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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 20222–20228
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Enhanced transmission of electromagnetic waves through 1D plasmonic crystals

Jin-Kyu So, Hoe-Cheon Jung, Sun-Hong Min, Kyu-Ha Jang, Seung-Ho Bak, and Gun-Sik Park  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 20222-20228 (2010)
http://dx.doi.org/10.1364/OE.18.020222


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Abstract

Transmission of electromagnetic waves through thick perfect conducting slabs perforated by one-dimensional arrays of rectangular holes was studied experimentally in the microwave frequency range. The observed thickness-dependent transmission clearly exhibits the evanescent and propagating nature of the involved electromagnetic excitations on the considered structures, which are effective surface plasmons and localized waveguide resonances, respectively. The 1D crystals showing transmission based on localized resonances further manifests the frequency-dependent effective refractive index depending on the filling ratio of the holes and accompanies resonant guided wave propagation.

© 2010 OSA

1. Introduction

Since it was found that the light transmission through periodic subwavelength apertures can be extraordinarily enhanced compared to that through a single subwavelength hole in a thin metallic screen [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(6668), 667–669 (1998). [CrossRef]

], this remarkable light transmission, known as extraordinary optical transmission (EOT), has invoked a lot of studies aiming to understand the underlying origin [2

2. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

]. Based on the analysis into the relationship between the resonant wavelength and the lattice period, the collective electromagnetic excitations on metal films such as surface plasmon polaritons (SPPs) [3

3. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

,4

4. 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(6), 1114–1117 (2001). [CrossRef] [PubMed]

] have been noted as the key player in such enhancement. However, later findings have elucidated the role of individual apertures, which is expressed as the shape dependent resonant wavelength and the Fabry-Perot resonances due to the waveguide modes in such apertures [5

5. K. J. 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(18), 183901 (2004). [CrossRef] [PubMed]

7

7. J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99(13), 137401 (2007). [CrossRef] [PubMed]

].

Along with the aforementioned achievements on two-dimensional (2D) hole arrays with high symmetry, there have been efforts to figure out the light transmission phenomena in minimal systems consisting of subwavelength holes with restricted symmetry such as one-dimensional (1D) chains of holes [8

8. 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(22), 227401 (2004). [CrossRef] [PubMed]

], orthogonal chains of holes [9

9. Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, “Optical antennas based on coupled nanoholes in thin metal films,” Nat. Phys. 3(12), 884–889 (2007). [CrossRef]

], and 2D hole arrays with minimal number of holes [10

10. F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84(15), 2742–2744 (2004). [CrossRef]

12

12. F. Przybilla, A. Degiron, C. Genet, T. W. 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(13), 9571–9579 (2008). [CrossRef] [PubMed]

]. Among these minimal systems, 1D chains of holes have been found to be the basic unit exhibiting EOT [8

8. 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(22), 227401 (2004). [CrossRef] [PubMed]

]. Under certain conditions such as cutoff wavelength larger than the half-period and thickness comparable to the considered wavelength, these 1D plasmonic crystals have been reported to behave effectively as dielectric media with the frequency-dependent index of refraction [14

14. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,17

17. Y. M. Shin, J. K. So, J. H. Won, and G. S. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

]. Moreover, this type of structures have been noted for its capability of guiding electromagnetic waves confined on the surface [13

13. Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]

], which is promising for plasmonic waveguide applications [14

14. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

] and even as an interaction structure for micro-free-electron-lasers [15

15. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beams,” Appl. Phys. Lett. 90(3), 031502 (2007). [CrossRef]

,16

16. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007). [CrossRef] [PubMed]

].

In this work, we study the transmission of electromagnetic waves through 1D arrays of rectangular holes in thick metal slabs using microwaves ranging from 6 to 12 GHz. To elucidate the different transmission mechanisms based on two types of collective electromagnetic excitations, effective surface plasmons [18

18. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

20

20. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006). [CrossRef] [PubMed]

] and localized resonances [14

14. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

,17

17. Y. M. Shin, J. K. So, J. H. Won, and G. S. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

], the geometrical parameters such as period and thickness of the 1D plasmonic crystals were varied while maintaining the dimension of individual holes.

