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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 16 — Aug. 9, 2004
  • pp: 3664–3672
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Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures

Hua Cao and Ajay Nahata  »View Author Affiliations


Optics Express, Vol. 12, Issue 16, pp. 3664-3672 (2004)
http://dx.doi.org/10.1364/OPEX.12.003664


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Abstract

We demonstrate that the resonantly enhanced transmission spectrum associated with a periodic array of subwavelength apertures is dependent upon the shape of the apertures. This is demonstrated using coherent terahertz radiation and aperture arrays fabricated in 75 µm thick stainless steel foils. We examine rectangular apertures with different aspect ratios as well as circular apertures. In the absence of periodicity in the arrays, no resonance features are present. For periodic arrays, we show that the ratio of the transmission coefficients for the two lowest order resonances can be directly related to the ratio of the appropriate aperture dimensions. From the time-domain waveforms, we find two independent, yet phase-coherent, transmission processes: non-resonant transmission related to the simple transmission through subwavelength apertures and a time-delayed resonant transmission related to the interaction of the THz pulse with the periodic aperture array. In these waveforms, we also observe a sign inversion for the primary bipolar pulse relative to the reference. This is shown to be a simple consequence of diffraction.

© 2004 Optical Society of America

1. Introduction

The demonstration of enhanced optical transmission through periodic arrays of subwavelength apertures [1

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]

] has elicited significant interest in recent years. While much of the initial work in this topic concentrated on understanding the underlying physical principles behind this phenomenon, there has been significant expansion recently in the range of investigations. For example, several studies have explored and demonstrated this phenomenon at mid-infrared [2

2. Y.-H. Ye and J.-Y. Zhang, “Middle-infrared transmission enhancement through periodically perforated metal films,” Appl. Phys. Lett. 84, 2977–2979 (2004). [CrossRef]

] and far-infrared [3

3. J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003). [CrossRef]

6

6. F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2744 (2004). [CrossRef]

] frequencies. In this latter spectral range, we have shown that periodic arrays fabricated in metal films allow for larger transmission coefficients and narrower resonance linewidths than have been observed at visible frequencies [4

4. H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004 [CrossRef] [PubMed]

]. There have also been several examples demonstrating the broader range of potential applications that may arise from the use of these structures. These include the demonstration of enhanced fluorescence from molecules attached to the metal surface [7

7. Y. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Opt. Lett. 28, 507–509 (2003). [CrossRef] [PubMed]

], highly directional radiation from the structured metal [8

8. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 220–222 (2002). [CrossRef]

], and the enhancement of nonlinear optical processes [9

9. A. Nahata, R.A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion using periodically nanostructured metal films,” Opt. Lett. 28, 423–425 (2003). [CrossRef] [PubMed]

].

2. Experimental details

The aperture arrays were fabricated in free-standing 75 µm thick stainless steel foils. We have previously shown that this substrate medium works well for the observation of resonantly enhanced transmission at THz frequencies [4

4. H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004 [CrossRef] [PubMed]

]. We first fabricated aperture arrays in a periodic square lattice with a center-to-center spacing of 1 mm. Four separate arrays, shown schematically in Fig. 1, were fabricated, each with a different aperture shape: Array A consisted of 400 µm diameter circular apertures, Array B consisted of 400 µm×400 µm square apertures, Array C consisted of 400 µm×300 µm rectangular apertures, and Array D consisted of 400 µm×200 µm rectangular apertures. We also fabricated a second set of apertures arrays utilizing the four aperture shapes described above. However, in this case, the aperture spacing was aperiodic and designed to yield non-resonant transmission behavior. It should be noted that the aperture-to-aperture spacing in these latter four arrays was not completely random, since a minimum spacing was enforced to eliminate the possibility of overlapping apertures [11

11. A. Dogariu, A. Nahata, R.A. Linke, L.J. Wang, and R. Trebino, “Optical pulse propagation through metallic nano-apertures,” Appl. Phys. B 74, s69–s73 (2002). [CrossRef]

]. Nevertheless, these four aperiodic arrays exhibited no resonance features and demonstrated qualitatively identical transmission properties. Therefore, we only show the observations of the 400 µm×400 µm square aperture array (Array E) that was fabricated to yield non-resonant behavior. In all cases, the aperture arrays measured 5 cm×5 cm.

The arrays were characterized using a standard THz time-domain spectroscopy system [12

12. D. Grischkowsky, in Frontiers in Nonlinear Optics, edited by H. Walther, N. Koroteev, and M.O. Scully (Institute of Physics Publishing, Philadelphia, 1992) and references therein.

]. Conventional photoconductive devices were used for both emission and detection. As is common in such spectroscopy systems, two off-axis paraboloidal mirrors were used to collect, collimate, and refocus the THz radiation from the emitter to the detector. The arrays were attached to a solid metal plate with a 5 cm×5 cm opening that was placed at the center of these two mirrors in the spectroscopy system. The 1/e THz beam diameter was smaller than the aperture opening in the metal holder, and therefore less than the spatial extent of the array. This was designed to minimize edge effects due to the finite size of the array. Reference spectra were obtained with the bare metal holder placed in the system. The THz radiation was horizontally polarized and normally incident on the aperture array. The orientation of the apertures with respect to the polarization direction is shown in Fig. 1.

Fig. 1. The four different aperture shapes used in this investigation and the polarization direction of the normally incident THz pulses. Array A consists of 400 µm diameter circular apertures, Array B consists of 400 µm×400 µm square apertures, Array C consists of 400 µm×300 µm rectangular apertures, Array D consists of 400 µm×200 µm rectangular apertures, and Array E consists of 400 µm×400 µm square apertures. In Arrays A-D, the apertures are periodically spaced by 1 mm. In Array E, the spacing is designed to yield a non-resonant transmission behavior. The dashed lines correspond to the aperture dimension at 45° with respect to the polarization direction, along the (+1, +1) axis. This last dimension is necessary for Fig. 5.

Time-domain THz spectroscopy allows for the measurement of the transmitted THz electric field [12

12. D. Grischkowsky, in Frontiers in Nonlinear Optics, edited by H. Walther, N. Koroteev, and M.O. Scully (Institute of Physics Publishing, Philadelphia, 1992) and references therein.

]. In order to compare the spectral transmission characteristics of the different arrays, we normalized the time-domain waveforms to the aperture fill fraction of Array A. Specifically, the aperture fill fraction of Array A is 0.1257. The waveforms of the other four arrays are corrected to match this fill fraction. Thus, the time-domain waveforms for Arrays B, C, D, and E are divided by 1.273, 0.955, 0.637, and 0.159, respectively. We then transformed the time-domain data to the frequency domain, allowing us to determine independently both the magnitude and phase of the normalized amplitude transmission coefficient, tN (f), using the relation

tN(f)=Etransmitted(f)Ereference(f)=tN(f)exp[iφN(f)].
(1)

In this expression, Ereference and Etransmitted are the reference and normalized transmitted THz fields, respectively, |tN(f)| and φN(f) are the magnitude and phase of the normalized amplitude transmission coefficient, respectively, and f is the THz frequency. Using this procedure, the normalized amplitude transmission coefficient of Array A is the same as the absolute amplitude transmission coefficient. Absolute coefficients for the other four arrays require an inverse correction for the aperture fill fraction.

3. Experimental results and discussion

The time-domain waveforms corresponding to the transmitted THz pulses through the five different aperture arrays, as well as the reference waveform, are shown in Fig. 2. The waveforms are offset from the origin for clarity. Expanded versions of these time-domain waveforms are given in the accompanying multimedia file. In contrast to our earlier demonstration of resonantly enhanced THz transmission [4

4. H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004 [CrossRef] [PubMed]

], the temporal scan window has been extended to more accurately obtain the linewidths of the resonance features. While each waveform was initially measured over a 320 ps temporal window, the waveforms in Fig. 2 were all truncated at 267 ps, since no useful signal information was present beyond this time delay value. There are several interesting features to note in these time-domain traces. If we compare the waveforms of Array A (circular apertures) and Array B (square apertures), there are some apparent differences. The oscillations after the main bipolar pulse for Array A exhibit a smaller peak-to-peak value than those of Array B, but extend for much longer in time. In general, the magnitude of the oscillations corresponds to the magnitude of the resonance feature, while the oscillation duration corresponds to the linewidth of that feature. As the aspect ratio of the square aperture increases, moving from Array B to D, the peak-to-peak value of the oscillations decreases, but the duration of the oscillations remains largely unchanged.

In comparing the reference waveform and the waveform associated with Array E to the waveforms obtained for the four periodic arrays, it appears that there are two independent, yet phase-coherent, contributions to the waveforms for Arrays A-D. The first contribution is a bipolar pulse that is similar in form to the reference waveform. This bipolar waveform does not exhibit any additional time delay relative to the reference pulse, within experimental error. We attribute this feature to the nonresonant transmission of the broadband THz pulses through the subwavelength aperture arrays, since it is present in all of the waveforms associated with the periodic and aperiodic arrays. The second contribution present in the waveforms associated with Arrays A-D is a damped oscillatory waveform. These oscillations contain the spectral features of the transmission resonances, as shown below. We attribute this latter contribution to the resonant interaction of the THz pulse with the periodically perforated metal film. It is important to note that the waveforms associated with Arrays A-E in Fig. 2 are multiplied by a factor of 10 for clarity. Thus, the nonresonant transmission (first contribution mentioned above) is strongly attenuated. The amplitude of the damped oscillations, though small relative to the reference, corresponds to a large amplitude transmission coefficient with a narrow resonance linewidth. We discuss this in detail below.

Fig. 2. Measured time-domain THz waveforms transmitted through five different aperture arrays fabricated in 75 µm thick free-standing stainless steel foils. [Expanded Fig. 2 (a), (b), (c)]

λpeak=Pi2+j2nsp=Pi2+j2εd.
(2)

Here, P is the physical periodicity, εd is the dielectric constant of the interfacial dielectric media (εd=1 in our case), and i and j are indices corresponding to the resonance order. Thus, we would expect to see only two SPP resonances in this frequency window at ~0.33 THz and 0.46 THz, corresponding to indices (i,j) equal to (±1,0) and (±1,±1), respectively. The fact that we observe resonance frequencies at slightly lower frequencies than predicted by Eq. (2) and that these frequencies vary slightly between Arrays A-D is not surprising, since Eq. (2) is only strictly valid for a plane metal film. A more correct description is expected to depend upon the shape, spatial distribution, and fill fraction of the apertures.

From Fig. 3, it is apparent that the magnitude of the normalized amplitude transmission coefficients of the lowest frequency resonances varies with aperture shape. As expected from the time-domain waveforms, the normalized transmission coefficient of the lowest order resonance is largest for the square apertures. The corresponding absolute transmission coefficient of the (±1,0) resonance for that aperture shape is ~0.8. This represents the largest transmission coefficient, to our knowledge, for such structures. The measured 3-dB linewidth for Array A was ~8 GHz, while the 3-dB linewidths for Arrays B-D varied between 9.5 GHz and 10.5 GHz. This is consistent with our earlier discussion regarding the duration of the oscillations in the time-domain waveforms. In contrast to our earlier measurements, we do not believe that these values are limited by the measurement technique. Using the phase spectra for each aperture, we can calculate the group delay for the transmitted time-domain waveform. Dogariu et al. have shown that this calculation matches experimentally observed values at optical frequencies [11

11. A. Dogariu, A. Nahata, R.A. Linke, L.J. Wang, and R. Trebino, “Optical pulse propagation through metallic nano-apertures,” Appl. Phys. B 74, s69–s73 (2002). [CrossRef]

]. It is also worth noting in the phase spectra that the low frequency phase shift for all five arrays is ~±, as expected from the discussion above.

One of the more interesting aspects of Fig. 3 is the observation that the ratio of the normalized amplitude transmission coefficient of the (±1,0) peak to the normalized amplitude transmission coefficient of the (±1,±1) peak varies with aperture shape. We can understand this variation based on the geometrical differences between the apertures. We demonstrate this quantitatively. For each aperture shape we subtract a scaled version of the magnitude spectrum for the aperiodic array from the magnitude spectrum of the corresponding periodic array. Thus, for example, we subtracted a scaled version of the magnitude spectrum of Array E from the magnitude spectrum of Array B. To first order, this removes the background transmission spectrum leaving only the transmission resonances. We use these modified magnitude spectra to demonstrate the aperture shape dependence of the transmission spectra.

Fig. 3. Magnitude of the normalized amplitude transmission spectra for (upper) Arrays A and B and (lower) Arrays B-E.
Fig. 4. Phase of the normalized amplitude transmission spectra for (upper) Arrays A and B and (lower) Arrays B-E.

Fig. 5. The ratio of the normalized amplitude transmission coefficients versus the ratio of relevant aperture dimensions. See text for details of the definitions of these ratios. The filled markers correspond to data points for the four periodic arrays. The dashed line is a linear least squares fit to the data for Arrays B-D.

Acknowledgments

We thank S. Blair for helpful discussions.

Note Added in Proof: We recently learned of a very similar study concerning the effect of the aperture shape on the enhanced transmission spectrum at optical frequencies by Koerkamp et al. [19

19. K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901/1–4 (2004). [CrossRef]

]. Their results and conclusions differ dramatically from those presented in this publication. The observed discrepancy may arise, in part, from the considerably different dielectric properties of the metal films between optical and THz frequencies. Further investigation is required.

References and links

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]

2.

Y.-H. Ye and J.-Y. Zhang, “Middle-infrared transmission enhancement through periodically perforated metal films,” Appl. Phys. Lett. 84, 2977–2979 (2004). [CrossRef]

3.

J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306 (2003). [CrossRef]

4.

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express 12, 1004–1010 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004 [CrossRef] [PubMed]

5.

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004). [CrossRef] [PubMed]

6.

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84, 2742–2744 (2004). [CrossRef]

7.

Y. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Opt. Lett. 28, 507–509 (2003). [CrossRef] [PubMed]

8.

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 220–222 (2002). [CrossRef]

9.

A. Nahata, R.A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion using periodically nanostructured metal films,” Opt. Lett. 28, 423–425 (2003). [CrossRef] [PubMed]

10.

R. Gordon, A.G. Brolo, A. McKinnon, A. Rajora, B. Leatham, and K.L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92, 037401 (2004). [CrossRef] [PubMed]

11.

A. Dogariu, A. Nahata, R.A. Linke, L.J. Wang, and R. Trebino, “Optical pulse propagation through metallic nano-apertures,” Appl. Phys. B 74, s69–s73 (2002). [CrossRef]

12.

D. Grischkowsky, in Frontiers in Nonlinear Optics, edited by H. Walther, N. Koroteev, and M.O. Scully (Institute of Physics Publishing, Philadelphia, 1992) and references therein.

13.

A. Nahata and T.F. Heinz, “Reshaping of freely propagating terahertz pulses by diffraction,” IEEE J. Sel. Top. Quantum Electron. 2, 701–708 (1996). [CrossRef]

14.

Lord Rayleigh, “On the passage of waves through fine slits in thin opaque screens,” Proc. Roy. Soc. A 89, 194–219 (1913). [CrossRef]

15.

C.J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954). [CrossRef]

16.

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

17.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Vol. 111 of Springer Tracts in Modern Physics, Springer-Verlag, Berlin, 1988).

18.

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 83, 6779–6782 (1998). [CrossRef]

19.

K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901/1–4 (2004). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6690) Optics at surfaces : Surface waves

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

History
Original Manuscript: June 2, 2004
Revised Manuscript: July 15, 2004
Published: August 9, 2004

Citation
Hua Cao and Ajay Nahata, "Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures," Opt. Express 12, 3664-3672 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3664


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References

  1. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, ???Extraordinary optical transmission through subwavelength hole arrays,??? Nature 391, 667-669 (1998). [CrossRef]
  2. Y.-H. Ye and J.-Y. Zhang, ???Middle-infrared transmission enhancement through periodically perforated metal films,??? Appl. Phys. Lett. 84, 2977-2979 (2004). [CrossRef]
  3. J. Gomez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, ???Enhanced transmission of THz radiation through subwavelength holes,??? Phys. Rev. B 68, 201306 (2003). [CrossRef]
  4. H. Cao and A. Nahata, "Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures," Opt. Express 12, 1004-1010 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1004</a>. [CrossRef] [PubMed]
  5. D. Qu, D. Grischkowsky, and W. Zhang, ???Terahertz transmission properties of thin, subwavelength metallic hole arrays,??? Opt. Lett. 29, 896-898 (2004). [CrossRef] [PubMed]
  6. F. Miyamaru and M. Hangyo, ???Finite size effect of transmission property for metal hole arrays in subterahertz region,??? Appl. Phys. Lett. 84, 2742-2744 (2004). [CrossRef]
  7. Y. Liu and S. Blair, ???Fluorescence enhancement from an array of subwavelength metal apertures,??? Opt. Lett. 28, 507-509 (2003). [CrossRef] [PubMed]
  8. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, ???Beaming light from a subwavelength aperture,??? Science 297, 220-222 (2002). [CrossRef]
  9. A. Nahata, R.A. Linke, T. Ishi, and K. Ohashi, ???Enhanced nonlinear optical conversion using periodically nanostructured metal films,??? Opt. Lett. 28, 423-425 (2003). [CrossRef] [PubMed]
  10. R. Gordon, A.G. Brolo, A. McKinnon, A. Rajora, B. Leatham, and K.L. Kavanagh, ???Strong polarization in the optical transmission through elliptical nanohole arrays,??? Phys. Rev. Lett. 92, 037401 (2004). [CrossRef] [PubMed]
  11. A. Dogariu, A. Nahata, R.A. Linke, L.J. Wang, and R. Trebino, ???Optical pulse propagation through metallic nano-apertures,??? Appl. Phys. B 74, s69-s73 (2002). [CrossRef]
  12. D. Grischkowsky, in Frontiers in Nonlinear Optics, edited by H. Walther, N. Koroteev, and M.O. Scully (Institute of Physics Publishing, Philadelphia, 1992) and references therein.
  13. A. Nahata and T.F. Heinz, ???Reshaping of freely propagating terahertz pulses by diffraction,??? IEEE J. Sel. Top. Quantum Electron. 2, 701-708 (1996). [CrossRef]
  14. Lord Rayleigh, ???On the passage of waves through fine slits in thin opaque screens,??? Proc. Roy. Soc. A 89, 194-219 (1913). [CrossRef]
  15. C.J. Bouwkamp, ???Diffraction theory,??? Rep. Prog. Phys. 17, 35-100 (1954). [CrossRef]
  16. H. Bethe, ???Theory of diffraction by small holes,??? Phys. Rev. 66, 163-182 (1944). [CrossRef]
  17. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Vol. 111 of Springer Tracts in Modern Physics, Springer-Verlag, Berlin, 1988).
  18. 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 83, 6779-6782 (1998). [CrossRef]
  19. K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, ???Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,??? Phys. Rev. Lett. 92, 183901/1-4 (2004). [CrossRef]

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