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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 1101–1106
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Extraordinary terahertz transmission in superconducting subwavelength hole array

Jingbo Wu, Hao Dai, Hao Wang, Biaobing Jin, Tao Jia, Caihong Zhang, Chunhai Cao, Jian Chen, Lin Kang, Weiwei Xu, and Peiheng Wu  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 1101-1106 (2011)
http://dx.doi.org/10.1364/OE.19.001101


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Abstract

We report the extraordinary terahertz (THz) transmission through subwavelength hole array in superconducting NbN film. As the temperature drops below the superconducting transition temperature, the transmission spectra experience distinct changes. The extraordinary transmission is greatly enhanced in superconducting state due to the enhancement of surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs). We have also observed temperature-dependent resonance frequency shift, which mainly depends on the coupling between SPPs and LSPs.

© 2011 OSA

1. Introduction

Extraordinary transmission, or enhanced transmission through metal subwavelength hole arrays at light frequencies, has attracted great interest due to potential engineering applications [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]

3

3. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

]. The enhanced transmission is attributed to the interaction between the electromagnetic wave and surface plasmon polaritons (SPPs). It strongly depends on the dielectric constant of metal; and large ratio of the real to imaginary dielectric constants (-εrmim) is favorable to the propagation of SPPs [3

3. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

,4

4. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, Berlin, 1988), Chap.2.

]. In terahertz (THz) region, this kind of transmission has been demonstrated in metal films [5

5. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29(8), 896–898 (2004). [CrossRef] [PubMed]

,6

6. W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43(1), 1–18 (2008). [CrossRef]

]. However, in this frequency region metals are highly conductive, and the ratio of -εrmim is less than 1; thus the explanation is not based on SPPs, which most people believe do not exist due to the above reasons, but based on the formation of SPP-like surface waves, or spoof surface plasmons, on the structured metal surfaces [7

7. 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]

].

2. Experiments and discussions

Used to make the samples are 200 nm-thick NbN films, deposited on 400 μm-thick MgO substrates (twin polished, <100> orientation) using RF magnetron sputtering. The typical critical temperature (Tc) of a film is 15.8 K. Rectangular or circular subwavelength holes are patterned photolithographically in the film to form an array. The samples are mounted on the cold stage in a continuous flow liquid helium cryostat, which is installed in the THz time domain spectroscopy (TDS) system. THz transmission spectra are measured in a temperature range of 8.2-300 K, using a bare MgO substrate as the reference.

Shown in Fig. 1(a)
Fig. 1 Microscopic images of (a) Sample 1 with geometrical parameters a = 100 μm, b = 30 μm and the period is P = 120 μm, and (b) Sample 3 with circular holes of diameters d = 80 μm, and the period is P = 120 μm.
is Sample 1, an array with rectangular subwavelength holes where the long side is a = 100 μm, the short side b = 30 μm and the period P = 120 μm (for Sample 2, also with rectangular holes but not shown here, b = 15 μm). The polarization of the electric field is chosen to be parallel to the short side of the rectangle hole. Sample 3, shown in Fig. 1(b), is an array with circular holes where the diameter is d = 80 μm and the period is P = 120 μm. The size of each sample above is 10 mm × 10 mm.

Figure 2
Fig. 2 THz Transmission spectra of Sample 1 at various temperatures.
shows the transmission spectra of Sample 1 from 300 K (bottom) to 8.2 K (top). The resonance around 600 GHz corresponds to the SPPs [ ± 1, 0] mode for hole array at NbN-MgO interface. The transmission spectra do not change much with the temperature when it is higher than Tc. As the temperature is further reduced so that the NbN film goes into superconducting state, the transmission experiences remarkable changes. The magnitude of the peak increases with decreasing temperature, indicating that the resonance gradually enhances, while the resonance frequency suddenly drops to minimum on the normal to superconducting transition and then gradually increases as temperature lowers further.