2. Enhanced transmission through 1D plasmonic crystals

The considered 1D plasmonic crystal is shown in Fig. 1
Fig. 1 Schematic of the 1D array of rectangular holes with the considered coordinates system.
, which is a 1D array (period d) of rectangular holes of sides s and a, perforated on a metallic slab of thickness L. Each sample was formed out of two aluminum plates, one flat plate and the other with periodic grooves on it. The width and depth of each groove were given as a = 4 mm and s = 17 mm, respectively. Thereafter, these two aluminum plates were joined into one to form a metallic structure with rectangular holes as shown in Fig. 1. To measure the transmission of microwaves through the structures, microwaves were generated by an Anritsu Vector Network Analyzer (VNA) and a traveling wave tube amplifier (TWTA) in the frequency range between 6 and 12 GHz [21

21. The travelling wave tube amplifier with ~60 dB gain was unavailable during the experiment for Fig. 2. This seriously lowered the signal levels compared to noise level, which caused the results in Fig. 2 to be noisy compared to those in Fig. 4.

]. The generated microwaves were radiated through a horn antenna and impinged on the sample with its electric field vector parallel to that of TE mode of the hole-waveguide. The transmitted waves were collected by another horn antenna behind the sample and fed back into the VNA. The whole measurement was conducted inside an anechoic chamber to prevent spurious effects due to diffraction and reflection.

In microwave frequency range where metals behave as perfect conductors, SPPs are no longer strongly bound to the surface. However, achieving strongly confined electromagnetic modes at such low frequencies is still possible by structuring the perfect conductors with subwavelength apertures [18

18. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,19

19. F. J. Garcia-Vidal, L. Martın-Moreno, and J. B. Pendry, “Surfaces with holes in them: newplasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

]. These strongly confined electromagnetic modes, effective surface plasmons, have been known to be responsible for EOT in 2D arrays of holes in perfect conductors [20

20. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006). [CrossRef] [PubMed]

]. To clarify the involvement of these effective surface plasmons together with the localized resonances in the considered 1D systems at microwave frequency range, the period and thickness of the array were varied around the cutoff wavelength λc, which was fixed to be 34 mm. The period d was varied to be 27, 30, and 35 mm while the thickness was ranging from 1 mm to 200 mm. The transmittance through each sample was obtained by normalizing the transmission spectra by the reference spectra measured without loading samples. Figure 2
Fig. 2 (a) Measured normalized-to-area transmission spectra based on effective surface plasmons, d = 35 mm. The reduction of peak height according to the increase of the thickness shows the evanescent nature of the waves involved in the transmission. (b) Measured normalized-to-area transmission spectra based on localized resonances, d = 27 mm. The increasing number of transmission peaks shows the propagating characteristics of the involved excitation
shows the transmission spectra (normalized to the total area of the holes) of normally incident microwaves for the samples with d = 35 mm (> λc) and d = 27 mm (< λc), while varying the thickness: 1, 10, and 50 mm. Each transmission spectrum is compared with those obtained from numerical simulation (solid curves) using CST Microwave Studio [23

23. C. S. T. Microwave Studio, ®, © 2008 CST - Computer Simulation Technology, Wellesley Hills, MA, USA, www.cst.com.

].

For d = 35 mm (> λc), the transmission through the structure is expected to be associated with the effective surface plasmons and thus several features of EOT in 2D hole arrays based on SPPs [4

4. 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(6), 1114–1117 (2001). [CrossRef] [PubMed]

] are observed in the experimental results shown in Fig. 2(a). The transmission resonances occur at wavelengths close to the period of the array and the resonance peak is blue-shifted from λ/d = 1.115 to λ/d = 1.007 as the thickness is increased from 1 mm to 50 mm, respectively. Meanwhile, the peak height decays as the thickness increases, which is attributed to the evanescent nature of the involved excitation, effective surface plasmons. The incident wave coupled to the surface mode on the top surface decays along the z-direction in the hole before it is coupled to the same mode on the bottom surface to finally couple out to free space.

