Abstract

Finite-difference-time-domain (FDTD) computer simulations reveal interesting features of the transmission of a linearly polarized plane-wave through a periodic array of sub-wavelength slits in a thick metal film (incident E-field perpendicular to the slits’ long axis). The results show that slit transmission has a quasi-periodic dependence on both the film thickness and the period of the slits. This indicates that resonant surface waves excited at the top and bottom facets of the metal film as well as resonant guided modes along the depth of the slits play major roles in determining the transmission efficiency of the array. When the slit periodicity is an integer-multiple of the surface-plasmon wavelength, transmission drops to zero regardless of film thickness; in other words, excitation of surface plasmons reduces the transmission efficiency. When the slit periodicity deviates from the aforementioned value, maximum transmission through the slits is achieved by adjusting the film thickness. In the thickness dimension, transmission maxima occur periodically, with a period of half the effective wavelength of the guided mode in each slit waveguide. Optimum transmission is thus achieved by simultaneously adjusting the film thickness and the period of the slits. Computed field profiles clarify the role played by the induced surface charges and currents in enhancing the light’s coupling efficiency into and out of the slits.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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J. Opt. A (1)

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, �??One-mode model and airy-like formulae for one-dimensional metallic gratings,�?? J. Opt. A 2, 48-51 (2000).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

J. R. Sambles, �??Photonics: more than transparent,�?? Nature 391, 641 (1998).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

M. M. J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105/1-11 (2002).
[CrossRef]

Phys. Rev. E (1)

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, �??Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit,�?? Phys. Rev. E 69, 26601(69), (2004).
[CrossRef]

Phys. Rev. Lett. (6)

Y. Takakura, �??Optical resonance in a narrow slit in a thick metallic screen�??, Phys. Rev. Lett. 86, 05601, (2001).
[CrossRef]

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, �??Multiple paths to enhance optical transmission through a single subwavelength slit,�?? Phys. Rev. Lett. 90, 213901(4) (2003).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, J. B. Pendry, �??Transmission resonances on metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 83, 02845 (1999).
[CrossRef]

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

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, �??Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,�?? Phys. Rev. Lett. 92, 107401(4) (2004).
[CrossRef]

F. Yang and J. R. Sambles, �??Resonant transmission of microwave through a narrow metallic slit,�?? Phys. Rev. Lett. 89, 63901(3) (2002).
[CrossRef]

Other (3)

H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1986).

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

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

Slit array having period p and aperture width W, in a metal film of thickness t. At the vacuum wavelength of λ o=1.0 µm, the film’s material (silver) has permittivity ε=(n+iκ)2=-48.8+3.16i. The incident beam is uniform along the x- and y-axes (i.e., plane-wave), having the polarization state shown in the lower left-hand side, which is denoted by E and referred to as transverse magnetic (TM). The other possible state of polarization, E or transverse electric (TE), shown on the lower right-hand side, will not be considered in this paper. In the reported simulations, the thickness t is varied from 0.l µm to 0.8 µm in 20 nm steps, while the period p is varied from 0.2 µm to 2.4 µm in 30 nm steps. (The total number of simulations, therefore, is 36×74=2664.) The considered range of p covers slightly over two wavelengths of the surface plasmon polaritons that can be excited in the host material (silver).

Fig. 2.
Fig. 2.

(Top) Computed map of the transmission efficiency η of a periodic array of slits in a silver film of thickness t, when t ranges from 0.1 to 0.8µm (vertical axis), while the slit period p ranges from 0.2 to 2.4 µm (horizontal axis). The slit-width is fixed at W=100nm, and the normally incident plane wave has wavelength λ o=1.0 µm. (Bottom) Plots of the minimum (blue) and maximum (red) transmission efficiency, η min, η max, versus the slit period p, obtained for each value of p by searching the map over the available range of simulated thicknesses (t : 0.1–0.8 µm). For a single, 100 nm-wide slit under otherwise identical conditions, the range of η was found in [16] to be between 70% and 210%.

Fig. 3.
Fig. 3.

Y Z-plane cross-sectional plots of the field magnitudes |Ez | (top row), |Hx | (middle row), and log_magnitude of the Poynting vector, log |S| (bottom row), for three different slit arrays. (Left column) p=0.96 µm, t=0.16 µm, η=492%. (Middle column) p=1.74 µm, t=0.7 µm, η=401%. (Right column) p=1.98 µm, t=0.44 µm, η=0.34%. The superposed arrows on the color-coded log |S| plots in the bottom row represent the direction of the flow of energy.

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