Abstract

Transmission enhancements of order 1000 have been reported for subwavelength hole arrays in metal films and attributed to surface plasmon (SP) resonance. We show that the properly normalized enhancement factor is consistently less than 7, and that similar enhancements occur in nonmetallic systems that do not support SPs. We present a new model in which the transmission is modulated not by coupling to SPs but by interference of diffracted evanescent waves generated by subwavelength features at the surface, leading to transmission suppression as well as enhancement. This mechanism accounts for the salient optical properties of subwavelength apertures surrounded by periodic surface corrugations.

© 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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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] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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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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2003 IEEE Antennas and Propagation Symp (1)

A. A. Oliner and D. R. Jackson, ???Leaky-surface plasmon theory for dramatically enhanced transmission through a sub-wavelength aperture, Part I: Basic features,??? Proc. IEEE Antennas and Propagation Symposium, Columbus OH, USA, June 2003 (AP-S Digest Vol. 2, pp. 1091???1094).

Appl. Opt. (4)

Appl. Phys. Lett. (6)

A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, ???Effects of hole depth on enhanced light transmission through subwavelength hole arrays,??? Appl. Phys. Lett. 81, 4327???4329 (2002).
[CrossRef]

S. Shinada, J. Hashizume, and F. Koyama, ???Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating,??? Appl. Phys. Lett. 83, 836???838 (2003).
[CrossRef]

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

A.P. Hibbins, J.R. Sambles, C.R. Lawrence, ???Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate,??? Appl. Phys. Lett. 81, 4661???4663 (2002).
[CrossRef]

M.J. Lockyear, A.P. Hibbins, J.R. Sambles, and C.R. Lawrence, ???Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture,??? Appl. Phys. Lett. 84, 2040???2042 (2004).
[CrossRef]

D.E. Grupp, H.J. Lezec, K.M. Pellerin, T.W. Ebbesen, and T. Thio, ???Fundamental role of metal surface in enhanced transmission through subwavelength apertures,??? Appl. Phys. Lett. 77, 1569???1571 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

C.Winnnewisser, F.T. Lewen, M. Schall, M.Walther, and H. Helm, ???Characterization and Application of Dichroic Filters in the 0.1-3-THz Region,??? IEEE Trans. Microwave Theory Tech. 48, 744???749(2000).
[CrossRef]

J. Opt. A. (1)

H.J. Lezec and T. Thio, ???Multiplicative two-surface enhanced transmission through subwavelength hole arrays???, submitted to JOptA.

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

MORIS 2004 (1)

J. Fujikata, T. Ishi, H. Yokota, K. Kato, M. Yanagisawa, M. Nakada, K. Ishihara, K. Ohashi, T. Thio and R.A. Linke, ???Surface plasmon enhancement effect and its application to near-field optical recording,??? presented at the Magneto-Optical Recording International Symposium 2004 (MORIS 2004), Yokohama, Japan (May 2004).

Nature (2)

E. Altewischer, M.P. van Exter, and J.P. Woerdman, ???Plasmon-assisted transmission of entangled photons,??? Nature (London) 418, 304???306 (2002).
[CrossRef]

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, ???Extraordinary optical transmission through sub-wavelength hole arrays,??? Nature (London) 391, 667???669 (1998).
[CrossRef]

Opt. Commun. (3)

J.M. Vigoureux, ???Analysis of the Ebbesen experiment in the light of evanescent short range diffraction,??? Opt. Commun. 198, 257???263 (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]

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (1)

H. A. Bethe, ???Theory of diffraction by small holes,??? Phys. Rev. 66, 163???182 (1944); C. J. Bouwkamp, ???On Bethe???s theory of diffraction by small holes,??? Philips Res. Rep. 5, 321???332 (1950).
[CrossRef]

Phys. Rev. B (6)

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]

J. Gmez-Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, ???Enhanced transmission of THz radiation through subwavelength holes,??? Phys. Rev. B 68, 201306(R) (2003).

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 (2003).
[CrossRef]

H. Lochbihler, ???Surface polaritons on gold-wire gratings,??? Phys. Rev. B 50, 4795???4801 (1994).
[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 (2003).
[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. E (1)

M. Sarrazin and J.-P. Vigneron, ???Optical properties of tungsten thin films perforated with a bidimensional array of subwavelength holes,??? Phys. Rev. E 68, 016603 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

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

P. Kramper, M. Agio, C.M. Soukoulis, A. Birner, F. Müller, R. B.Wehrspohn, U. Gösele, and V. Sandoghdar, ???Highly directional emission from photonic crystal waveguides of subwavelength width,??? Phys. Rev. Lett. 92, 113903 (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 (2002).
[CrossRef] [PubMed]

W.L. Barnes, W.A. Murray, J. Dintlinger, 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 (2004).
[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]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T.W. Ebbesen, ???Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,??? Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Science (1)

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, M. Martín-Moreno, F.J. García-Vidal and T.W. Ebbesen, ???Beaming light from a sub-wavelength aperture,??? Science 297, 820???822 (2002).
[CrossRef] [PubMed]

Other (4)

E. Hecht, Optics, (Addison-Wesley, Reading MA, 1998).

J.D. Kraus and K.R. Carver, Electromagnetics, (McGraw-Hill, New York, 1973).

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

B.A. Munk, Frequency Selective Surfaces: Theory and Design, (Wiley, New York, 2000).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Optical characterization of an N×N array (P=410 nm) of cylindrical holes (d=150 nm) in a silver film (t=175 nm) on glass, overcoated with index-matching fluid. (a,b,c) SEM micrographs of structures for N=1, 4, and 9, respectively (horizontal field of view FOV=5µm, observation angle with respect to normal a=45°); (d) as-collected transmission spectra for selected N; (e) corresponding per-hole transmission coefficient TR,N (λ) for selected N.

Fig. 2.
Fig. 2.

Optical characterization of a 9×9 array of cylindrical holes in a suspended Ag film as a function of array period P and hole diameter d. (a) Per-hole transmission coefficient TR ,9(λ) for selected P (at constant d) and transmission coefficient TR ,1(λ) of an equivalent isolated hole; (b) resulting array enhancement factor G 9(λ)=TR ,9=TR ,1 for selected P; (c) per-hole transmission coefficients TR ,9(λ) (thick lines) and TR ,1(λ) (thin lines) for selected d (at constant P); (d) resulting array enhancement factor G 9(λ) for selected d.

Fig. 3.
Fig. 3.

(a) As-collected transmission spectra of 15×15 hole arrays in suspended films of: tungsten (W, t=400 nm, d=300 nm, P=600 nm); amorphous silicon (a-Si, t=200 nm, d=250 nm, P=550 nm); and silver (Ag, t=300 nm, d=250 nm, P=750 nm); (b) zero-order transmission (Ag, T[0]) and first-order reflectivity (Ag, R[1]) of a 25×25 array (P=820 nm) of holes (d=250 nm) in suspended Ag (t=300 nm), compared to first-order reflectivity (Si, R[1]) of a 25×25 array (P=820 nm) of cylindrical dimples (d=300 nm, depth h≃1 µm) in undoped Si.

Fig. 4.
Fig. 4.

Geometry of optical scattering by a hole in a screen in (a) real space and (b) k-space.

Fig. 5.
Fig. 5.

Characterization of CDEW amplitude and phase by in-plane interferometry. (a) Device geometry: double row of cylindrical holes (d=250 nm, P=500 nm) in a suspended Ag film (t=300 nm) with row-row spacing L varied in integer multiples of P; (b and c) SEM micrographs of devices with L=1.5 and 3 µm, respectively (FOV=7.6 µm, a=52°); (d) wavelength positions of interference maxima λm,K (where m is interference order), plotted as a function of L: experimental data (symbols), CDEW model (dashed lines), and SP model (dotted line, shown only for case m=K); (e) CDEW amplitude C as function of traveled distance L: experimental data (symbols) and 1/L fit (dashed line).

Fig. 6.
Fig. 6.

Characterization of distance-dependence of CDEW amplitude by interferometry in a circular configuration. (a) Device geometry: single hole (d=300 nm) in a silver film (t=250 nm) on glass surrounded by a single circular groove (width w=150 nm, depth h=100 nm) with radius R varied in integer multiples of P=600 nm; (b and c) SEM micrographs of devices with R=3 and 4.2 µm, respectively (FOV=12.5 µm, a=52°); (d) enhancement factor G(λ) plotted for increasing normalized radius K=R/P; (e) CDEW amplitude C as a function of normalized traveled radial distance K=R/P: experimental data (symbols) and 1/R fit (solid line).

Fig. 7.
Fig. 7.

Spectral effect of increasing the number of surface-wave sources: experimental results compared to simple analytical predictions for single slit surrounded by ±N periodic grooves. (a) SEM micrograph (FOV=12.7 µm, a=45°) of experimental device consisting of a single slit (width w=100 nm, length l=10 µm) in a silver film (t=340 nm) on glass, surrounded by ±5 grooves (P=650 nm, w=100 nm, h≃50 nm); (b) experimental transmission spectra, N varied from 1 to 5 with other parameters constant as in (a); (c) intensity modulation at slit entrance predicted by SP model; (d) intensity modulation at slit entrance predicted by CDEW model.

Fig. 8.
Fig. 8.

Cascaded two-surface modulation function [A(λ)]2 for a 9×9 hole array facing identical dielectric media on both sides: function derived from experimental data of Fig. 1 compared to prediction of CDEW model.

Fig. 9.
Fig. 9.

Surface-wave detector consisting of a single hole (d=300 nm) surrounded by 16 ring grooves (w=150 nm, h=100 nm) in a silver film (t=250 nm) on glass. Grooves form a concentric grating with period P=600 nm, starting at radius 4P. (a) SEM micrograph of device (FOV=30.4 µm, a=52°); (b) effect on gain spectrum G(λ) of increasing holegrating radial distance by increments of P/10.

Equations (4)

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E ( x , z = 0 ) = E 0 π [ Si ( k 0 ( x + d 2 ) ) Si ( k 0 ( x d 2 ) ) ] ,
E ( x ) = E 0 π d x cos ( k 0 x + π 2 ) .
T C ( λ ) = A 1 ( λ ; n 1 , P 1 , d 1 ) T H ( λ ; n H , d , t ) A 2 ( λ ; n 2 , P 2 , d 2 ) f C ( λ ; NA , P 2 , d 2 ) ,
A 1 ( λ ) = ( 1 + 2 j = 1 N α d jP cos ( 2 π λ n eff jP + π 2 ) ) 2 ,

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