Abstract

One of the keys to understanding the extraordinary optical transmission in a subwavelength metal slit is in what field mode is excited. We find that, compared to the usual surface plasmon polariton (SPP), the wavelength of the excited mode is squeezed and will become smaller as the slit width does. This mode is called an in-slit SPP. We show how the wavelength of this mode can be solved by a formula and clearly analyze the physical reason for the wavelength squeeze. Furthermore, the similarities and differences of the wavelength squeeze between normal incidence and oblique incidence are pointed out.

© 2009 Optical Society of America

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References

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
    [CrossRef]
  2. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779-6782 (1998).
    [CrossRef]
  3. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
    [CrossRef] [PubMed]
  4. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
    [CrossRef]
  5. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608-1615 (2006).
    [CrossRef]
  6. U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419-15421 (1998).
    [CrossRef]
  7. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  8. P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
    [CrossRef]
  9. 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]
  10. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martn-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29, 2500-2502 (2004).
    [CrossRef] [PubMed]
  11. Y. Poujet, J. Salvi, and F. I. Baida, “90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays,” Opt. Lett. 32, 2942-2944 (2007).
    [CrossRef] [PubMed]
  12. A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
    [CrossRef]
  13. Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
    [CrossRef]
  14. S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
    [CrossRef]
  15. The commercially available software developed by Rsoft Design Group http://www.rsoftdesign.com is used for the numerical simulations.
  16. Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
    [CrossRef]
  17. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  18. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  19. In fact, the physical meaning of Rekz/Imkz>25 is unclear unless both the real and imaginary part of kz are known. However, taking into account Eq. , among the solutions, this condition means the corresponding mode can propagate at least 50λ0 in the slit.
  20. J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
    [CrossRef]

2009 (1)

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

2008 (1)

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

2007 (1)

2006 (2)

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

2005 (1)

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

2004 (2)

J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martn-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29, 2500-2502 (2004).
[CrossRef] [PubMed]

2001 (1)

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

2000 (3)

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

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]

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
[CrossRef]

1999 (1)

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

1998 (3)

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419-15421 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

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

1972 (1)

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

Astilean, S.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Baida, F. I.

Beruete, M.

Bravo-Abad, J.

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martn-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29, 2500-2502 (2004).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Campillo, I.

Christy, R. W.

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

Dolado, J. S.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

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

Enoch, S.

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]

Garcia-Vidal, F. J.

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

García-Vidal, F. J.

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martn-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29, 2500-2502 (2004).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Ghaemi, H. F.

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

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Grupp, D. E.

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

Gu, B. Y.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

Heitmann, D.

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419-15421 (1998).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
[CrossRef]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Johnson, P. B.

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

Lalanne, P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Lalanne, Ph.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Lan, S.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

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

Lockyear, M. J.

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
[CrossRef]

Martín-Moreno, L.

J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Martn-Moreno, L.

Möller, K. D.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

Nevière, M.

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]

Palamaru, M.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Pendry, J. B.

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

Popov, E.

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]

Porto, J. A.

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

Poujet, Y.

Raether, H.

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

Reinisch, R.

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]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Approximate model for surface-plasmon generation at slit apertures,” J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Salvi, J.

Sambles, J. R.

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
[CrossRef]

Schröter, U.

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419-15421 (1998).
[CrossRef]

Sorolla, M.

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

Thio, T.

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

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Wang, H. Y.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Zhao, L. M.

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

Zhou, Y. S.

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

Europhys. Lett. (1)

Y. S. Zhou, B. Y. Gu, H. Y. Wang, and S. Lan, “Multi-reflection process of extraordinary optical transmission in a single subwavelength metal slit,” Europhys. Lett. 85, 24005 (2009).
[CrossRef]

J. Appl. Phys. (1)

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities,” J. Appl. Phys. 99, 124903 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48-51 (2000).
[CrossRef]

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

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998).
[CrossRef]

Opt. Commun. (1)

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (5)

Y. S. Zhou, B. Y. Gu, S. Lan, and L. M. Zhao, “Time-domain analysis of mechanism of plasmon-assisted extraordinary optical transmission,” Phys. Rev. B 78, 081404(R) (2008).
[CrossRef]

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

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

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, 15419-15421 (1998).
[CrossRef]

Phys. Rev. E (1)

J. Bravo-Abad, L. Martín-Moreno and F. J. García-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

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

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Other (3)

The commercially available software developed by Rsoft Design Group http://www.rsoftdesign.com is used for the numerical simulations.

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

In fact, the physical meaning of Rekz/Imkz>25 is unclear unless both the real and imaginary part of kz are known. However, taking into account Eq. , among the solutions, this condition means the corresponding mode can propagate at least 50λ0 in the slit.

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Figures (6)

Fig. 1
Fig. 1

Schematic plot of the structure under study. An incident plane wave with wavelength λ 0 = 1 μ m normally illuminates the slit from below. As the slit width is W = 0.1 μ m and film thickness is D = 1.8 μ m , the distribution of magnetic field H y is depicted. The space inside the slit can be divided into three regions, one which is named as an effective dielectric region (EDR) and sandwiched by two scattering regions. The right part shows the value of H y at x = W 2 in the EDR for three D values.

Fig. 2
Fig. 2

The wavelength of in-slit SPP mode when λ 0 = 1 μ m as a function of slit width W. Solid curve: analytical solution from Eq. (2). Crosses: numerical results in a slit by FDTD simulation for normal incidence ( θ = 0 ° ) . Circles: simulated results with θ = 30 ° . Triangles: simulated results with θ = 60 ° .

Fig. 3
Fig. 3

Simulated normalized transmittances of a TM wave as a function of the slit depth D for four slit widths. (a) θ = 30 ° . (b) θ = 60 ° .

Fig. 4
Fig. 4

Wave vectors of the in-slit SPP mode as a function of slit width W for λ 0 = 1 μ m . Since the figures have different orders of magnitude, the curves are plotted by logarithm with base 10.

Fig. 5
Fig. 5

A comparison of H y profile in a subwavelength slit. The basic parameters for simulation are θ = 30 ° , W = 0.6 μ m , and D = 6 μ m . (a) Simulated result. (b) The linear combination of the lowest two modes solved from Eq. (2): H y ( 0 ) + 0.65 e i 0.2 π H y ( 1 ) .

Fig. 6
Fig. 6

Simulated normalized transmittances of a normal incident TM wave as a function of the slit depth D for five slit widths.

Tables (1)

Tables Icon

Table 1 The Eigenvalues of k z in an Infinitely Long Metal Slit

Equations (2)

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λ SPP = λ 0 ( ε 1 + ε 2 ) ε 1 ε 2 ,
( k x 1 ε 1 + i k x 2 ε 2 tan k x 2 W 2 ) ( k x 2 ε 2 + i k x 1 ε 1 tan k x 2 W 2 ) = 0 ,

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