OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9571–9579
« Show journal navigation

Efficiency and finite size effects in enhanced transmission through subwavelength apertures

F. Przybilla, A. Degiron, C. Genet, T.W. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno  »View Author Affiliations


Optics Express, Vol. 16, Issue 13, pp. 9571-9579 (2008)
http://dx.doi.org/10.1364/OE.16.009571


View Full Text Article

Acrobat PDF (1337 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate transmission efficiency and finite size effects for the subwavelength hole arrays. Experiments and simulations show how the finite size effects depend strongly on the hole diameter. The transmission efficiency reaches an asymptotic upper value when the array is larger than the surface plasmon propagation length on the corrugated surface. By comparing the transmission of arrays with that of the corresponding single holes, the relative enhancement is found to increase as the hole diameter decreases. In the conditions of the experiments the enhancement is one to two orders of magnitude but there is no fundamental upper limit to this value.

© 2008 Optical Society of America

1. Introduction

It is now well established that an array of subwavelength apertures in an opaque metal film can give rise to a transmission much larger than the sum of the transmissions of the individual holes taken separately. The transmission enhancement relies on the resonant excitation of surface plasmons (SPs) by the incident light. This interaction is made possible by the additional momentum (grating momentum) provided by the scattering of the incident light by the hole array [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 (1998). [CrossRef]

, 2

2. 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 (2001). [CrossRef] [PubMed]

, 3

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

]. In addition, excitation of localized surface plasmons [4–6

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

] and other modes [7–11

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

] may also play a role in the process although the grating momentum appears to define the main resonances of the transmission spectrum [3

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

, 12

12. A. Degiron 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 (2005). [CrossRef]

, 13

13. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004). [CrossRef] [PubMed]

], specially in the case of arrays of circular holes. As the number of period increases, the structure factor peaks appearing at reciprocal lattice vectors get better defined, the size of the structure is therefore expected to influence the coupling of light with SPs. Indeed, experimental measurements in the infrared [14

14. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743 (1999). [CrossRef]

], in the THz wave region [15

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

] and in the visible [16

16. J. Henzie, M. H. Lee, and T.W. Odom, “Multiscale patterning of plasmonic metamaterials,” Nat. Nanotechnol. 2, 549 (2007). [CrossRef]

] confirm this expectation. In addition, finite size also affects the re-emission pattern from the array [17

17. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120 (2006). [CrossRef]

].

Since arrays of apertures are always finite, it is important to understand in detail all the consequences of the actual size for both fundamental reasons and when considering the numerous applications of such structures [3

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

]. In the following, we report both experimental and theoretical work on finite size effects in 2D arrays of subwavelength holes in the visible, focusing on the spectral response of arrays, the role of the SP propagation length and its connection to the maximum enhancement factor that can be achieved for the transmission.

2. Finite size effects in the enhanced transmission phenomenon

For the first part of this study, we fabricated finite square arrays of sub-wavelength holes of different sizes. The structures milled through a 275nm freestanding Ag film using focused ion beam (FIB, Ga ions), consist of holes arranged in a square lattice of period P=600nm. The advantage of a freestanding metal film is that the dielectric constant is the same on both sides of the film, a configuration that optimizes transmission efficiencies [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. 200, 1 (2001). [CrossRef]

]. An optical microscope coupled to a spectrometer was used to measure the transmission spectra of the samples that were illuminated by a collimated incident beam at normal incidence. The transmitted light is collected with a 40× objective (with 0.6 numerical aperture).

λ(i,j)=Pi2+j2εmεdεm+εd
(1)

where εm and εd are respectively the dielectric constants of the metal and the dielectric (in this case air), and P the period of the array. The actual peaks are red-shifted compared to the predictions of Eq. (1) since it doesn’t take into account the presence of holes and scattering losses. Nevertheless it provides a simple means to label and associate the various peaks with the corresponding (i, j) scattering order.

