Abstract

We investigate transmission of a normally incident, linearly polarized plane wave through a circular sub-wavelength hole in a metal film filled by a high index dielectric medium. We demonstrate for the first time that the transmission efficiency of such holes exhibits a Fabry-Pérot-like behaviour versus thickness of the metal film, similar to that exhibited by sub-wavelength slits in metal films illuminated by TM-polarized plane waves. We show that by reducing the imaginary part of the propagation constant of the hybrid HE11 mode and by fortifying the Fabry-Pérot resonance, the high index dielectric filling can greatly enhance light transmission through a circular sub-wavelength hole.

© 2005 Optical Society of America

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References

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  1. H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944).
    [Crossref]
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).
  3. A. R. Zakharian, M. Mansuripur, and J. V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12, 2631–2648 (2004),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2631.
    [Crossref] [PubMed]
  4. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990).
  5. R. Wannemacher, “Plasmon supported transmission of light through nanometric hole in metallic thin films,” Optics Comm. 195, 107–118 (2001).
    [Crossref]
  6. J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, New York, 2002).
  7. A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
    [Crossref]
  8. F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-25-1475.
    [PubMed]
  9. T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
    [Crossref]
  10. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3694.
    [Crossref] [PubMed]
  11. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  12. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
    [Crossref]
  13. Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
    [Crossref] [PubMed]
  14. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).
  15. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

2004 (2)

2002 (2)

A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-25-1475.
[PubMed]

2001 (3)

T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
[Crossref]

R. Wannemacher, “Plasmon supported transmission of light through nanometric hole in metallic thin films,” Optics Comm. 195, 107–118 (2001).
[Crossref]

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[Crossref] [PubMed]

1997 (1)

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1944 (1)

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944).
[Crossref]

Bethe, H. A.

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Degiron, A.

Ebbesen, T. W.

Garcia de Abajo, F. J.

Hafner, C.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

Hippins, A. P.

A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, New York, 2002).

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Lawrence, C. R.

A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

Linke, R. A.

T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
[Crossref]

Mansuripur, M.

Moloney, J. V.

Mrozowski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
[Crossref]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).

Okoniewski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

Pellerin, K. M.

T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
[Crossref]

Sambles, J. R.

A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

Stuchly, M. A.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

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.

T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
[Crossref]

Wannemacher, R.

R. Wannemacher, “Plasmon supported transmission of light through nanometric hole in metallic thin films,” Optics Comm. 195, 107–118 (2001).
[Crossref]

Zakharian, A. R.

Appl. Phys. Lett. (1)

A. P. Hippins, J. R. Sambles, and C. R. Lawrence, “Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett. 81, 4661–4663 (2002).
[Crossref]

IEEE Microwave Guided Wave Lett. (1)

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple Treatment of Multi-Term Dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7, 121–123 (1997).
[Crossref]

Opt. Express (3)

Optics Comm. (1)

R. Wannemacher, “Plasmon supported transmission of light through nanometric hole in metallic thin films,” Optics Comm. 195, 107–118 (2001).
[Crossref]

Optics Lett. (1)

T. Thio, K. M. Pellerin, and R. A. Linke, “Enhanced light transmission through a single subwavelength aperture,” Optics Lett. 26, 1972–1974 (2001).
[Crossref]

Phys. Rev. (1)

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (1944).
[Crossref]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (1)

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601–5603 (2001).
[Crossref] [PubMed]

Other (5)

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1990).

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, New York, 2002).

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Figures (8)

Fig. 1.
Fig. 1.

Illustration of the modeled system. A cylindrical hole of radius r in a laterally infinite silver film of thickness t is illuminated by a normally incident, linearly polarized plane wave. The refractive indices of the hole, silver film, incident medium and the exit medium are denoted by n c, n Ag, n 0, and n 1, respectively.

Fig. 2.
Fig. 2.

Complex propagation constant (β = βre + jβim) of guided HE1n modes (n = 1: solid line, n = 2: dashed line, n = 3: dotted-dashed line) as a function of the hole radius (r) for an infinitely long air hole in a silver medium. λ0 = 488nm, k0 = 2π/λ 0 .

Fig 3.
Fig 3.

Complex propagation constant (β = βre + jβim) of guided HE11 modes as a function of the hole radius (r) for an infinitely long dielectric-filled (n c = 1.0: solid line, n c = 2.0: dashed line, n c = 3.0: dashed-dotted line) hole in a silver medium. λ0 = 488nm, k0 = 2π /λ0.

Fig. 4.
Fig. 4.

Complex propagation constant (β = βre + jβim) of guided HE11 mode of a dielectric hole in an infinitely thick silver medium as a function of the refractive index of the hole (n c) for two different hole radii: r = 50nm (solid line) and r = 25nm (dashed line).

Fig. 5.
Fig. 5.

Transmission efficiency (η) of a dielectric hole in a silver film versus thickness t of the film. The silver film is illuminated by a normally incident, linearly polarized plane wave. The medium within the hole has refractive index n c and the hole’s radius r = 25nm.

Fig. 6.
Fig. 6.

Same as Fig. 5 but with r = 50nm.

Fig. 7.
Fig. 7.

Complex propagation constant (β = βre + jβim) of guided TM0n modes (n = 1: solid line, n = 2: dashed line) as a function of the hole radius (r) for an infinitely long ai-filled hole in a silver medium. λ0 = 488nm, k0 = 2π/λ0.

Fig. 8.
Fig. 8.

Comparison between the complex propagation constants (β = βre + jβim) of guided HE11 (solid line) and TM01 (dashed line) modes as a function of the hole radius (r) for a dielectric-filled hole (n c = 2) in an silver medium. The inset illustrates the electric field distributions of HE11 and TM01 modes.

Equations (2)

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E ρ ϕ z = m = 0 E m ρ z exp ( jmϕ ) ,
H ρ ϕ z = m = 0 H m ρ z exp ( jmϕ ) ,

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