OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 6920–6930
« Show journal navigation

Enhanced optical transmission at the cutoff transition

E. Laux, C. Genet, and T. W. Ebbesen  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 6920-6930 (2009)
http://dx.doi.org/10.1364/OE.17.006920


View Full Text Article

Acrobat PDF (292 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The phenomenon of extraordinary transmission in the optical regime for circular hole arrays in optically thick metal films is studied as a function of hole size and depth. In the limit of small holes compared to the depth, the transmission properties follow a waveguide type behavior. By describing the transmission process as resulting from the interference between a resonant and a non-resonant contribution, a transition is clearly revealed through the specific spectral variations of the resonance at a given hole depth. This transition is associated to a change in the attenuation through the hole as its size increases, and corresponds to the optimal condition for surface plasmon excitation.

© 2009 Optical Society of America

1. Introduction

Since the first observations of the extraordinary optical transmission (EOT) phenomenon [1

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

], hole arrays have generated wide interest as they offer unique features and possibilities which have led to a variety of applications [2

2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

] in different fields from sensors [3

3. J. V. Coe, S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. Sudnitsyn, and F. Hrovat, “Extraordinary IR Transmission with metallic arrays of subwavelength holes,” Anal. Chem. 78, 1384–1390 (2006). [CrossRef] [PubMed]

, 4

4. R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41, 1049–1057 (2008). [CrossRef] [PubMed]

] to photonic devices [5

5. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” to appear in Rev. Mod. Phys.

].

λ(i,j)=Pi2+j2εmεdεm+εd
(1)

Here, εm and εd are the dielectric constants of the metal and the dielectric medium forming the interfaces of the film, and (i, j) are the scattering orders of the square array. Note that the SP modes can be excited on both interfaces of the hole array, each giving rise to a set of transmission peaks which are offset by the difference in the εd of the dielectric media in contact with the metal. The actual peak positions are typically redshifted as compared to the prediction of Eq. (1) which can be explained by a Fano-type analysis [6

6. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). [CrossRef]

, 7

7. 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]

, 8

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

]. The EOT is sensitive to geometrical parameters such as the dimensions of the individual apertures [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]

, 10

10. F. J. García de Abajo, “Colloquim: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

, 11

11. 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]

, 12

12. K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85, 4316–4318 (2004). [CrossRef]

, 13

13. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength holes,” Opt. Express 16, 9571–9579 (2008). [CrossRef] [PubMed]

] and the optical properties of metal [14

14. F. Przybilla, A. Degiron, J.-Y. Laluet, C. Genet, and T.W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006). [CrossRef]

, 15

15. S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008). [CrossRef]

]. The role of the hole shape has for instance been studied extensively [16

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

, 17

17. A. Degrion and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A: Pure Appl. Opt. 7, S90–S96 (2005). [CrossRef]

] and it is clear that both the presence of localized modes and a cutoff function at level of the individual apertures can strongly modulate the transmission spectrum of an array.

Fig. 1. SEM images (magnification 65kx) of holes in a square array (period P = 460nm) made from 30×30 holes, milled through a 260nm thick Au film, with hole diameters d = 150nm(a) and d = 250nm(b)

Typically, the EOT phenomenon has been studied in the limit of hole sizes small compared to the resonance wavelength. In this subwavelength regime, the electromagnetic fields decay exponentially inside the hole with the hole depth [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]

, 11

11. 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]

]. Here we are particularly interested in analyzing the EOT in the transition through this cutoff limit. This is simply done by increasing the hole diameter d relative to the period and therefore to the transmission peak wavelength of the array. By doing this for different hole depths h, we can access in our analysis different ratios of h/d and h/λ.

We focus on the influence of hole diameter and depth and compare the measured peak intensities to waveguide theory and corresponding spectra to a Fano-type analysis. We find a clear evidence for a transition which influences the EOT phenomenon.