The magnitudes of the transmission peak and the temperature-dependent resonance frequencies for sample 1 and 2 are displayed in Fig. 3(a)
Fig. 3 Measured (a) resonance frequency and (b) transmission peak as a function of temperature for Sample 1 and 2.
and 3(b). For Sample 1, the transmission maximum increases from 49.0% at 19 K to 89.8% at 8.2 K, and the transmission intensity normalized to the area occupied by the holes reaches 4.3 at 8.2 K taking into account that 20.8% of the sample area is occupied by the holes. The maximum resonance frequency shift is about 68 GHz, about 11% of resonance frequency at 19 K. Sample 2 shares the same temperature-dependent features except difference in amplitude.

In order to understand how the properties of SPPs change when the sample goes from superconducting to normal, we deduce the temperature-dependent dielectric function of a NbN film (15 nm-thick) by measuring its transmission spectra with a THz-TDS system. The dielectric constant at 0.6 THz is plotted in Fig. 4(a)
Fig. 4 Measured (a) real part and imaginary part of dielectric constants and (b) the propagation length of NbN film at 0.6 THz as a function of T/Tc.
. Obviously, in superconducting state, the rmim value is much larger than it is in normal state. Thus, the internal damping of NbN film for SPPs should be much weaker in superconducting state than in normal state. The internal damping can be evaluated by the propagation length (δsp) on smooth surfaces without structures, which is approximated as follows [4

4. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, Berlin, 1988), Chap.2.

]
δsp=1/2Im(ksp)=c/2ωIm(εmεdεm+εd)1/2,
(1)
where ksp is the wave vector of SPPs, εm and εd are the dielectric functions of the conductor and substrate respectively. The calculated δsp is displayed in Fig. 4(b). It shows that δsp greatly increases from 0.078 m at T = 1.18Tc to 1.8 m at T = 0.58Tc. As a result, the propagation of SPPs suffers less internal damping in superconducting state than in normal state because of the increased -εrmim, and SPP-enhanced transmission improves much from this low internal damping [13

13. A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays,” Opt. Lett. 31(17), 2637–2639 (2006). [CrossRef] [PubMed]

]. At this point it is important to note that the data in Fig. 3 are taken with a sample where NbN film is 200 nm-thick, while in Fig. 4 the film is 15 nm-thick. The thickness difference between the films, as well as the possible quality difference, may quantitatively cause some discrepancy but the measurement results do qualitatively provide us with some direct evidences of how the superconductivity of the NbN film affect the transmission.

For SPP-enhanced transmission, the thickness of the metal film is also an important factor. The transmission peak gets enhanced as the thickness of the film is increased towards the skin depth [14

14. A. K. Azad and W. Zhang, “Resonant terahertz transmission in subwavelength metallic hole arrays of sub-skin-depth thickness,” Opt. Lett. 30(21), 2945–2947 (2005). [CrossRef] [PubMed]

]. In normal state, the skin depth of NbN at 600 GHz is about 593 nm (conductivity is 1.2 × 106 S/m from our measurement), the thickness of NbN film is about one third of the skin depth. When temperature is below 0.9Tc, the skin depth approaches penetration depth (λ), which represents the distance that electromagnetic wave could penetrate into the superconductor [15

15. M. Tinkham, Introduction to superconductivity, (McGraw-Hill, New York, 1980)

,16

16. B. B. Jin, T. Dahm, S.-I. Lee, and N. Klein, “Anomalous coherence peak in the microwave conductivity of MgB2 thin film at 7.2 GHz,” Physica C 468(11-12), 861–864 (2008). [CrossRef]

]. Based on our measurements, the penetration depth at 9 K is 369 nm. Thus the NbN film thickness is 54.2% of the skin depth, indicating that the relative optical thickness is remarkably increased in superconducting state. Therefore, the optically thicker NbN film in superconducting state also contributes to the enhanced extraordinary transmission.

