayats, A. Stanishevsky, and C.C. Davis, ???Optical control of photon tunneling through an array of nanometer scale cylindrical channels,??? Phys. Rev. B 66, 205414 (2002).
    [CrossRef]
  6. S.A. Darmanyan and A.V. Zayats, ???Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,??? Phys. Rev. B 67, 035424 (2003).
    [CrossRef]
  7. H. Raether, Surface Plasmons, Springer-Verlag, Berlin, 1988.
  8. T.W. Ebbesen, J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, ???Extraordinary optical transmission through subwavelength hole arrays,??? Nature (London) 391, 667???669 (1998).
    [CrossRef]
  9. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, ???Surface plasmons enhance optical transmission through sub-wavelength holes,??? Phys. Rev. B 58, 6779???6782 (1998).
    [CrossRef]
  10. T.J. Kim, T. Thio, T.W. Ebbesen, D.E. Grupp, and H.J. Lezec, ???Control of optical transmission through metals perforated with subwavelenth holes arrays,??? Opt. Lett. 24, 256???258 (1999).
    [CrossRef]
  11. L. Salomon, F. Grillot, A.V. Zayats, F. de Fornel, ???Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,??? Phys. Rev. Lett. 86, 1110???1113 (2001).
    [CrossRef] [PubMed]
  12. L. Martin-Moreno, F.J. Gar??ýa-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]
  13. U. Schröter and D. Heitmann, ???Surface-plasmon-enhanced transmission through metallic gratings,??? Phys. Rev. B 58, 15419???15422 (1998).
    [CrossRef]
  14. J.A. Porto, F.J. Gar??ýa-Vidal, and J.B. Pendry, ???Transmission resonances on metallic gratings with very narrow slits,??? Phys. Rev. Lett. 83, 2845???2848 (1999).
    [CrossRef]
  15. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, ???Theory of light transmission through subwavelength periodic hole arrays,??? Phys. Rev. B 62, 16100???16108 (2000).
    [CrossRef]
  16. A.V. Zayats, L. Salomon, and F. de Fornel, ???How light gets through periodically nanostructured metal films: a role of surface polaritonic crystals,??? J. Microsc. 210, 344???349 (2003).
    [CrossRef] [PubMed]
  17. N. Bonod, S. Enoch, P.F. Li, E. Popov, and M. Nevière, ???Resonant optical transmission through thin metallic films with and without holes,??? Opt. Express 11, 482???490 (2003) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-482">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-5-482</a>.
    [CrossRef] [PubMed]
  18. A.M. Dykhne, A.K. Sarychev, and V.M. Shalaev, ???Resonant transmittance through metal films with fabricated and light-induced modulation,??? Phys. Rev. B 67, 195402 (2003).
    [CrossRef]
  19. D. Gérard, L. Salomon, F. de Fornel, and A.V. Zayats, ???Ridge-enhanced optical transmission through a continuous metal film,??? Phys. Rev. B 69, 113405 (2004).
    [CrossRef]
  20. S.A. Darmanyan, M. Nevière, and A.V. Zayats, ???Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,??? Phys. Rev. B 70, 15AUG (2004).
    [CrossRef]
  21. M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design, Marcel Dekker, New-York, 2003.
  22. E. Popov, M. Nevière, ???Differential theory for diffraction gratings: a new formulation for TM polarization with rapid convergence,??? Opt. Lett. 25, 598???600 (2000).
    [CrossRef]
  23. A.V. Krasavin, N.I. Zheludev, and A.V. Zayats, ???High-contrast modulation of light with light by control of surface plasmon-polariton wave coupling,??? to be published.

J. Microsc.

A.V. Zayats, L. Salomon, and F. de Fornel, ???How light gets through periodically nanostructured metal films: a role of surface polaritonic crystals,??? J. Microsc. 210, 344???349 (2003).
[CrossRef] [PubMed]

J. Opt. A: Pure Appl. Opt.

A.V. Zayats and I.I. Smolyaninov, ???Near-field photonics: surface plasmons polaritons and localized surface plasmons,??? J. Opt. A: Pure Appl. Opt. 5, S16???S50 (2003).
[CrossRef]

Nature

T.W. Ebbesen, J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, ???Extraordinary optical transmission through subwavelength hole arrays,??? Nature (London) 391, 667???669 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, ???Theory of light transmission through subwavelength periodic hole arrays,??? Phys. Rev. B 62, 16100???16108 (2000).
[CrossRef]

U. Schröter and D. Heitmann, ???Surface-plasmon-enhanced transmission through metallic gratings,??? Phys. Rev. B 58, 15419???15422 (1998).
[CrossRef]

A.M. Dykhne, A.K. Sarychev, and V.M. Shalaev, ???Resonant transmittance through metal films with fabricated and light-induced modulation,??? Phys. Rev. B 67, 195402 (2003).
[CrossRef]

D. Gérard, L. Salomon, F. de Fornel, and A.V. Zayats, ???Ridge-enhanced optical transmission through a continuous metal film,??? Phys. Rev. B 69, 113405 (2004).
[CrossRef]

S.A. Darmanyan, M. Nevière, and A.V. Zayats, ???Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,??? Phys. Rev. B 70, 15AUG (2004).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, ???Surface plasmons enhance optical transmission through sub-wavelength holes,??? Phys. Rev. B 58, 6779???6782 (1998).
[CrossRef]

