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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 16 — Aug. 9, 2004
  • pp: 3694–3700
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Analysis of the transmission process through single apertures surrounded by periodic corrugations

A. Degiron and T.W. Ebbesen  »View Author Affiliations


Optics Express, Vol. 12, Issue 16, pp. 3694-3700 (2004)
http://dx.doi.org/10.1364/OPEX.12.003694


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Abstract

We have analyzed the transmission process through single subwavelength apertures surrounded by a set of periodic grooves in optically thick Ag films. On one hand, we found that the intensity of both single- and double-corrugated structures follows just one exponential regime as a function of the hole depth. On the other hand, it is shown that the transmission process can be separated into three independent steps: coupling in, transmission through the aperture and coupling out. This is in contrast with the transmission through hole arrays reported by previous studies where two transmission regimes were found. These findings are of relevance not only for further understanding the enhanced transmission but also for any applications based on this phenomenon.

© 2004 Optical Society of America

According to standard diffraction theories, the transmission of a subwavelength aperture of diameter d is very weak because light cannot propagate through it if its wavelength λ>2d [1

1. H.A. Bethe, “Theory of diffraction by small holes,” Phys, Rev. 66, 163–182 (1944). [CrossRef]

]. It has been shown that this can be overcome by orders of magnitude by surrounding a single subwavelength aperture with a periodic structure such as a hole array or by a periodic corrugation [2

2. 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]

17

17. T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

]. This enhancement arises from the coupling of the incident light with surface plasmon polaritons (SPPs) through the surface grating. In the case of single apertures, it has been shown furthermore that a periodic texture on the exit side can give rise to a beam with a small angular divergence, very different from the expected quasi-isotropic diffraction of a small hole [18

18. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martín-Moreno, F.J. García-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002). [CrossRef] [PubMed]

21

21. W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

]. Many investigations have been performed, both theoretical and experimental, and it is now established that these phenomena have a more general meaning. For instance it has been shown that the same results apply in the microwave region [22

22. A. P. Hibbins and J. R. Sambles, “Grating enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett 81, 4661–4663 (2002). [CrossRef]

,23

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

], or for perfect conductors [9

9. L. Martín-Moreno, F.J. García-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]

,19

19. 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]

], because the presence of the indentations in the metal provides an effective refractive index allowing the launching of SPP like surface waves. Very recently, the principle of the beaming has been predicted and observed at the exit of a photonic crystal [24

24. E. Moreno, F.J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004). [CrossRef]

,25

25. P. Kramper, M. Agio, C.M. Soukoulis, A. Birner, F. Müller, R.B. Wehrpohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett 92, 113903 (2004). [CrossRef] [PubMed]

].

In order to further understand the details of the transmission process through single apertures surrounded by corrugations, we have analyzed the effect of the aperture depth in bull’s eye structures (single apertures surrounded by concentric periodic grooves) in various configurations. We show among other things that the transmission can be divided into three independent steps whose product determines the total transmission intensity. This has consequences for further use of these structures for practical applications.

The structures were milled by focused ion beam in optically thick Ag films using an FEI Strata DB 235 system. We worked with free-standing metal membranes, which allow us to pattern either one or both surfaces of the film. The samples were then optically characterized by measuring their far-field transmission spectra with an optical microscope coupled to a spectrometer. In what follows, we will present the results obtained in the case of a periodic array of concentric grooves with period P=600 nm, groove width 240 nm and groove thickness 50 nm. The aperture diameter chosen for this study is 270 nm.

Fig. 1. Transmission spectra of cylindrical apertures surrounded by 5 concentric grooves on the input side, for a range of hole depths h. The geometric parameters are detailed in the text.
Fig. 2. Intensity as a function of h for bull’s eye structures with corrugations on the input side (diamonds), and on both sides (squares). The data are derived from Figs. 1 and 3 at three different wavelengths: λ=650 nm (black), λ=700 nm (red), λ=750 nm (blue).

We began by investigating the role of the aperture depth h on the transmission of a bull’s eye structure with corrugations only on the input side. Fig. 1 shows the results for a range of depths between 800 nm and 200 nm. All spectra exhibit a huge transmission peak at λ=650 nm, resulting from the excitation of SPP on the input side. As the hole become shallower, the peak position redshifts. In addition, Fig. 2 shows that the intensity at a given wavelength follows an exponential decay, which is the expected signature of the transmission in the absence of propagative modes inside the hole. This is the same evolution as that predicted and observed for hole arrays with deep holes, where the SPPs excited on both sides of the film remain uncoupled [4

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

,9

9. L. Martín-Moreno, F.J. García-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]

].

Fig. 3. Transmission spectra of cylindrical apertures surrounded by 5 concentric grooves on both sides, for a range of hole depths h.

As we show now, these results suggest that the enhancement of the input side is not correlated with the enhancement and the beaming of the exit side. This can be understood if one assumes that the transmission process can be separated into three independent steps: coupling in, transmission and coupling out. Let us first consider the case of a corrugation only on the input side. According to the above hypothesis, the transmitted intensity Ici can be written as:

Ici(λ,h)=fci(λ).T(λ,h).fe(λ),
(1)

where fci is the coupling function of the corrugated input side i, T is the cutoff function of the central aperture and fe is the coupling out function of the aperture on the exit side e. Note that fci and fe are assumed independent of h, and T represents the exponential decay of Fig. 2. The same remarks can be applied for a single hole without corrugations, except that the transmission I(λ, h) differs by the input function fi(λ):

I(λ,h)=fi(λ).T(λ,h).fe(λ),
(2)

Hence, the ratio Ici/I is independent of h:

Ici(λ,h)I(λ,h)=fci(λ)fi(λ).
(3)

We can verify this point by dividing each spectrum of Fig. 1 with that of an uncorrugated single hole with same dimensions. Indeed as can be seen in Fig. 4, in such a case all the curves are identical, hence confirming our hypothesis.

Fig. 4. Ratio between the transmission spectra of Fig. 1 and those of isolated apertures without corrugations of same dimensions.

If we wish to make a similar analysis for the double sided structures, we must take care to divide the data by the right reference. In other words, because the diffraction pattern of an aperture surrounded by corrugations on the output side is very different from that of a simple aperture, the comparison here had to be done between double-sided structures and apertures with corrugation just on the output side. In such case, they both have the same diffraction pattern and therefore the transmission intensity collected by the microscope can be compared. Following the same reasoning as above (Eq. (1) and (2)), the transmitted intensity Ice of a single aperture with a corrugation only on the exit side is given by the product :

Ice(λ,h)=fi(λ).T(λ,h).fce(λ),
(4)

where fce(λ) is the contribution from the corrugated exit surface. On the other hand the transmission Icie(λ, h) of double sided structures is then:

Icie(λ,h)=fci(λ).T(λ,h).fce(λ).
(5)

If we now take the ratio between Eq. (5) and (4), one obtains the same ratio as in Eq. (3), namely:

Icie(λ,h)Ice(λ,h)=fci(λ)fi(λ).
(6)

The experimental ratios Icie(λ, h)/Ice(λ, h) in Fig. 5 shows that indeed they are again invariant with depth and furthermore that they are superimposible with the corresponding curves in Fig. 4. This confirms the hypotheses made in formulating Eq. (1)(6).

In summary, the transmission mechanism through a single aperture can be divided into three independent steps, namely coupling in, transmission and coupling out. The transmitted intensity can be seen as the product of functions associated with each step. The coupling in function reflects the amount of incident light converted into evanescent waves at the entrance of the subwavelength aperture. The evanescent field is then exponentially attenuated by the cut-off function of the hole. At the exit side, the evanescent waves recombine into propagative waves with an efficiency given by the coupling out function.

Fig. 5. Ratio between the transmission spectra of Fig. 3 and those of holes of same dimensions surrounded by a bull’s eye structure on the exit side only.