On the other hand, the LSPs greatly affect the intensity and frequency of the transmission resonance [17

17. 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(1-3), 61–66 (2004). [CrossRef]

,18

18. Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008). [CrossRef] [PubMed]

]. The equivalent circuit model was first used in analyzing frequency selective surfaces [24

24. B. A. Munk, Frequency Selective Surface,Theory and Design, (Wiley, New York, 2000), Chap. 1.

], and then was applied to studying the transmission property of single subwavelength hole [19

19. Y. Bao, Studies on Extraordinary Transmission of Sub-wavelength Apertures in Infrared Region, (Ph.D. thesis, Nanjing University, 2008)

]. As shown in Fig. 5
Fig. 5 (a) Diagram of rectangle hole array in NbN film and (b) the equivalent circuit.
, the carriers are driven by electric field to move along the edges parallel to the polarization direction, so these edges provide inductance (Lg) and resistance (R) in series, and the edges orthogonal to polarization direction can be equivalent to capacitor (C). Besides, the inertial mass of superconductor carriers in alternating electric fields is manifested by kinetic inductance (Lk). Thus, each hole can be equivalent to an LC resonator whose impedance is Z = L/RC, where L = Lg + Lk. If we use transmission line as the analog of the THz pulse propagation path, the transmission line is shunted by this LC resonator. The derived transmission coefficient is as follows [20

20. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H.-U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

]
T=1+ns1+ns+Z0/Z,
(2)
where ns is the refractive index of the substrate, Z0 and Z are the impedances of vacuum and LC resonator respectively. When the temperature goes below Tc, the ohmic loss is sharply reduced, while the change of L and C is much smaller. Thus, the impedance of LC resonator increases and transmission coefficient increases consequently. In other words, the strengthened oscillation of LSPs around each hole in superconducting state contributes to the enhancement of extraordinary transmission.

According to the Fano model, the resonance frequency shift arises from the coupling between SPP-enhanced transmission and non-SPP transmission, for example, LSP-enhanced transmission [21

21. 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(4-6), 331–336 (2003). [CrossRef]

,22

22. J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91(7), 071122 (2007). [CrossRef]

]. The stronger the coupling is, the more red-shift of the resonance frequency appears. We attribute the change of coupling strength to the effect of superconductor’s kinetic inductance (Lk). When temperature decreases below Tc, the emergent Lk lowers the cut-off frequency of the subwavelength hole, which delimits the propagating and non-propagating regimes of the incident electromagnetic wave. As a consequence, the coupling between SPP-enhanced and LSP-enhanced transmission intensifies, and a distinct red-shift of the resonance frequency occurs around Tc [21

21. 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(4-6), 331–336 (2003). [CrossRef]

]. Besides, the temperature dependence of Lk can be used to explain why the resonance frequency goes up gradually when the temperature further decreases. In fact, for a superconducting film with a finite thickness d, Lk can be approximated as Lk≈μ0λcoth(d/λ), where μ0 is permeability of vacuum, and λ is the penetration depth [20

20. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H.-U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

]. According to the two-fluid theory, λ decreases as temperature lowers down due to increased density of superconductor carriers [15

15. M. Tinkham, Introduction to superconductivity, (McGraw-Hill, New York, 1980)

]. As the temperature decreases further, Lk gradually reduces with decreasing λ. Thus, the cut-off frequency of the hole increases, and the coupling between LSP-enhanced and SPP-enhanced transmissions becomes weaker and weaker.

As mentioned earlier, an input polarization along the short side of a rectangular hole is optimal in the sense that the oscillation of LSPs around the hole is the strongest among all possible input orientations [17

17. 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(1-3), 61–66 (2004). [CrossRef]

]. In the case of a circular hole, however, there is no such optimal polarization and the oscillation of LSPs around the hole is less strong, which inevitably leads to quantitatively different switching behavior at resonance. In order to look at this in greater details, we have measured the transmission spectra of Sample 3 which is an array of circular holes in NbN film as shown in Fig. 1(b). Figure 6(a)
Fig. 6 (a) THz transmission spectra at various temperature and (b) resonance frequency and transmission peak as a function of temperature for Sample 3.
shows the measured transmission spectra in the temperature region of 8.2-300 K. In normal state, the transmission maximum is lower than that of Samples 1 and 2. Meanwhile, the red-shift of resonance from the SPPs [ ± 1,0] mode (the calculated mode frequency is 815.4 GHz based on formula 1 from reference [2

2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]) is much smaller, that is consistent with the experiment results in optical regime [23

23. 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]

]. In the LC resonator model, the equivalent capacitance is much smaller for a circular hole and the resonance strength of LSPs is much weaker, both compared with the case for a rectangular hole. It results in much weaker coupling strength and smaller resonance frequency red-shift according to Fano model [21

21. 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(4-6), 331–336 (2003). [CrossRef]

].