W.L. Barnes, T.W. Preist, S.C. Kitson, and J.R. Sambles, ???Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,??? Phys. Rev. B 54, 6227???6244 (1996).
[CrossRef]

M. Kretschmann and A.A. Maradudin, ???Band structures of two-dimensional surface-plasmon polaritonic crystals,??? Phys. Rev. B 66, 245408 (2002).
[CrossRef]

I.I. Smolyaninov, A.V. Zayats, A. Stanishevsky, and C.C. Davis, ???Optical control of photon tunneling through an array of nanometer scale cylindrical channels,??? Phys. Rev. B 66, 205414 (2002).
[CrossRef]

S.A. Darmanyan and A.V. Zayats, ???Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,??? Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Phys. Rev. Lett.

S.I. Bozhevolnyi, J. Erland, K. Leosson, P.M.W. Skovgaard, and J.M. Hvam, ???Waveguiding in surface Plasmon polariton band gap structures,??? Phys. Rev. Lett. 86, 3008???3011 (2001).
[CrossRef] [PubMed]

J.A. Porto, F.J. Gar??ýa-Vidal, and J.B. Pendry, ???Transmission resonances on metallic gratings with very narrow slits,??? Phys. Rev. Lett. 83, 2845???2848 (1999).
[CrossRef]

L. Salomon, F. Grillot, A.V. Zayats, F. de Fornel, ???Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,??? Phys. Rev. Lett. 86, 1110???1113 (2001).
[CrossRef] [PubMed]

L. Martin-Moreno, F.J. Gar??ýa-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]

Other

M. Nevière and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design, Marcel Dekker, New-York, 2003.

H. Raether, Surface Plasmons, Springer-Verlag, Berlin, 1988.

A.V. Krasavin, N.I. Zheludev, and A.V. Zayats, ???High-contrast modulation of light with light by control of surface plasmon-polariton wave coupling,??? to be published.

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 (10)

Fig. 1.
Fig. 1.

Schematic of a nanostructured film.

Fig. 2.
Fig. 2.

Schematics of the band-gap structure near the second SPP band-gap in the case of weak (a) and strong (b) coupling regimes: (f +, f -) film SPP Bloch modes, (g +,g -) SPP modes in the different Brillouin zones.

Fig. 3.
Fig. 3.

(Colour) Reflection (a), absorption (b), and transmission (c) spectra of the nanostructured silver film (H=100 nm) at different angles of incidence: (black) θ=0°, (blue) θ=2°, (red) θ=4°. The structure consists of the silver ridges (h=20 nm, d=250 nm and D=500 nm) on both film interfaces.

Fig. 4.
Fig. 4.

Dispersion of the SPP Bloch modes in the vicinity of the second band-gap on a periodic structure in a weak coupling regime. The parametres of the structure are the same as in Fig. 3

Fig. 5.
Fig. 5.

(Colour) The magnetic field Hz distribution in the near-field region of the metallic structure at the wavelengths corresponding to (a) lower (λ=564 nm) and (b) upper (λ=506 nm) branches of the SPP Bloch modes around the second band-gap in a weak-coupling regime. Angle of incidence is θ=4°. The parametres of the film are the same as in Fig. 3. Geometry of the film is also shown.

Fig. 6.
Fig. 6.

(Colour) Reflection (a), absorption (b), and transmission (c) spectra of the nanostructured silver film (H=40 nm) at different angles of incidence: (black) θ=0°, (blue) θ=1°, (green) θ=2°, (red) θ=4°. The structure consists of the silver ridges (h=20 nm, d=250 nm and D=500 nm) on both film interfaces.

Fig. 7.
Fig. 7.

Dispersion of the SPP Bloch modes in the vicinity of the second band-gap on a periodic structure in a strong coupling regime. The parametres of the structure are the same as in Fig. 6.

Fig. 8.
Fig. 8.

(Colour) (a) The magnetic field Hz distribution in the near-field region of the metallic structure and (b) the intensity distribution of the transmitted field over the structure at the wavelength corresponding to the crossing of the SPP modes of different symmetries in a strong-coupling regime (λ=539 nm, θ=2°). The parametres of the structure are the same as in Fig. 6.

Fig. 9.
Fig. 9.

(Colour) The magnetic field Hz (a,b) and electric field Ex (c,d) distributions in the near-field of the metallic structure at the wavelengths corresponding to (a,c) f - g + (λ=527 nm) and (b,d) f + g + (λ=552 nm) SPP Bloch modes at around the second-band gap in a strong-coupling regime. Angle of incidence is θ=0°. The parametres of the structure are the same as in Fig. 6. Geometry of the film is also shown.

Fig. 10.
Fig. 10.

(Colour) The magnetic field Hz distribution in the near-field region of the metallic structure at the wavelengths corresponding to (a) f - g - (λ=493 nm), (b) f - g + (λ=555 nm), (c) f + g - (λ=527 nm), and (d) f + g + (λ=579 nm) film SPP Bloch modes around the respective second-band gaps in a strong-coupling regime. Angle of incidence is θ=4°. The parametres of the structure are the same as in Fig. 6. Geometry of the film is also shown.

Metrics