At first we measured the transmission spectra of arrays with increasing number of holes (N) with constant diameter d=268nm as shown in Fig. 1(a). The peaks can be labelled by (i, j) according to the predictions of Eq. (1). Let us focus on the (1,0) peak at around 680nm which is spectrally isolated. The maximum transmission increases with N, and eventually exceeds unity as normalized to the hole area. In this regime, the photon flux emerging from a given aperture is larger than the flux incident on this aperture. This corresponds to the extraordinary optical transmission (EOT) regime [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 (1998). [CrossRef]

]. With the particular parameters of this sample, this special condition is already fulfilled for the 21×21 hole array. It should be also noted that the resonance peak profile becomes asymmetric with a blue shift as N increases. This is consistent with an increase in the SP resonant contribution with respect to that of the direct transmission through the holes. Consequently as the SP mode becomes spectrally better defined with N, it takes on the typical asymmetrical shape expected from the Fano analysis [19

19. 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]

, 20

20. 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 (2003). [CrossRef]

].

Fig. 1. (Color online) (a) Experimental transmission spectra for finite size arrays made of 5×5, 11×11, 21×21 and 31×31 holes. The arrays were milled in thick 275nm suspended Ag film with a period P=600nm and a hole diameter d=268nm. Transmissions are normalized to the hole area. The ticks indicate the position of main resonances labelled according the index (i, j) presented in Eq. (1). (b) Transmission spectra, normalized also to the area occupied by the holes, obtained from the numerical simulations using the modal expansion (ME) formalism. The geometrical parameters are the same as in the experiments. Inset: Comparison of ME and finite difference time domain (FDTD) calculations for the infinite array.
Fig. 2. (a) Experimental normalized maximum transmitted intensities as a function of the number of holes (N) for increasing hole diameters (d=216, 268 and 294nm). (b) Experimental full width at half maximum (FWHM) corresponding to the data presented in panel (a). (c) and (d) Results of the numerical simulations using the same geometrical parameters as in the experiments presented in panel (a) and (b). Errors bars are determined from the data dispersions obtained from several measurements on separate structures on a test sample.

In order to have more insights into the phenomenon, we repeated the experiment for different hole diameters. The measurements, presented in Fig. 2(a), follow the same tendency as described previously, i.e., maximum transmitted intensity rises as N increases. However as can be seen, the larger the hole diameter, the faster a transmission saturation is reached. As seen on Fig. 2(c), theoretical calculations based on ME clearly capture experimental trends, with however slight differences in intensities. As stressed above, ME calculations always predict higher transmissions and smaller FWHMs than FDTD simulations. This amounts to a systematic difference in the theory that is sufficient to explain the discrepancies between experiments and ME simulations, as seen when comparing Figs. 2(a) and (c). Nevertheless both simulations and experimental capture the fact that the transmission increases with the size of the array and reaches a saturation. The rate at which the transmission reaches saturation increases with d.

To reveal the underlying mechanism it is interesting to follow the full widths at half maximum (FWHM) of the resonances, which is a measure of the lifetime of the SPs on the array [2

2. 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 (2001). [CrossRef] [PubMed]

, 24

24. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K.J. Yee, J.W. Park, J. Kim, Q.H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]

]. As shown in Fig. 2(b), for all the diameters considered, FWHM decreases towards horizontal asymptotes as N is increased. These lower limits correspond to the total losses of the systems, i.e. internal (absorption inside the metal) and radiative losses (largest contribution).

Fig. 3. (a) and (b) Scanning electron microscopy images of an array of 40×40 holes (P=430nm and d=300nm) milled through a 295nm thick Au film. (c) Corresponding single hole. Images presented in panels (b) and (c) have the same scale. As it can be seen in panels (b) and (c), geometrical parameters of the holes are as identical as possible at the level of the array or at the single hole level.

