Abstract

Extensive 3-D finite-difference time-domain simulations are carried out to elucidate the nature of surface plasmon polaritons (SPPs) and localized surface plasmon polaritons (LSPs) generated by nanoscale holes in thin metallic films interacting with light. Both isolated nanoholes and square arrays of nanoholes in gold films are considered. For isolated nanoholes, we expand on an earlier discussion of Yin et al. [Appl. Phys. Lett. 85, 467–469 (2004)] on the origins of fringe patterns in the film and the role of near-field scanning optical microscope probe interactions. The associated light transmission of a single nanohole is enhanced when a LSP excitation of the nanohole itself is excited. Periodic arrays of nanoholes exhibit more complex behavior, with light transmission peaks exhibiting distinct minima and maxima that can be very well described with Fano lineshape models. This behavior is correlated with the coupling of SPP Bloch waves and more directly transmitted waves through the holes.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  26. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Second Edition (Wiley, New York, 1983) p. 344.
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    [CrossRef]
  29. U. Fano, "Effects of Configuration Interaction on Intensities and Phase Shifts," Phys. Rev. 124, 1866-1878 (1961).
    [CrossRef]
  30. 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(1-4) (2004).
    [CrossRef] [PubMed]
  31. J. M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, "Metallodielectric gratings with subwavelength slots: Optical properties," Phys Rev. B 68, 205103(1-7) (2003).
    [CrossRef]
  32. 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(1-4) (2002).
    [CrossRef] [PubMed]
  33. W. Fan, S. Zhang, B. Minhas, K.J. Malloy, and R.J. Brueck, "Enhanced infrared transmission through subwavelength coaxial metallic arrays," Phys. Rev. Lett. 94, 033902(1-4) (2005).
    [CrossRef] [PubMed]

Appl. Optics

R.D. Grober, T. Rutherford, and T.D. Harris, "Model approximation for the electromagnetic field of a near-field optical probe," Appl. Optics 19, 3488-3495 (1996).
[CrossRef]

Appl. Phys. Lett.

L. Yin, V.K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S.-H. Chang, S.K. Gray, G.C. Schatz, D.E. Brown, and C.W. Kimball, "Surface plasmons at single nanoholes in Au films," Appl. Phys. Lett. 85, 467-469 (2004).
[CrossRef]

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

IEEE Ant. and Prop. Mag.

G. Guiffaut and K. Mahdjoubi, "A parallel FDTD Algorithm using the MPI library," IEEE Ant. and Prop. Mag. 43, 94-103 (2001).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Chem. B

K.L. Kelly, E. Coronado, L.L. Zhao, and G.C. Schatz, "The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment," J. Phys. Chem. B 107, 668-677 (2003).
[CrossRef]

Nano Lett.

J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Kall, "Optical spectroscopy of nanometric holes in thin gold films," Nano Lett. 4, 1003-2007 (2004).
[CrossRef]

Nature

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. Commun.

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

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004).
[CrossRef]

R. Wannemacher, "Plasmon-supported transmission of light through nanometric holes in metallic thin films," Opt. Commun. 195, 107-118 (2001).
[CrossRef]

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

Philips Res. Rep.

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

Phys Rev. B

J. M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, "Metallodielectric gratings with subwavelength slots: Optical properties," Phys Rev. B 68, 205103(1-7) (2003).
[CrossRef]

Phys. Rev.

U. Fano, "Effects of Configuration Interaction on Intensities and Phase Shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

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

Phys. Rev. B

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(1-7) (2003).
[CrossRef]

S.K. Gray and T. Kupka, "Propagation of light in metallic nanowire arrays: Finite-difference time-domain results for silver cylinders," Phys. Rev. B 68, 045415(1-11) (2003).
[CrossRef]

P.B. Johnson and R.W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

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 (1-8) (2003).
[CrossRef]

H. F. Ghaemi, T. Thio, and 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]

Phys. Rev. Lett.

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, 1110-1117 (2001).
[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(1-4) (2004).
[CrossRef] [PubMed]

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(1-4) (2002).
[CrossRef] [PubMed]

W. Fan, S. Zhang, B. Minhas, K.J. Malloy, and R.J. Brueck, "Enhanced infrared transmission through subwavelength coaxial metallic arrays," Phys. Rev. Lett. 94, 033902(1-4) (2005).
[CrossRef] [PubMed]

Other

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, New York, 1988).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Second Edition (Wiley, New York, 1983) p. 344.