2. Spectral evolution as a function of hole size and depth

Circular hole arrays (30×30 holes), like those shown in Fig. 1, were milled on Au films using a focused ion beam (FIB). Different thicknesses (thickness h varying from 140–560nm) were prepared by sputtering Au on glass substrates. Array period was fixed at 460nm and the hole diameter for each array was gradually increased from 100 to 400nm and transmission spectra were recorded using a microscope coupled to a spectrometer, using a white collimated light beam and are shown in Fig. 2. It should be noted that the holes are not completely circular but have a slightly conical form and the consequent error on the hole diameters is estimated at ±5%.

The transmission spectra are characterized by a set of peaks and we will focus on the most isolated one, which is also at the longest wavelength, around 800nm, corresponding to the (i, j) = (1, 0) mode of the glass-metal interface, see Eq. (1). The fact that our analysis is carried out for hole arrays milled in an asymmetric dielectric environment (i.e. the dielectric media on both sides of the film are different, air and glass) enables us to isolate one SP mode (one transmission peak) associated to a specific interface and avoid the additional variable introduced by coupling between modes of the two interfaces. Such coupling which can result in peak broadening/splitting and enhancement has been carefully studied [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]

, 18

18. 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. bf200, 1–7 (2001). [CrossRef]

, 19

19. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijck, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008). [CrossRef]

].

Fig. 2. Transmission spectra of square arrays of circular holes (30×30 holes) with a period of 460nm milled through an Au film of thickness 180nm deposited on a glass substrate. The color scale corresponds to different hole sizes.

The (1, 0) transmission intensity increases with the hole size and the peak position shifts first to the red. For the hole sizes larger than 250nm, we observe that the resonances broaden and no longer shift to larger wavelengths.

3. Comparing the evolution of the EOT intensity with waveguide theory

Measurements such as those in Fig. 2 were repeated for different film thicknesses (hole depths). In Fig. 3, the (1, 0) transmission intensity has been plotted as a function of the area of the hole for each hole depth. These curves show a sigmoidal shape with 0 and 1 as the natural limits when the hole area becomes respectively very small and very large as compared to the period. For thin films (140–220nm) the transmission can exceed unity before dropping back to one as the holes size approaches the period. Some modulation is apparent in the curves and this will be discussed in part 4. As the films become thicker, the rise in intensity with hole area becomes slower as expected for such small holes.

A simple waveguide approach already helps in understanding the evolution of peak intensities of Fig 3. Within this frame, the transmission through a hole is a function of both the hole depths and the propagation constants of the waveguide modes. Considering each hole as a cylinder in a perfect metal conductor (PEC), we determine the associated wavevectors considering guided modes [20

20. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

]. For thick enough films and circular holes, the transmission is mainly governed by the fundamental TE 11 mode with associated wavevector:

k0=(2πλ)2(ar)2.
(2)

The value a is set by the geometry of the guide and in the case of a cylindrical structure is given by the first root of the first order Bessel function as a = 1.841.

Fig. 3. Normalized transmission peak intensities associated to the (1, 0) SP mode excited on the metal-glass interface for different film thickness as a function of hole diameter. This resonance enhances the transmission through the holes and for certain arrays, the normalized transmission can exceed unity (black horizontal line): the regime of EOT.

From the ratio between the incident wavelength λ and hole radius r set by the geometry of the guide, the modes are either propagating, when k 0 is imaginary or evanescent when k 0 turns real. In our work, we will essentially follow a given resonance λres and in the simple waveguide picture, the limit rc = λresa/2π below which all the guided modes become evanescent, is generally referred to as the cutoff radius.

At this point, we will solely concentrate on the attenuation that is induced by such a sub-wavelength waveguide. We define the transmission T as by the ratio between the input and output fluxes of the Poynting vector of a plane wave through such a waveguide. By doing this, we consider the holes as isolated and knowingly neglect the implications of the fact that the holes form an array. The transmission for radii smaller than rc is mainly governed by how the electromagnetic field is attenuated inside the guide as a function of depth, whereas above rc all the light that enters the holes is transmitted. To account for the penetration of the electromagnetic field into the metal, we increase the radius r of each waveguide by the corresponding skin depth (sd) evaluated at λres, while we still use the real hole size to determine the input flux in order to have the same normalization as for our experimental data (in such a way that for r>rc, the normalized transmission can be larger than 1). The transmission T is then given by:

T={(r+sd)2r2e2(ar+sd)2(2πλres)2hifr<rc(r+sd)2r2ifr>rc
(3)

In Fig. 4, the transmission peak intensities that were measured for different hole sizes and depths are plotted on a logarithmic scale together with the calculated transmissions through subwavelength cylindrical waveguides following Eq. (3). All the calculated curves meet for a specific hole size (~ 410nm hole diameter), associated with the cutoff beyond which light can propagate freely through the hole. This means that taken as classical waveguides, none of the studied holes is large enough to guide waves.

If we would consider the metal without skin depth (sd = 0), all the curves from Fig. 4 would be shifted to larger hole sizes, as each hole would appear smaller to the incoming light. For instance the cutoff radius would in this case fall around 470nm

Fig. 4. Normalized transmission peak intensities that were measured for varying hole sizes and depths. The continuous lines give the transmission expected through subwavelength cylindrical waveguides at 800nm, as given by Eq. (3)

The general evolution of the curves calculated from Eq. (3) follows well the experimental data, especially in the limit of films which are thick compared to the hole size. The transmission intensities found from the calculation are however 2–3 orders of magnitude smaller than what is measured by the experiments. More sophisticated models than Eq. (3) have been proposed to describe the optical behavior of single apertures but they consider either lossless metals [21

21. P. B. Catrysse, H. Shin, and S. Fan, “Propagating modes in subwavelength cylindrical holes,” J. Vac. Sci. Technol. B 23, 2675–2678 (2005). [CrossRef]

,22

22. C. Yeh and F. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008). [CrossRef]

] or square apertures ([23

23. R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a rela metal,” Opt. Express 13, 1933-38 (2005). [CrossRef] [PubMed]

,24

24. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006). [CrossRef]

] which do not directly apply to the present data. In addition, collective effects need to be taken into account which is precisely why arrays of holes, having SP resonances, generate far higher transmissions than single apertures as the comparison above shows.

4. Analysis of the evolution of the transmission peaks

Although the general evolution of the intensities at resonance seems to follow a waveguide behavior, it is obvious that it is not possible to explain this complex phenomenon thoroughly without considering the influence of SP modes excited at the surface of the array. This is particularly clear for the small depths (see Fig. 3 and 4), which has led us to chose for this analysis a specific depth of h = 190nm. The SP modes that are induced by the periodicity of the holes array according to Eq. (1), need to be considered together with the direct scattering generated by each hole. In fact, the transmission process through an array of holes can be seen as an interference between a non-resonant contribution given by the transmission through each hole, taken as isolated, and a resonant contribution stemming from the excitation of a SP mode. This contribution amounts to a coupling between the holes in the extended array [6

6. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). [CrossRef]

, 7

7. 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]

, 8

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

]. This picture clearly oversimplifies the problem as supplementary contribution do affect the phenomenon (see [25

25. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008). [CrossRef] [PubMed]

,26

26. F. J. Garca-Vidal, E. Moreno, J. A. Porto, and L. Martn-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005). [CrossRef]

] for a more realistic theoretical description), but yet, it can provide some interesting insight into the transmission process as we will see below.

Fig. 5. Normalized transmission spectra measured for different hole sizes in a 190nm thin Au film deposited on a glass substrate. The numbers on the right-hand side of the graph give hole diameters in nanometers. In the chosen spectral bandwidth, each spectrum is fitted using Eq. (4)

Following this picture and as detailed in [7

7. 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]

, 8

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

], the profile of the transmission coefficient T takes the specific shape as a function of the frequency a of the field:

T=α[ω(ω0Δ)ρ]2[ω(ω0Δ)]2+Γ2.
(4)

Δω=12πPΓωωω.
(5)

Figure 6 displays the variation of the transmission peak intensity as a function of the hole diameter. The peak intensity increases with the hole diameter until a diameter of about 250nm, from where it starts to saturate. First considering the peak positions as globally stationary as the holes get larger, the data shown on Fig. 6 is grossly reminiscent of what is expected for a waveguide with a cutoff diameter (at a fixed wavelength) around 250nm

Fig. 6. Normalized transmission peak intensity measured as a function of hole size.

