Abstract

We study theoretically ultrafast light propagation through a periodic array of holes in a silver film deposited on a dielectric substrate using a three-dimensional finite-difference time-domain (FDTD) simulation. We focus on studying the effects of the coherent coupling between resonant surface plasmon polariton (SPP) excitations at the top and bottom interfaces of the metal film on the transmission dynamics. In a free standing film, the SPP excitations at both interfaces are fully in resonance and pronounced temporal oscillations in the energy flow between the bottom and top interfaces give evidence for coupling between the (±1,0) SPP modes via photon tunneling through the holes. Variation of the dielectric constant of the substrate lifts the energetic degeneracy between the two modes and thus decreases the coupling and suppresses the energy oscillations. New SPP-enhanced transmission peaks appear when higher order modes at the substrate/metal interface are brought into resonance with the (±1,0) air/metal resonance and efficient mode coupling is achieved. Both temporal transmission dynamics and near-field mode profiles are reported and their implications for tailoring the optical properties of these two-dimensional plasmonic crystals are discussed.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. C. J. Bouwkamp, "On Bethe's theory of diffraction by small holes," Philips Res. Rep. 5. 321-332 (1950).
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    [CrossRef]
  35. C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003).
    [CrossRef]

Appl. Phys. Lett. (4)

M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999).
[CrossRef]

A. Dechant and A.Y.Elezzabi, �??Femtosecond optical pulse propagation in subwavelength metallic slits,�?? Appl. Phys. Lett. 84 , 4678-4680 (2004).
[CrossRef]

S. C. Hohng, Y. C. Yoon, D. S. Kim, V. Malyarchuk, R. Müller, Ch. Lienau, J. W. Park, K. H. Yoo, J. Kim, H. Y. Ryu, and Q. H. Park, "Light emission from the shadows: surface plasmon nano-optics at near and far fields," Appl. Phys. Lett. 81, 3239-3241 (2002).
[CrossRef]

B. Lamprecht, J. R. Krenn, G. Schider, H. Ditlbacher, M. Salerno, N. Felidj, A. Leitner, and F. R. Aussenegg, "Surface plasmon propagation in microscale metal stripes," Appl. Phys. Lett. 79, 51-53 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

St. A. Cummer, �??An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy,�?? IEEE Trans. Antennas Propag. 45, 392-400 (1997).
[CrossRef]

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

S. Enoch, E. Popov, M. Neviere, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure Appl. Opt. 4, S83-S87 (2002).
[CrossRef]

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

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics:surface plasmon polaritons and localized surface plasmons, " J.. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

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. Comm. (1)

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Opt. Comm. 200, 1-7 (2001).
[CrossRef]

Opt. Commun. (1)

C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Philips Res. Rep. (1)

C. J. Bouwkamp, "On Bethe's theory of diffraction by small holes," Philips Res. Rep. 5. 321-332 (1950).

Phys. Rev. (1)

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. B (9)

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

P. B. Johnson and R. W. Christy, "Optical constants of 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]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, "Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings," Phys. Rev. B 54, 6224-6227 (1996).
[CrossRef]

U. Schröter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration, �?? Phys. Rev. B 60, 4992-4999 (1999).
[CrossRef]

R. Müller, V. Malyarchuk, and C. Lienau, "A three-dimensional theory on light-induced near-field dynamics in a metal film with a periodic array of nanoholes," Phys. Rev. B 68, 205415 (2003).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, "Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: An analytical study," Phys. Rev. B 67, 035424 (2003).
[CrossRef]

F. I. Baida and D .Van Labeke, �??Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,�?? Phys. Rev.B 67, 155314 (2003).
[CrossRef]

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Phys. Rev. B. (1)

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B. 67, 085415 (2003)
[CrossRef]

Phys. Rev. E (1)

P. N. Stavrinou and L. Solymar, "Pulse delay and propagation through subwavelength metallic slits," Phys. Rev. E 68, 066604 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, "Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,". Phys. Rev. Lett. 86, 1110-1113 (2001).
[CrossRef] [PubMed]

