Abstract

Using the Fourier modal method, we study the enhanced transmission exhibited by arrays of square coaxial apertures in a metallic film. The calculated transmission spectrum is in good agreement with FDTD calculations. We show that the enhanced transmission can be explained when we consider a few guided modes of a coaxial waveguide.

© 2003 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. Wolf, �??Extraordinary optical transmission through sub-wavelength hole arrays,�?? Nature 391, 667 (1998).
    [CrossRef]
  2. 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 (1999).
    [CrossRef]
  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, 114 (2001).
    [CrossRef]
  4. Q. Cao and P. Lalanne, �??Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef] [PubMed]
  5. S. Astilean, P. Lalanne, and M. Palamaru, �??Light transmission through metallic channels much smaller than the wavelength,�?? Opt. Commun. 175, 265 (2000).
    [CrossRef]
  6. M. M. J. Treacy, �??Dynamical diffraction in metallic optical gratings,�?? Appl. Phys. Lett. 75, 606 (1999).
    [CrossRef]
  7. M. M. J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  8. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, �??Horizontal and vertical surface resonances in transmission metallic gratings,�?? J. Opt. A:Pure Appl. Opt. 4, S154 (2002).
    [CrossRef]
  9. L. Li, �??New formulation of the Fourier modal method for corssed surface-relief gratings,�?? J. Opt. Soc. Am. A 11, 2758-2767 (1997).
    [CrossRef]
  10. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, �??Theory of light transmission through subwavelength periodic hole arrays,�?? Phys. Rev. B 62, 16100 (2000).
    [CrossRef]
  11. F. I. Baida and D. Van Labeke, �??Light transmission by subwavelength annular aperture arrays in metallic films,�?? Opt. Commun. 209, 17-22 (2002).
    [CrossRef]
  12. G. Granet and J. P. Plumey, �??Parametric formulation of the Fourier modal method for crossed surface-relief gratings,�?? J. Opt. A: Pure Appl. Opt. 4, S145 (2002).
    [CrossRef]

Appl. Phys. Lett. (1)

M. M. J. Treacy, �??Dynamical diffraction in metallic optical gratings,�?? Appl. Phys. Lett. 75, 606 (1999).
[CrossRef]

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

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, �??Horizontal and vertical surface resonances in transmission metallic gratings,�?? J. Opt. A:Pure Appl. Opt. 4, S154 (2002).
[CrossRef]

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

L. Li, �??New formulation of the Fourier modal method for corssed surface-relief gratings,�?? J. Opt. Soc. Am. A 11, 2758-2767 (1997).
[CrossRef]

Nature (1)

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

Opt. Commun. (2)

F. I. Baida and D. Van Labeke, �??Light transmission by subwavelength annular aperture arrays in metallic films,�?? Opt. Commun. 209, 17-22 (2002).
[CrossRef]

S. Astilean, P. Lalanne, and M. Palamaru, �??Light transmission through metallic channels much smaller than the wavelength,�?? Opt. Commun. 175, 265 (2000).
[CrossRef]

Phys. Rev. B (2)

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

M. M. J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105 (2002).
[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 (1999).
[CrossRef]

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, 114 (2001).
[CrossRef]

Q. Cao and P. Lalanne, �??Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Other (1)

G. Granet and J. P. Plumey, �??Parametric formulation of the Fourier modal method for crossed surface-relief gratings,�?? J. Opt. A: Pure Appl. Opt. 4, S145 (2002).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Coaxial square aperture in a metallic film.

Fig. 2.
Fig. 2.

Transmission of a square coaxial aperture calculated with the FDTD (blue curve) and the Fourier modal method (red curve).

Fig. 3.
Fig. 3.

Dispersion curves of the first mode. Blue curve, real part; red curve, imaginary part. The presence of dips is probably due to the right angle corners.

Fig. 4.
Fig. 4.

Dispersion curves of the second mode. Blue curve, real part; red curve, imaginary part.

Fig. 5.
Fig. 5.

Modulus of the transverse electric field of the first guided mode.

Fig. 6.
Fig. 6.

Modulus of the transverse electric field of the second guided mode.

Fig. 7.
Fig. 7.

Twenty-first modal amplitude coefficients inside the coaxial on the upper face. The red bar corresponds to an attenuated guided wave.

Fig. 8.
Fig. 8.

Twenty-first modal amplitude coefficients inside the coaxial on the lower face. The red bar corresponds to an attenuated guided wave.

Fig. 9.
Fig. 9.

The ten first complex propagating constants associated to the ten first modes that are exited on the upper face inside the coaxial waveguide. The red one corresponds to an attenuated guide wave; its value is γ=1.39—0.006i.

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