This can be refined, by analyzing the evolution of all the fitting parameters. Their specific variations provides further evidence for a transition that occurs for hole diameters around 250nm for the chosen depth.

Finally, the fitting results for the global prefactor α are plotted in Fig. 8. This prefactor reflects the transmittance of the isolated hole. Bethe has suggested that for subwavelength holes in perfect metal films infinitely thin, this prefactor should be associated with an effective (magnetic) dipole [28

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

]. The non-resonant contribution is thus expected to follow globally the dipolar (d/λres)4 scaling. This seems to be actually verified for the smallest of our holes, as seen on Fig. 8. To understand this, we note that in this case both the hole sizes (d= 100 – 250nm) and the hole depth (h = 190nm) are much smaller than the resonance wavelength λres ~ 800nm. Within these ranges, the exponential decay of the field through a hole in an array is hence a rather slow varying function of the hole diameter, exactly as in Bethe’s idealized picture. This scaling fails for larger holes and is an additional signature of the differences in the transmission process between small and large holes, the qualitative change being again located around a diameter of 250nm. In a recent study, Nikitin et al. [29

29. A. Yu. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfet electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008). [CrossRef]

] have addressed this problem theoretically in the context of isolated holes milled in a perfect metal films of various thickness. The optical properties of very small holes milled through thin films are essentially dictated by a large induced dipole moment. For larger holes however, multipole moments must be taken into account. As these higher terms can be associated to higher waveguide modes for a given finite hole depth, it is not surprising to see an abrupt increase in the global prefactor α at the cutoff transition.

Fig. 7. Evolution of the fitting parameters (a) width Γ (at FWHM of the resonance), (b) spectral shifts Δ from the natural resonance position λ 0 and (c) strength ratio ρ between the two contributions as a function of the hole diameter.
Fig. 8. Evolution of the global prefactor α associated to the (non-resonant) transmittance through each hole. Fitting results given from Eq. (4) are plotted as black squares. The red line displays a simple (d/λres)4 dependence.

It should be noted that this transition does not only have repercussions on the transmission process, but also strongly modifies nonlinear effects, such as increasing second harmonic generation (SHG) [33

33. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangersma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

]. Working at a wavelength of 800nm, Nieuwstadt et al. [33

33. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangersma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

] also report evidence for the cutoff transition for hole widths around 250nm, in good agreement with our results. The reason that this transition is defined for much smaller holes than what is calculated from Eq. (2), lies in the properties of real metals, neglected in the PEC approximation. Different work [23

23. R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a rela metal,” Opt. Express 13, 1933-38 (2005). [CrossRef] [PubMed]

, 24

24. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006). [CrossRef]

, 32

32. F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002). [PubMed]

, 34

34. S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007). [CrossRef] [PubMed]

] have addressed this issue in the context of nanoscale holes, and confirmed that the interaction of the electromagnetic field with the metal enables the propagation of much longer wavelengths inside a metal waveguide than what can be expected in the PEC approximation.

In conclusion, hole size and depth are not independent parameters in the transmission through circular holes arrays. By analyzing the transmission as a function of hole diameter, a waveguide behavior is clearly seen although the transmission intensity can only be accounted for by the presence of SPs. When the holes start to sustain propagating modes, a transition in the transmission process is revealed, which defines an effective cutoff diameter (for a given wavelength) of the hole. This transition is characterized in particular by a strong broadening of the resonance peak and by a maximum shift in the resonance position. It is worth noting that such a transition appears to be linked to the optimal SP excitation condition on the hole array which is important for sensing applications and more generally speaking for coupling molecules and surface plasmons.