For d = 27 mm(< λc), the transmission resonances occur near the cutoff wavelength of the hole waveguide, λ/d = 1.26, as shown in Fig. 2(b). However, the peak height does not decay as the thickness increases in contrary to the case for d = 35 mm. Instead, Fabry-Perot resonances appear with the increase of the thickness, which is clearly seen for L = 50 mm where three Fabry-Perot peaks are observed above λ/d = 1. Each peak corresponds to the fundamental waveguide mode with the different phase variations along the hole-waveguide [17

17. Y. M. Shin, J. K. So, J. H. Won, and G. S. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

].

To corroborate the involvement of the evanescent and propagating electromagnetic modes in these two types of enhanced transmissions, the electric field profiles at the resonances for L = 50 mm were also obtained from numerical simulation. The two contour plots in Fig. 3
Fig. 3 The contour plots of electric field magnitude shows clearly (a) the evanescent field profile of effective surface plasmons for d = 35 mm and (b) the waveguide mode for d = 27 mm at the resonant wavelengths when the thickness is 50 mm.
show the electric field distribution in the y-z plane at the transmission peaks λ/d = 1.007 and 1.261 for d = 35 and 27 mm, respectively. The evanescent field profile of the effective surface plasmons excited on the top surface due to the incident waves is clearly seen in Fig. 3(a). On the other hand, Fig. 3(b) shows the excited fundamental waveguide mode at the localized resonance.

3. Frequency-dependent index of refraction

According to this homogenization, the effective refractive index, n, increases as the filling ratio, d/a, increases, which would be exhibited as more densely located Fabry-Perot resonances above the cutoff frequency. Since the number of resonances increases for thicker samples according to the basic relation of Fabry-Perot resonance, kL = mπ, transmission spectra were recorded for thicker samples with L = 200mm to clearly see the density change of resonances. Figure 4
Fig. 4 Normalized transmission spectra for 200 mm thick samples with different filling ratios: d/a = 6.75, 7.5, and 8.75.
shows the transmission spectra of samples having filling ratio of 6.75 (d = 27 mm), 7.5 (d = 30 mm), and 8.75 (d = 35 mm). As expected, Fabry-Perot resonances for higher filling ratio are more densely packed as shown in Fig. 4. However, due to diffraction, the frequency dependence is observed in a finite range of frequency above the cutoff frequency and below the Rayleigh minimum, c/d. At normal incidence, samples with d = 27, 30, and 35 mm experience the first order diffraction at the normalized frequencies 1.259, 1.133, and 0.971, respectively.

4. Conclusion

In conclusion, we showed that enhanced transmission of electromagnetic waves still occurs in 1D plasmonic crystals consisting of arrays of rectangular holes in thick perfect conducting slabs using microwaves ranging from 6 to 12 GHz. The observed thickness-dependent transmission spectra clearly exhibits the evanescent and propagating nature of the involved electromagnetic excitations, which are effective surface plasmons and localized resonances, for d>λc and d<λc, respectively. Although limited to a finite frequency range, for d<λc, this 1D structure shows frequency dependence in its effective dielectric response, which is observed as density change of Fabry-Perot resonances. This dielectric response is further corroborated by the concomitant existence of guided modes.

Acknowledgements

This work was supported by National Research Foundation of Korea Grant funded by the Korean Goverment(grant code: 2009-0083512)

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(6668), 667–669 (1998). [CrossRef]

2.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

3.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

4.

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(6), 1114–1117 (2001). [CrossRef] [PubMed]

5.

K. J. 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(18), 183901 (2004). [CrossRef] [PubMed]

6.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]

7.

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99(13), 137401 (2007). [CrossRef] [PubMed]

8.

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(22), 227401 (2004). [CrossRef] [PubMed]

9.

Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, “Optical antennas based on coupled nanoholes in thin metal films,” Nat. Phys. 3(12), 884–889 (2007). [CrossRef]

10.

F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84(15), 2742–2744 (2004). [CrossRef]

11.

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garcia-Vidal, L. Martin-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2(2), 120–123 (2006). [CrossRef]

12.