The above experiments show that as the hole diameter decreases for a given period, the SP propagation length increases, resulting in larger field enhancements on the surface of the array. Consequently, the transmission efficiency relative to a single hole is expected to rise when d decreases. Moreover, calculations (data not shown) indicate that the transmission efficiency of an infinite array increases with the ratio P/d.

3. Relative efficiency of the enhanced transmission

To have an idea of the relative enhancement that can be achieved, we compared the transmission of an hole array to the transmission of a single isolated hole. For this part of the study, we fabricated square arrays made up of 40×40 holes (P=430nm) and their corresponding single holes, for hole diameters of d=150, 200, 250 and 300nm. Scanning electron microscope (SEM) images for the d=300nm case are rendered in Fig. 3. All the structures were milled in the same 295nm Au film deposited on glass substrate. An index matching liquid tuned to the refractive index of glass is put afterwards on top of the structure in order to work again in a symmetrical configuration. At this point it must be stressed that great care was taken during the fabrication process to achieve the same quality in milling large hole arrays and single isolated holes. The choice of the 40×40 size array was large enough for the transmission to be at saturation for four diameters considered (in the presence of index matching liquid) and still allow the fabrication of high quality hole arrays within discretization capacity of the FIB. SEM images of our structures show that geometrical parameters differ by less than 10nm from the specified value.

Fig. 4. (Color online) Transmission spectra of a d=300nm single hole milled in a 295nm thick Au film obtained by increasing the numerical aperture of the collecting objective. Each curve is an average of the spectra of 3 isolated holes of the same dimensions. Inset: Measured transmission as a function of the solid angle of collection evaluated at 600nm and 800nm.

Figures 5(a) and 5(b) show the transmission spectra of hole arrays and those of the corresponding single holes. As expected the transmission increases with hole diameter, being enhanced at some wavelengths or suppressed at other wavelengths as compared to the isolated holes. Furthermore the transmission peaks become broader with increasing hole diameter as we have already discussed before and show a slight red shift as already observed [28

28. 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 (2004). [CrossRef]

]. In addition transmission value at transmission minima increases with the hole diameter indicating that direct transmission through the hole array increase. Note that Fabry-Perot modes have been predicted to give a strong spectral signature when the holes are filled with a high index dielectric [29

29. H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005). [CrossRef]

]. In the index matching conditions used here, calculations (not shown) indicate that such Fabry-Perot modes are very weak and broad which explains why their spectral signture is not apparent.

Fig. 5. (Color online) (a) and (b) Respectively experimental transmission spectra of an array of 40×40 holes (P=430nm), and a single hole made in the same 295nm Au film with increasing diameter (d=150, 200, 250 and 300nm). The film was deposited on a glass substrate and covered with an index matching fluid (n=1.53). The increase of transmission and of the noise in the long wavelength limit mainly visible for the d=150nm hole correspond to the noise level of our experimental setup which typically increase with the wavelength. For all the structures, the transmitted light as been collected using the same objective (Nikon Plan Fluor 100×) with numerical aperture fixed to 1.3. Each single hole curve is an average of the spectra of 3 isolated holes of the same dimensions. (c) and (d) Corresponding theoretical results. All the data are presented in logarithmic scale.

The ratio of the transmission of the array to that of the single hole over the whole spectral window is shown in Fig. 6(a). This representation permits us to easily follow the enhancement factor of an array relative to a single isolated hole. At the main resonance this enhancement is approximately 8, 12, 18 and 40 for d=300, 250, 200 and 150nm respectively. The resonance at smaller wavelength corresponding to the (1,1) mode display much smaller enhancement due to the fact that Au becomes increasingly unfavourable to SPs as the wavelength decreases [30

30. 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: Appl. Opt. 8, 458 (2006). [CrossRef]

]. Below ca. 500nm, SPs cannot be sustained due to the value of the real part of the Au dielectric constant [30

30. 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: Appl. Opt. 8, 458 (2006). [CrossRef]

]. Theoretical results are rendered in Figs. 5(c), 5(d) and 6(b) showing a good qualitative agreement with the experimental findings. In these calculations we have assumed that the holes are also filled with a dielectric of refraction index equal to 1.53.