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, 1114-1117 (2001).
[CrossRef] [PubMed]

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K .J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, "Full photonic band gap for surface modes in the visible,"Phys. Rev. Lett. 77, 2670-2673 (1996).
[CrossRef] [PubMed]

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]

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 (4)

H. Raether, Surface plasmons, Springer Tracts in Modern Physics Vol. 111, (Springer, Berlin, 1988).

E. D. Palik (Ed.), Handbook of optical constants of solids (Academic Press, San Diego,1985)

R. E. Collin, Field theory of guided waves (Mc Graw-Hill, New York, 1960).

A. Taflove and S. C. Hagness, Computational Electrodynamics. The Finite- Difference Time-Domain Method, 2nd ed. (Artech House, Boston. 2000).

Supplementary Material (3)

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of a metal film perforated with an array of holes and deposited on a substrate with a refractive index ns . The medium above the film is air. a0 is the lattice constant, d the hole diameter and h the film thickness. (a) Cross section through x-z plane. The input wave is polarized along x and illuminates the bottom metal surface at normal incidence. (b) Top view.

Fig. 2.
Fig. 2.

Photon flux density z,norm vs time in a hole channel at z = 0, (bottom interface, black) and z = h (top interface, red) for substrate refractive indices ns = 1.00 to 1.80, (a)–(e).The input pulse (green) is shown in (a).

Fig. 3
Fig. 3

Field energy density ex,norm vs time inside a hole at z = 0 (black line) and at z = h (red line) for ns = 1.00 to 1.80, (a)–(e).

Fig. 4.
Fig. 4.

Spatial distribution of time-averaged squared electric field strengths (a) E x 2 ̄ , (b) E y 2 ̄ , (c) E x 2 ̄ + E y 2 ̄ in the x-y planes of the substrate/metal interface (bottom row, z = -2.5 nm) and the air/silver interface (top row, z = h + 2.5 nm) at time t = 45fs. The refractive index of the substrate is ns = 1.37 and the incident beam is polarized along the x-direction. A logarithmic color scale is used. The intensity of E y 2 ̄ at the top interface (b) is enhanced by a factor of 10.

Fig. 5.
Fig. 5.

Same as Fig. 4 but squared z-component of the electric field, E ̅ z 2 at the substrate/silver interface at z = -2.5 nm (a) and at the air/silver interface at z = h + 2.5 nm (b). A logarithmic color scale is used.

Fig. 6.
Fig. 6.

Time-averaged squared field strength on the substrate/silver interface (bottom row) and the air/silver interface (top row) at time t = 45fs (logarithmic color scale). (a) E x 2 ¯ , (b) E z 2 ¯ . The refractive index of the substrate is ns = 1.80. The intensity scale for E z 2 ¯ at the bottom interface is from 0.01 to 10.

Fig. 7.
Fig. 7.

Movie sequences showing the time evolution of squared electric field strengths, averaged over one optical period T = 2π/ω, in the x-y-plane (logarithmic color scale) at (a) the bottom (t = 40fs) and (b) the top interface (t = 40 fs) for a freestanding metal film, ns = 1.00, and excitation with a 10fs optical pulse (3.9 MB movie).

Fig. 8.
Fig. 8.

Movie sequences showing the time evolution of squared electric field strengths in the x - y -plane (logarithmic color scale) at (a) the bottom (t = 40 fs) and (b) the top interface (t = 40 fs) for ns = 1.37, and excitation with a 10fs optical pulse (3.4 MB movie).

Fig. 9.
Fig. 9.

Movie sequences showing the time evolution of squared electric field strengths in the x-y-plane (logarithmic color scale) at (a) the bottom and (b) the top interface for ns = 1.80, and excitation with a 10fs optical pulse (2.8 MB movie).

Equations (5)

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× E = μ 0 H t
× H = εε 0 E t + J
J t + γ J = ε 0 ω p 2 E ,
ε m ( ω ) = 1 ω p 2 ω 2 + iγω .
ω p q i = 2 πc p 2 + q 2 a 0 n i ε m + n i 2 ε m

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