F. Przybilla, A. Degiron, C. Genet, T. W. 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(13), 9571–9579 (2008). [CrossRef] [PubMed]

13.

Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]

14.

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]

15.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beams,” Appl. Phys. Lett. 90(3), 031502 (2007). [CrossRef]

16.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007). [CrossRef] [PubMed]

17.

Y. M. Shin, J. K. So, J. H. Won, and G. S. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]

18.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

19.

F. J. Garcia-Vidal, L. Martın-Moreno, and J. B. Pendry, “Surfaces with holes in them: newplasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

20.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006). [CrossRef] [PubMed]

21.

The travelling wave tube amplifier with ~60 dB gain was unavailable during the experiment for Fig. 2. This seriously lowered the signal levels compared to noise level, which caused the results in Fig. 2 to be noisy compared to those in Fig. 4.

22.

A. Mary, S. Rodrigo, L. Martín-Moreno, and F. García-Vidal “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007). [CrossRef]

23.

C. S. T. Microwave Studio, ®, © 2008 CST - Computer Simulation Technology, Wellesley Hills, MA, USA, www.cst.com.

24.

P. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Moller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. A, Pure Appl. Opt. 2, 48 (2000). [CrossRef]

25.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

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

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 26, 2010
Revised Manuscript: July 23, 2010
Manuscript Accepted: July 28, 2010
Published: September 8, 2010

Citation
Jin-Kyu So, Hoe-Cheon Jung, Sun-Hong Min, Kyu-Ha Jang, Seung-Ho Bak, and Gun-Sik Park, "Enhanced transmission of electromagnetic waves through 1D plasmonic crystals," Opt. Express 18, 20222-20228 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20222


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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(6668), 667–669 (1998). [CrossRef]
  2. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
  3. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
  4. 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(6), 1114–1117 (2001). [CrossRef] [PubMed]
  5. K. J. 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(18), 183901 (2004). [CrossRef] [PubMed]
  6. Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]
  7. J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99(13), 137401 (2007). [CrossRef] [PubMed]
  8. 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(22), 227401 (2004). [CrossRef] [PubMed]
  9. Y. Alaverdyan, B. Sepulveda, L. Eurenius, E. Olsson, and M. Kall, “Optical antennas based on coupled nanoholes in thin metal films,” Nat. Phys. 3(12), 884–889 (2007). [CrossRef]
  10. F. Miyamaru and M. Hangyo, “Finite size effect of transmission property for metal hole arrays in subterahertz region,” Appl. Phys. Lett. 84(15), 2742–2744 (2004). [CrossRef]
  11. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garcia-Vidal, L. Martin-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2(2), 120–123 (2006). [CrossRef]
  12. F. Przybilla, A. Degiron, C. Genet, T. W. 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(13), 9571–9579 (2008). [CrossRef] [PubMed]
  13. Z. Ruan and M. Qiu, “Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface,” Appl. Phys. Lett. 90(20), 201906 (2007). [CrossRef]
  14. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16(9), 6216–6226 (2008). [CrossRef] [PubMed]
  15. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beams,” Appl. Phys. Lett. 90(3), 031502 (2007). [CrossRef]
  16. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007). [CrossRef] [PubMed]
  17. Y. M. Shin, J. K. So, J. H. Won, and G. S. Park, “Frequency-dependent refractive index of one-dimensionally structured thick metal film,” Appl. Phys. Lett. 91(3), 031102 (2007). [CrossRef]
  18. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  19. F. J. Garcia-Vidal, L. Martın-Moreno, and J. B. Pendry, “Surfaces with holes in them: newplasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
  20. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Waveguide arrays as plasmonic metamaterials: transmission below cutoff,” Phys. Rev. Lett. 96(7), 073904 (2006). [CrossRef] [PubMed]
  21. The travelling wave tube amplifier with ~60 dB gain was unavailable during the experiment for Fig. 2. This seriously lowered the signal levels compared to noise level, which caused the results in Fig. 2 to be noisy compared to those in Fig. 4.
  22. A. Mary, S. Rodrigo, L. Martín-Moreno, and F. García-Vidal “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007). [CrossRef]
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