It is interesting to note that outside of the SP resonances of the hole arrays, the transmission ratios are roughly unity and essentially independent of hole diameter. On the other hand, the enhancement factor at resonance does increase as the diameter decreases, since the SP propagates further, as discussed earlier. This confirms yet again the importance of SPs in enhancing the transmission of hole arrays.

Fig. 6. (Color online) (a) Ratio of the transmission of the array to the transmission of the corresponding single hole for d=150, 200, 250 and 300nm. (b) Corresponding theoretical results. All the data are presented in logarithmic scale.

4. Conclusion

Acknowledgments

Financial support by the EC under project No. FP6-2002-IST-1-507879 (Plasmo-Nano-Devices) and by the spanish MEC under contract MAT2005-06608-C02 is gratefully acknowledged.

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 (1998). [CrossRef]

2.

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 (2001). [CrossRef] [PubMed]

3.

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

4.

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

5.

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 (2004). [CrossRef]

6.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005). [CrossRef]

7.

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

8.

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] [PubMed]

9.

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

10.

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

11.

T. Rindzevicius, Y. Alaverdyan, B. Sepulveda, T. Pakizeh, M. Käll, R. Hillenbrand, J. Aizpurua, and F. J. García de Abajo, “Nanohole plasmons in optically thin gold films,” J. Phys. Chem. C 111, 1207 (2007). [CrossRef]

12.

A. Degiron 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 (2005). [CrossRef]

13.

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004). [CrossRef] [PubMed]

14.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743 (1999). [CrossRef]

15.

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

16.

J. Henzie, M. H. Lee, and T.W. Odom, “Multiscale patterning of plasmonic metamaterials,” Nat. Nanotechnol. 2, 549 (2007). [CrossRef]

17.

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2, 120 (2006). [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 (2001). [CrossRef]

19.

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]

20.

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 (2003). [CrossRef]

21.

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]

22.

E.D. Palik, Handbook of Optical Constants of Solids (London, Academic1985)

23.

A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M.L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005). [CrossRef]

24.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K.J. Yee, J.W. Park, J. Kim, Q.H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]

25.

C. Obermüller and K. Karrai, “Far field characterisation of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408 (1995). [CrossRef]

26.

E. Popov, M. Nevière, A. Sentenac, N. Bonod, A. L. Fehrembach, J. Wenger, P.-F. Lenne, and H. Rigneault, “Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen,” J. Opt. Soc. Am. A 24, 339 (2007). [CrossRef]

27.

C. Obermüller, K. Karrai, G. Kolb, and G. Abstreiter, “Transmitted radiation through a subwavelength-sized tapered optical fiber tip,” Ultramicroscopy 61, 171 (1995). [CrossRef]

28.

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 (2004). [CrossRef]

29.

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005). [CrossRef]

30.

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: Appl. Opt. 8, 458 (2006). [CrossRef]

31.

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

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: April 7, 2008
Revised Manuscript: May 2, 2008
Manuscript Accepted: May 3, 2008
Published: June 13, 2008

Citation
F. Przybilla, A. Degiron, C. Genet, T. Ebbesen, F. de Léon-Pérez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, "Efficiency and finite size effects in enhanced transmission through subwavelength apertures," Opt. Express 16, 9571-9579 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9571


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 sub-wavelength hole arrays," Nature 391, 667 (1998). [CrossRef]
  2. L. Mart????n-Moreno, F. J. Garc?a-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 (2001). [CrossRef] [PubMed]
  3. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39 (2007). [CrossRef] [PubMed]
  4. R. Wannemacher, "Plasmon-supported transmission of light through nanometric holes in metallic thin films," Opt. Commun. 195, 107 (2001). [CrossRef]
  5. 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 (2004). [CrossRef]
  6. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory," Phys. Rev. B 72, 045421 (2005). [CrossRef]
  7. F. J. Garc?a de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475 (2002).
  8. F. J. Garc?a-Vidal, E. Moreno, J. A. Porto and L. Mart?n-Moreno, "Transmission of light through a single rectangular hole," Phys. Rev. Lett. 95, 103901 (2005). [CrossRef] [PubMed]
  9. 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 (2005). [CrossRef] [PubMed]
  10. F. J. Garc?a-Vidal, L. Mart?n-Moreno, Esteban Moreno, L. K. Kumar, and R. Gordon, "Transmission of light through a single rectangular hole in a real metal," Phys. Rev. B 74, 153411 (2006). [CrossRef]
  11. T. Rindzevicius, Y. Alaverdyan, B. Sepulveda, T. Pakizeh, M. Kall, R. Hillenbrand, J. Aizpurua and F. J. Garc?a de Abajo, "Nanohole plasmons in optically thin gold films," J. Phys. Chem. C 111, 1207 (2007). [CrossRef]
  12. A. Degiron 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 (2005). [CrossRef]
  13. J. Bravo-Abad, F. J. Garc?a-Vidal and L. Mart?n-Moreno, "Resonant transmission of light through finite chains of subwavelength holes in a metallic film," Phys. Rev. Lett. 93, 227401 (2004). [CrossRef] [PubMed]
  14. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff and T. W. Ebbesen, "Surface-plasmon-enhanced transmission through hole arrays in Cr films," J. Opt. Soc. Am. B 16, 1743 (1999). [CrossRef]
  15. F. Miyamaru and M. Hangyo, "Finite size effect of transmission property for metal hole arrays in subterahertz region," Appl. Phys. Lett. 84, 2742 (2004). [CrossRef]
  16. J. Henzie, M. H. Lee and T. W. Odom, "Multiscale patterning of plasmonic metamaterials," Nat. Nanotechnol. 2, 549 (2007). [CrossRef]
  17. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garc?a-Vidal, L. Mart?n-Moreno and T. W. Ebbesen, "How light emerges from an illuminated array of subwavelength holes," Nat. Phys. 2, 120 (2006). [CrossRef]
  18. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Mart????n-Moreno and F. J. Garc?a-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Opt. Commun. 200, 1 (2001). [CrossRef]
  19. 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]
  20. 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 (2003). [CrossRef]
  21. S. G. Rodrigo, F. J. Garc?a-Vidal and L. Mart?n-Moreno, "Influence of material properties on extraordinary optical transmission through hole arrays," Phys. Rev. B 77, 075401 (2008). [CrossRef]
  22. E. D. Palik, Handbook of Optical Constants of Solids (London, Academic 1985)
  23. A. Vial, A.-S. Grimault, D. Macias, D. Barchiesi, and M.L. de la Chapelle, " Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method," Phys. Rev. B 71, 085416 (2005). [CrossRef]
  24. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K.J. Yee, J. W. Park, J. Kim, Q. H. Park and C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]
  25. C. Obermuller, and K. Karrai, "Far field characterisation of diffracting circular apertures," Appl. Phys. Lett. 67, 3408 (1995). [CrossRef]
  26. E. Popov, M. Neviere, A. Sentenac, N. Bonod, A. L. Fehrembach, J. Wenger, P.-F. Lenne and H. Rigneault, "Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen," J. Opt. Soc. Am. A 24, 339 (2007). [CrossRef]
  27. C. Obermuller, K. Karrai, G. Kolb and G. Abstreiter, "Transmitted radiation through a subwavelength-sized tapered optical fiber tip," Ultramicroscopy 61, 171 (1995). [CrossRef]
  28. 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 (2004). [CrossRef]
  29. H. Shin, P. B. Catrysse, and S. Fan, "Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes," Phys. Rev. B 72, 085436 (2005). [CrossRef]
  30. 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: Appl. Opt. 8, 458 (2006). [CrossRef]
  31. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163 (1944). [CrossRef]

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited