Abstract

We investigate the interference of the surface plasmon polariton (SPP) with an incident beam on a metallic slit using the FDTD. We find that the bulk waves radiated at the slit edge by scattering of the SPP leak into the slit and induce accumulated charges within the skin depth, which excite new SPPs on the slit side-walls. The SPP on the top surface of aperture is coupled into the slit and induces the 2D asymmetric field distributions, including the horizontal and vertical Fabry-Perot multi-reflection resonator modes. We show that the addition of these modes with the slit waveguide modes induced by a normally incident beam is the interference between the SPP and the incident beam, which enhances or suppresses the slit transmission, depending on their relative phase.

© 2007 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 (London) 391, 667-669 (1998).
    [CrossRef]
  2. T. Thio, K. M. Pellerin, R. A. Linke, T. W. Ebbesen, and H. J. Lezec, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001).
    [CrossRef]
  3. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
    [CrossRef] [PubMed]
  4. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
    [CrossRef] [PubMed]
  5. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004).
    [CrossRef] [PubMed]
  6. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through slit apertures in metallic films," Opt. Express 12, 6106-6121 (2004).
    [CrossRef] [PubMed]
  7. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005).
    [CrossRef] [PubMed]
  8. J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999).
    [CrossRef]
  9. J. A. Sanchez-Gil and A. A. Maradudin, "Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects," Opt. Express 12, 883-894 (2004).
    [CrossRef] [PubMed]
  10. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd edition, (Artech House, Boston, 2000).
  11. A. D. Rakic, A. B. Djuristic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films," Appl. Opt. 37, 5271-5283 (1998).
    [CrossRef]
  12. H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  13. T. A. Leskova, "Theory of a Fabry-Perot Type Interferometer for Surface Polaritons," Solid State Commun. 50, 869-873 (1984).
    [CrossRef]
  14. Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
    [CrossRef] [PubMed]

2005

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005).
[CrossRef] [PubMed]

2004

2001

1999

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

1998

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

A. D. Rakic, A. B. Djuristic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films," Appl. Opt. 37, 5271-5283 (1998).
[CrossRef]

1984

T. A. Leskova, "Theory of a Fabry-Perot Type Interferometer for Surface Polaritons," Solid State Commun. 50, 869-873 (1984).
[CrossRef]

Alkemade, P. F. A.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Blok, H.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Djuristic, A. B.

Dubois, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

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 (London) 391, 667-669 (1998).
[CrossRef]

Elazar, J. M.

Eliel, E. R.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Gbur, G.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Ghaemi, H. F.

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

Hooft, G.W.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Kuzmin, N.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Lenstra, D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

Leskova, T. A.

T. A. Leskova, "Theory of a Fabry-Perot Type Interferometer for Surface Polaritons," Solid State Commun. 50, 869-873 (1984).
[CrossRef]

Lezec, H. J.

Linke, R. A.

Majewski, M. L.

Mansuripur, M.

Maradudin, A. A.

J. A. Sanchez-Gil and A. A. Maradudin, "Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects," Opt. Express 12, 883-894 (2004).
[CrossRef] [PubMed]

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

Moloney, J. V.

Pellerin, K. M.

Rakic, A. D.

Sanchez-Gil, J. A.

J. A. Sanchez-Gil and A. A. Maradudin, "Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects," Opt. Express 12, 883-894 (2004).
[CrossRef] [PubMed]

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

Schouten, H. F.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

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.

Visser, T. D.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

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 (London) 391, 667-669 (1998).
[CrossRef]

Xie, Y.

Zakharian, A. R.

Appl. Opt.

Nature (London)

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

Opt. Express

Opt. Lett.

Phys. Rev. B

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359-8367 (1999).
[CrossRef]

Phys. Rev. Lett.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G.W. Hooft, D. Lenstra, and E. R. Eliel, "Plasmon-assisted two-slit transmission: Young’s experiment revisited," Phys. Rev. Lett. 94, 053901 (2005).
[CrossRef] [PubMed]

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

Solid State Commun.

T. A. Leskova, "Theory of a Fabry-Perot Type Interferometer for Surface Polaritons," Solid State Commun. 50, 869-873 (1984).
[CrossRef]

Other

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd edition, (Artech House, Boston, 2000).

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

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Figures (6)

Fig. 1.
Fig. 1.

(a) Model schematic. (b) Transmission Ts of the slit (a=250nm, t=300nm) with a single beam incident on the groove, as a function of SPP propagation distance L.

Fig. 2.
Fig. 2.

Modulus of Ex , Ey , and Hz when a single SPP is incident on a slit (a) width a=500nm at resonance; (b) a =3S0nm out of resonance and (c) a=250nm at resonance. (d) Phase distribution for a=250nm. In all figures, slit thickness t=300nm and SPP propagation distance L=520nm.

Fig. 3.
Fig. 3.

Poynting S⃑ (blue arrows) and surface current density vectors J⃑ (red arrows) for single incident SPP illumination. The length of arrows is proportional to the amplitude. Signs +/- indicate polarities of accumulated electric charges, which are related to the gradient of J⃑. Slit width a=250nm, thickness t=300nm.

Fig. 4.
Fig. 4.

Variation of (a) squared transmitted intensity normalized with slit width a for various slit widths a and thicknesses t for a sole incident SPP. Standing wave fringes inside the slit in (b) vertical F-P modes (a=120nm, t=1μm) and (c) horizontal F-P modes (a=1μm, t=310nm).

Fig. 5.
Fig. 5.

Poynting S⃑ (blue arrows) and surface current density vectors J⃑ (red arrows) for a single normal incident beam on the slit (a=250nm, t=300nm). The length of arrows is proportional to the amplitude. Signs +/- indicate polarities of accumulated electric charges.

Fig. 6.
Fig. 6.

Slit transmittance Ts (normalized on the transmission of a single normal beam on the slit) as a function of the slit-groove distance L. Slit parameters: a=250nm, t=300nm.

Equations (1)

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ε ( ω ) = ε r , + k = 0 K f k ω p 2 ω k 2 ω 2 + Γ k

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