On normal to superconducting transition, a switching process similar to that of Samples 1 and 2 occurs, as shown in Fig. 6(b). With circular holes, the contribution of superconductivity to enhancing the transmission efficiency is also evident as shown by the fact that the transmission maximum increases by a factor of 1.4 from 19 K to 8.2 K. Meanwhile, the maximum resonance frequency shift is less than 2%, much smaller than 11% for Sample 1. The smaller frequency shift could be attributed to weaker coupling between LSPs and SPPs. In superconducting state, the emergent Lk does lower the cut-off frequency of hole and enhances the coupling strength. However, considering that the oscillation of LSPs remains to be very weak as stated above, the enhancement of coupling strength is quite limited [17

17. 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(1-3), 61–66 (2004). [CrossRef]

]. As a result, the switching of resonance frequency is greatly degraded.

3. Summary

In conclusion, we have demonstrated that the enhanced THz transmission through subwavelength hole array in NbN film and the resonance frequency can be tuned by the temperature, thus manifesting the role superconductivity plays. The enhancement of resonance strength is attributed to the enhancement of SPPs and LSPs in superconducting state. And the change in coupling between LSPs and SPPs determines the red-shift of the resonance frequency. The enhanced transmission and tuning feature show good prospect in THz electronic devices.

Acknowledgments

This work is supported by the MOST 973 Project (No.2007CB310404, No.2011CBA00107) of China, the National Natural Science Foundation (Grant no. 61071009, 61027008), the Program for New Century Excellent Talents in University (NCET-07-0414) and the Specialized Research Fund for doctoral program of higher education (20090091110040).

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.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

3.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]

4.

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, Berlin, 1988), Chap.2.

5.

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29(8), 896–898 (2004). [CrossRef] [PubMed]

6.

W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43(1), 1–18 (2008). [CrossRef]

7.

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]

8.

A. Tsiatmas, A. R. Buckingham, V. A. Fedotov, S. Wang, Y. Chen, P. A. J. de Groot, and N. I. Zheludev, “Superconducting plasmonics and extraordinary transmission,” Appl. Phys. Lett. 97(11), 111106 (2010). [CrossRef]

9.

Z. Tian, R. Singh, J. Han, J. Gu, Q. Xing, J. Wu, and W. Zhang, “Terahertz superconducting plasmonic hole array,” Opt. Lett. 35(21), 3586–3588 (2010). [CrossRef] [PubMed]

10.

A. Pimenov, Submillimeter-Wave Electrodynamics of Superconductors, (Mathematisch-Naturwissenschaftliche Fakultät der Universität Augsburg, Augsburg, 2001), Chap.2.

11.

H.-T. Chen, H. Lu, A. K. Azad, R. D. Averitt, A. C. Gossard, S. A. Trugman, J. F. O’Hara, and A. J. Taylor, “Electronic control of extraordinary terahertz transmission through subwavelength metal hole arrays,” Opt. Express 16(11), 7641–7648 (2008). [CrossRef] [PubMed]

12.

M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q.-H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef] [PubMed]

13.

A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays,” Opt. Lett. 31(17), 2637–2639 (2006). [CrossRef] [PubMed]

14.

A. K. Azad and W. Zhang, “Resonant terahertz transmission in subwavelength metallic hole arrays of sub-skin-depth thickness,” Opt. Lett. 30(21), 2945–2947 (2005). [CrossRef] [PubMed]

15.

M. Tinkham, Introduction to superconductivity, (McGraw-Hill, New York, 1980)

16.

B. B. Jin, T. Dahm, S.-I. Lee, and N. Klein, “Anomalous coherence peak in the microwave conductivity of MgB2 thin film at 7.2 GHz,” Physica C 468(11-12), 861–864 (2008). [CrossRef]

17.

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(1-3), 61–66 (2004). [CrossRef]

18.

Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008). [CrossRef] [PubMed]

19.

Y. Bao, Studies on Extraordinary Transmission of Sub-wavelength Apertures in Infrared Region, (Ph.D. thesis, Nanjing University, 2008)

20.

S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H.-U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

21.

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(4-6), 331–336 (2003). [CrossRef]

22.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91(7), 071122 (2007). [CrossRef]

23.

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]

24.

B. A. Munk, Frequency Selective Surface,Theory and Design, (Wiley, New York, 2000), Chap. 1.

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(300.6495) Spectroscopy : Spectroscopy, teraherz
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: November 29, 2010
Revised Manuscript: January 6, 2011
Manuscript Accepted: January 7, 2011
Published: January 10, 2011

Citation
Jingbo Wu, Hao Dai, Hao Wang, Biaobing Jin, Tao Jia, Caihong Zhang, Chunhai Cao, Jian Chen, Lin Kang, Weiwei Xu, and Peiheng Wu, "Extraordinary terahertz transmission in superconducting subwavelength hole array," Opt. Express 19, 1101-1106 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1101


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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. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  3. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
  4. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, Berlin, 1988), Chap.2.
  5. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29(8), 896–898 (2004). [CrossRef] [PubMed]
  6. W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43(1), 1–18 (2008). [CrossRef]
  7. 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]
  8. A. Tsiatmas, A. R. Buckingham, V. A. Fedotov, S. Wang, Y. Chen, P. A. J. de Groot, and N. I. Zheludev, “Superconducting plasmonics and extraordinary transmission,” Appl. Phys. Lett. 97(11), 111106 (2010). [CrossRef]
  9. Z. Tian, R. Singh, J. Han, J. Gu, Q. Xing, J. Wu, and W. Zhang, “Terahertz superconducting plasmonic hole array,” Opt. Lett. 35(21), 3586–3588 (2010). [CrossRef] [PubMed]
  10. A. Pimenov, Submillimeter-Wave Electrodynamics of Superconductors, (Mathematisch-Naturwissenschaftliche Fakultät der Universität Augsburg, Augsburg, 2001), Chap.2.
  11. H.-T. Chen, H. Lu, A. K. Azad, R. D. Averitt, A. C. Gossard, S. A. Trugman, J. F. O’Hara, and A. J. Taylor, “Electronic control of extraordinary terahertz transmission through subwavelength metal hole arrays,” Opt. Express 16(11), 7641–7648 (2008). [CrossRef] [PubMed]
  12. M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q.-H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef] [PubMed]
  13. A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays,” Opt. Lett. 31(17), 2637–2639 (2006). [CrossRef] [PubMed]
  14. A. K. Azad and W. Zhang, “Resonant terahertz transmission in subwavelength metallic hole arrays of sub-skin-depth thickness,” Opt. Lett. 30(21), 2945–2947 (2005). [CrossRef] [PubMed]
  15. M. Tinkham, Introduction to superconductivity, (McGraw-Hill, New York, 1980)
  16. B. B. Jin, T. Dahm, S.-I. Lee, and N. Klein, “Anomalous coherence peak in the microwave conductivity of MgB2 thin film at 7.2 GHz,” Physica C 468(11-12), 861–864 (2008). [CrossRef]
  17. 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(1-3), 61–66 (2004). [CrossRef]
  18. Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008). [CrossRef] [PubMed]
  19. Y. Bao, Studies on Extraordinary Transmission of Sub-wavelength Apertures in Infrared Region, (Ph.D. thesis, Nanjing University, 2008)
  20. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H.-U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]
  21. 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(4-6), 331–336 (2003). [CrossRef]
  22. J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91(7), 071122 (2007). [CrossRef]
  23. 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]
  24. B. A. Munk, Frequency Selective Surface,Theory and Design, (Wiley, New York, 2000), Chap. 1.

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