One consequence is that, for a given hole depth, shape, and lateral dimensions, the only way to modify the transmission properties of a subwavelength aperture is to act upon the coupling and decoupling of light. Indeed, the cut-off function follows in any case the exponential law of a single aperture without corrugations, whereas the coupling in and out functions can be controlled by patterning the metal surface. If the surface presents a periodic texture, the coupling process is mediated by exciting SPPs on the grating. In the case of an input corrugation, this gives rise to a strong enhancement of the transmission at wavelengths slightly higher than the periodicity. If a grating is patterned on the output surface, the light exiting the structure at a given SPP wavelength is mainly reemitted in a narrow beam. The input and the output coupling functions can be optimized as shown in other studies [16

16. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001). [CrossRef]

,17

17. T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

,19

19. 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]

] by tailoring for instance the width and depth of the groove structures for a given transmission wavelength. It should be noted that the presence of groove modes plays a key role both for the beaming induced by the output corrugation and for the field enhancement on the input side [19

19. 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]

].

It should also be pointed out that the coupling and decoupling process for a single subwavelength hole without corrugations also involves surface plasmons. These modes are different from SPPs launched on a grating, as they are localized surface plasmons on the aperture ridge and have no dispersion [26

26. 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. (to be published).

]. Their excitation leads to the presence of broad peaks in the transmission spectra of the holes. The boost in transmission is not as strong as the enhancement provided by SPPs launched along a corrugated surface, therefore its spectral effects can be hidden if the attenuation through the hole is too important. The presence of a secondary peak at λ=800 nm for the shallowest samples of Fig. 1 and Fig. 3 are in fact signatures of such localized modes.

For hole arrays, two transmission regimes were predicted and found depending on the hole depth [4

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

,9

9. L. Martín-Moreno, F.J. García-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]

]. For deep holes, the SPPs of the two surfaces remain uncoupled and the intensity is also exponentially sensitive to the aperture depth, while for shallow holes the SPP modes of both sides couple leading to a leveling off of the intensity. The results presented here show that both single and doubled sided bull’s eye structures display only the exponential regime on hole depth even for the shallowest samples. For the single sided structure, it is not surprising, however, one might have expected coupling between modes in the double sided structures. This is probably explained by the fact that in the case of single apertures surrounded by corrugations, the interaction area (i.e. the hole section) between the two surfaces is very small compared to the overall structure. In the case of hole arrays, each period provides an interaction channel.

One question that remains is whether the output side corrugation contributes to the transmission enhancement. In conditions similar to our experiments, a theoretical analysis indicates just a weak contribution [13

13. 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]

]. Our results can not provide any information in this regard because we are not able to collect the total transmitted intensity over 2π. However the reciprocity principle requires that if everything is symmetrical, then it doesn’t matter which side a corrugation is in order for the enhancement to occur. In our experiments, it is not possible to obtain completely symmetric conditions since the wave-front is modified after passage through the aperture and we are unable to recreate such a complex wave-front in the reverse path. In this regard, it should be remembered that in a hole array, the wave-front of the transmitted light and the incident light are both planar and the transmission enhancement is independent on which side the SPP modes are located [2

2. 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]

,5

5. E. Altewischer, M.P. van Exter, and J.P. Woerdman, “Non reciprocal reflection of a subwavelength hole array,” Opt. Lett. 28, 1906–1908 (2003). [CrossRef] [PubMed]

,6

6. 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 (2004). [CrossRef] [PubMed]

].

Acknowledgments

The authors gratefully acknowledge H.J. Lezec for stimulating discussions and suggestions. We thank the E.C. under project FP6 NMP4-CT-2003-505699 for support.

References and links

1.

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

2.

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]

3.

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmon enhance optical transmission through subwavelength holes,” Phys. Rev. B 586779–6782 (1998). [CrossRef]

4.

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

5.

E. Altewischer, M.P. van Exter, and J.P. Woerdman, “Non reciprocal reflection of a subwavelength hole array,” Opt. Lett. 28, 1906–1908 (2003). [CrossRef] [PubMed]

6.

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 (2004). [CrossRef] [PubMed]

7.

J.A. Porto, F.J. García-Vidal, and J.B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

8.

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]

9.

L. Martín-Moreno, F.J. García-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]

10.

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]

11.

J.-M. Vigoureux, “Analysis of the Ebbesen experiment in the light of evanescent short range diffraction,” Opt. Comun. 198, 257–263 (2001). [CrossRef]

12.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Strong discontinuities in the complex photonic band structure of transmission metallic gratings,” Phys. Rev. B 63, 33107 (2001). [CrossRef]

13.

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]

14.

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]

15.

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]

16.

T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001). [CrossRef]

17.

T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

18.

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

19.

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]

20.

F.J. García-Vidal, L. Martín-Moreno, H.J. Lezec, and T.W. Ebbesen, “Focusing light with a subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003). [CrossRef]

21.

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

22.

A. P. Hibbins and J. R. Sambles, “Grating enhanced microwave transmission through a subwavelength aperture in a thick metal plate,” Appl. Phys. Lett 81, 4661–4663 (2002). [CrossRef]

23.

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

24.

E. Moreno, F.J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004). [CrossRef]

25.

P. Kramper, M. Agio, C.M. Soukoulis, A. Birner, F. Müller, R.B. Wehrpohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett 92, 113903 (2004). [CrossRef] [PubMed]

26.

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. (to be published).

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Focus Issue: Extraordinary light transmission through sub-wavelength structured surfaces

History
Original Manuscript: June 11, 2004
Revised Manuscript: July 30, 2004
Published: August 9, 2004

Citation
A. Degiron and T. Ebbesen, "Analysis of the transmission process through single apertures surrounded by periodic corrugations," Opt. Express 12, 3694-3700 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3694


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References

  1. H.A. Bethe, ???Theory of diffraction by small holes,??? Phys, Rev. 66, 163-182 (1944). [CrossRef]
  2. 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]
  3. H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, ???Surface plasmon enhance optical transmission through subwavelength holes,??? Phys. Rev. B 58 6779-6782 (1998). [CrossRef]
  4. A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, ???Effects of hole depth on enhanced light transmission through subwavelength apertures,??? Appl. Phys. Lett. 81, 4327-4329 (2002). [CrossRef]
  5. E. Altewischer, M.P. van Exter, and J.P. Woerdman, ???Non reciprocal reflection of a subwavelength hole array,??? Opt. Lett. 28, 1906-1908 (2003). [CrossRef] [PubMed]
  6. 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 (2004). [CrossRef] [PubMed]
  7. J.A. Porto, F.J. García-Vidal, and J.B. Pendry, ???Transmission resonances on metallic gratings with very narrow slits,??? Phys. Rev. Lett. 83, 2845-2848 (1999). [CrossRef]
  8. 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]
  9. L. Martín-Moreno, F.J. García-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]
  10. 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]
  11. J.-M. Vigoureux, ???Analysis of the Ebbesen experiment in the light of evanescent short range diffraction,??? Opt. Comun. 198, 257-263 (2001). [CrossRef]
  12. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, ???Strong discontinuities in the complex photonic band structure of transmission metallic gratings,??? Phys. Rev. B 63, 33107 (2001). [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, ???Enhanced light transmission through a single subwavelength aperture,??? Opt. Lett. 26, 1972-1974 (2001). [CrossRef]
  17. T. Thio, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, G.D. Lewen, A. Nahata, and R.A. Linke, ???Giant optical transmission of sub-wavelength apertures: physics and applications,??? Nanotechnology 13, 429-432 (2002). [CrossRef]
  18. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martín-Moreno, F.J. García-Vidal, and T.W. Ebbesen, ???Beaming light from a subwavelength aperture,??? Science 297, 820-822 (2002). [CrossRef] [PubMed]
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