J.D. Jackson, Classical Electrodynamics, Second Edition (Wiley, New York, 1975) pp. 438-441.

G.B. Arfken and H.J. Weber, Mathematical Methods for Physicists, (Academic Press, New York, 1995).

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

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Figures (10)

Fig. 1.
Fig. 1.

Time-averaged |Ex |2 for an isolated d=200 nm diameter nanohole in a 100 nm thick gold film on top of a glass layer: (a) z=4 nm, x-y profile; (b) x-z cut for y=0 of result in (a); (c) same as (b) but for the case of no hole present; (d) result of subtracting the amplitudes in (b) and (c) and taking the absolute square of the result. The field shown is the Fourier transform at incident wavelength λ=532 nm of our FDTD result.

Fig. 2.
Fig. 2.

Profiles of scaled field components, Ex′=Ex kspp /() and Ez ′=Ez/A, along the incident polarization direction (x with y=0) just above (z=4 nm) the metal film. Symbols are the FDTD results and curves correspond to the Bessel function fits described in the text.

Fig. 3.
Fig. 3.

Comparison of theoretically estimated NSOM signal (solid red symbols) with the total intensity (dashed black line) and the intensity of parallel electric field component (solid blue line) on the metal surface of a single nanohole.

Fig. 4.
Fig. 4.

Transmission spectrum of a single d=200 nm nanohole in a 100 nm thick metal film on glass, treating the metal as gold (solid curve) and as a perfect electrical conductor (dashed curve). The metal film is sandwiched between glass and air, with the light incident from the glass side.

Fig. 5.
Fig. 5.

Transmission spectra for 2-D periodic square arrays of d=200 nm nanoholes with square lattice spacing D=600 nm in a 100 nm thickmetal film. (a) Treating the metal film as gold. (b) Treating the metal film as a PEC.

Fig. 6.
Fig. 6.

| Ez |2 for the 2-D square hole array in a gold film of Fig. 5(a). (a)(f) correspond to λ=610 nm, 620 nm, …, 660 nm.

Fig. 7.
Fig. 7.

| Ex |2 for the 2-D hole array in the gold film of Fig. 5(a). (a)–(f) correspond to λ=610 nm, 620 nm, …, 660 nm.

Fig. 8.
Fig. 8.

|Ez |2 for the 2D hole array in (a) gold and (b) PEC films at wavelength 600 nm. The contrast has been increased by a factor of 3 comparing to other figures in order to show the weak Wood’s anomaly features.

Fig. 9.
Fig. 9.

Multiple resonance Fano model fit (solid curve) to the FDTD transmission data (symbols) for the 2D array of holes in a gold film.

Fig. 10.
Fig. 10.

Charge distribution of the (1,0)air mode at (a) the transmission minimum, and (b) the transmission maximum.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ε A u ( ω ) = ε ω D 2 ω 2 + i γ D ω
T ( λ ) = [ T tot ( λ ) T film ( λ ) ] ( I i n c π a 2 ) ,
k S P P ω c ( ε A u ε d ε A u + ε d ) 1 2
E S P P A ( z ̂ i α k S P P ρ ̂ ) H 1 ( 1 ) ( k S P P ρ ) cos ( φ ) exp ( α z ) exp ( i ω t ) ,
H m ( 1 ) ( k S P P ρ ) = J m ( k S P P ρ ) + i Y m ( k S P P ρ ) .
H m ( 1 ) ( k S P P ρ ) ( 2 π k S P P ρ ) 1 2 exp ( i k S P P ρ ) exp ( i 2 m + 1 4 π )
λ S P P = D ( n x 2 + n y 2 ) 1 2 ( ε A u ε d ε A u + ε d ) 1 2
T Fano ( ω ) T b = T a ( ε + q ) 2 1 + ε 2 , ε = ω ω r γ r 2 .
T multiple ( ω ) T b = T a ( 1 + Σ r q r ε r ) 2 1 + ( Σ r ε r 1 ) 2

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