Acknowledgments

The author would like to thank Frederic Przybilla for fruitful discussions. This work has been funded by the French Agence Nationale de la Recherche under contract ANR 06-BLAN-0275.

References and links

1.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

2.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

3.

J. V. Coe, S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. Sudnitsyn, and F. Hrovat, “Extraordinary IR Transmission with metallic arrays of subwavelength holes,” Anal. Chem. 78, 1384–1390 (2006). [CrossRef] [PubMed]

4.

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41, 1049–1057 (2008). [CrossRef] [PubMed]

5.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” to appear in Rev. Mod. Phys.

6.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). [CrossRef]

7.

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]

8.

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

F. J. García de Abajo, “Colloquim: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

11.

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]

12.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85, 4316–4318 (2004). [CrossRef]

13.

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength holes,” Opt. Express 16, 9571–9579 (2008). [CrossRef] [PubMed]

14.

F. Przybilla, A. Degiron, J.-Y. Laluet, C. Genet, and T.W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006). [CrossRef]

15.

S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Influence of material properties on extraordinary optical transmission through hole arrays,” Phys. Rev. B 77, 075401 (2008). [CrossRef]

16.

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

17.

A. Degrion and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A: Pure Appl. Opt. 7, S90–S96 (2005). [CrossRef]

18.

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. bf200, 1–7 (2001). [CrossRef]

19.

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijck, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77, 115437 (2008). [CrossRef]

20.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

21.

P. B. Catrysse, H. Shin, and S. Fan, “Propagating modes in subwavelength cylindrical holes,” J. Vac. Sci. Technol. B 23, 2675–2678 (2005). [CrossRef]

22.

C. Yeh and F. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008). [CrossRef]

23.

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a rela metal,” Opt. Express 13, 1933-38 (2005). [CrossRef] [PubMed]

24.

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006). [CrossRef]

25.

H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008). [CrossRef] [PubMed]

26.

F. J. Garca-Vidal, E. Moreno, J. A. Porto, and L. Martn-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005). [CrossRef]

27.

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gomez Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76, 241102 (2007). [CrossRef]

28.

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

29.

A. Yu. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfet electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008). [CrossRef]

30.

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

31.

E. Popov, N. Bonod, M. Neviere, H. Rigneault, P.-F. Lenne, and P. Chaumet, “Surface plasmon excitation on a single subwavelength hole in a metallic sheet,” Appl. Opt. 44, 2332–2337 (2005). [CrossRef] [PubMed]

32.

F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002). [PubMed]

33.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangersma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

34.

S. Collin, F. Pardo, and J.-L. Pelouard, “Waveguiding in nanoscale metallic apertures,” Opt. Express 15, 4310–4320 (2007). [CrossRef] [PubMed]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(240.6680) Optics at surfaces : Surface plasmons
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: December 4, 2008
Revised Manuscript: February 2, 2009
Manuscript Accepted: February 4, 2009
Published: April 13, 2009

Citation
E. Laux, C. Genet, and T. W. Ebbesen, "Enhanced optical transmission at the cutoff transition," Opt. Express 17, 6920-6930 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-6920


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
  2. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007). [CrossRef] [PubMed]
  3. J. V. Coe, S. M. Williams, K. R. Rodriguez, S. Teeters-Kennedy, A. Sudnitsyn, and F. Hrovat, "Extraordinary IR Transmission with metallic arrays of subwavelength holes," Anal. Chem. 78, 1384-1390 (2006). [CrossRef] [PubMed]
  4. R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, " A new generation of sensors based on extraordinary optical transmission," Acc. Chem. Res. 41, 1049-1057 (2008). [CrossRef] [PubMed]
  5. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, "Light passing through subwavelength apertures," to appear in Rev. Mod. Phys.
  6. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961). [CrossRef]
  7. 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]
  8. C. Genet, M. P. van Exter, and J. P. Woerdmann, "Fano-type interpretation of red-shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331-336 (2003). [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. F. J. García de Abajo, " Colloquim: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007). [CrossRef]
  11. 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]
  12. K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Influence of hole size on the extraordinary transmission through subwavelength hole arrays," Appl. Phys. Lett. 85, 4316-4318 (2004). [CrossRef]
  13. F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J,  Bravo-Abad, F. J. García -Vidal, and L. Martín -Moreno, "Efficiency and finite size effects in enhanced transmission through subwavelength holes," Opt. Express 16, 9571-9579 (2008). [CrossRef] [PubMed]
  14. F. Przybilla, A. Degiron, J.-Y. Laluet, C. Genet, and T.W. Ebbesen, "Optical transmission in perforated noble and transition metal films," J. Opt. A: Pure Appl. Opt. 8, 458-463 (2006). [CrossRef]
  15. S. G. Rodrigo, F. J. García -Vidal, and L. Martín -Moreno, "Influence of material properties on extraordinary optical transmission through hole arrays," Phys. Rev. B 77, 075401 (2008). [CrossRef]
  16. K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst and L. Kuipers, "Strong influence of hole spahe on extraordinary transmission through periodic arrays of subwavelength holes," Phys. Rev. Lett. 92, 183901 (2004). [CrossRef]
  17. A. Degrion and T. W. Ebbesen, "The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures," J. Opt. A: Pure Appl. Opt. 7, S90-S96 (2005). [CrossRef]
  18. 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]
  19. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijck, and M. P. van Exter, "Observation of coupling between surface plasmons in index-matched hole arrays," Phys. Rev. B 77, 115437 (2008). [CrossRef]
  20. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  21. P. B. Catrysse, H. Shin, and S. Fan, "Propagating modes in subwavelength cylindrical holes," J. Vac. Sci. Technol. B 23, 2675-2678 (2005). [CrossRef]
  22. C. Yeh and F. Shimabukuro, The Essence of Dielectric Waveguides (Springer, 2008). [CrossRef]
  23. R. Gordon and A. G. Brolo, "Increased cut-off wavelength for a subwavelength hole in a rela metal," Opt. Express 13, 1933-38 (2005). [CrossRef] [PubMed]
  24. F. J. García -Vidal, L.  Martín -Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, "Transmission of light through a single rectangular hole in a real metal," Phys. Rev. B 74, 153411 (2006). [CrossRef]
  25. H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008). [CrossRef] [PubMed]
  26. F. J. García -Vidal, E. Moreno, J. A. Porto and L. Martín -Moreno, "Transmission of light through a single rectangular hole," Phys. Rev. Lett. 95, 103901 (2005). [CrossRef]
  27. J. Bravo-Abad, L. Martín -Moreno, F. J. García -Vidal, E. Hendry, and J. Gomez Rivas, "Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes," Phys. Rev. B 76, 241102 (2007). [CrossRef]
  28. H. A. Bethe, "Theory of diffraction by small holes, " Phys. Rev. 66,163 (1944). [CrossRef]
  29. A. Yu. Nikitin, D. Zueco, F. J. García -Vidal, and L.  Martín -Moreno, "Electromagnetic wave transmission through a small hole in a perfet electric conductor of finite thickness," Phys. Rev. B 78, 165429 (2008). [CrossRef]
  30. 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]
  31. E. Popov, N. Bonod, M. Neviere, H. Rigneault, P.-F. Lenne, and P. Chaumet, "Surface plasmon excitation on a single subwavelength hole in a metallic sheet," Appl. Opt. 44, 2332-2337 (2005). [CrossRef] [PubMed]
  32. F. J. García de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475-1484 (2002). [PubMed]
  33. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangersma, S. Enoch, and L. Kuipers, "Strong modification of the nonlinear optical response of metallic subwavelength hole arrays," Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]
  34. S. Collin, F. Pardo, and J.-L. Pelouard, "Waveguiding in nanoscale metallic apertures," Opt. Express 15, 4310-4320 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited