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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 11 — Nov. 26, 2007
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Tunable transmission at 100 THz through a metallic hole array with a varying hole channel shape

Arvind Battula, Yalin Lu, R. J. Knize, Kitt Reinhardt, and Shaochen Chen  »View Author Affiliations


Optics Express, Vol. 15, Issue 22, pp. 14629-14635 (2007)
http://dx.doi.org/10.1364/OE.15.014629


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Abstract

Extraordinary optical transmission spectrum for a two-dimensional metallic hole array (2D-MHA) changes with the hole channel shape. In this paper a new converging-diverging channel (CDC) shape is proposed. A three-dimensional (3D) finite element method is utilized to analyze the transmission characteristics of the 2D-MHA with CDC. The transmission peaks are blue-shifted when the gap at the throat of CDC is reduced. Similar blue-shift in the transmission peaks are observed for a straight channel MHA when the aperture size is reduced. The transmission for the straight channel MHA is not sensitive to the metal film thickness. But, for a CDC MHA the transmission varies with the metal film thickness. Also, the CDC shape gives an extra degree of geometrical variable to 2D-MHA for tuning the transmission peak location with potential applications in nanolithography, imaging and biosensing.

© 2007 Optical Society of America

1. Introduction

However the effect of hole channel shape on the transmission characteristics has not received much attention. The hole size along with the channel shape will have significant impact on the transmission efficiency because the holes are expected to mediate the SPP coupling between both surfaces. Hence in the present study the subwavelength hole having converging diverging channel (CDC) is studied specifically along with the straight channel for transmission properties. This proposed CDC shape would still allow similar EOT effects but, would give an extra degree of freedom in a geometric variable to tune the transmission spectrum. This extra degree of freedom is the gap at the throat of the CDC channel (Fig. 1). A similar study [29

29. A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging-diverging channels,” Appl. Phys. Lett. 89, 131113 (2006). [CrossRef]

] was performed on subwavelength metallic slits having a CDC and it was found that the transmission resonance bands would move close to each other in the spectrum locations when decreasing the throat size of CDC.

2. Computational method

Figure 1 shows a schematic view of the square array of holes having CDC shape in a metallic film with the definition of different parameters: the period of hole array (d), the aperture size (A), the thickness of the metallic film (t), the slope or angle of the CDC shape (θ) and the gap at the throat (g). Figure 1(b) shows a cross-sectional view of the CDC channel with an angle (θ), which would relate ‘A’ and ‘g’ by a simple equation g = A - tan(θ)*t. The metallic film considered is silver (Ag) and for most part of the current study we used a fixed value for the period (d = 19.0 μm) and thickness (t = 2.0 μm). Although the transmission resonances of the holes depend on their period and thickness, they are fixed in this study to explore the effect of different aperture dimension and throat size. Nevertheless, it should be pointed out that the effects discussed in this present study do appear for any other range of hole parameters provided that ‘A’ is very small in comparison to ‘d’. Also the frequency of incident light has to be well below the plasma frequency of the metal and for the present study we considered the frequency to be around 100 THz or 20 μm wavelength. The silver dielectric constant was described by a Drude model ε = ε, - ω2 p / (ω2 + iγω) by taking ε = -175.0, ωp = 1.1 × 1016 s-1, and γ = 10.51 × 1013 s-1 in order to fit the empirical data given by [30

30. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

] in the 100 THz frequency region. The electromagnetic fields were assumed to be time harmonic and the resulting governing equation for the steady-state distribution is solved by using a commercially available 3-dimensional (3D) finite element software (COMSOL 3.2a) [31

31. COMSOL 3.2a Reference Manual, version 3.2 ed. (Comsol AB, 2005).

]. The computational domain considered is a single unit cell surrounded by either periodic boundary conditions or by perfectly matching layer (PML) as given in [32

32. A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, “Comprehensive FDTD modelling of photonic crystal waveguide components,” Opt. Express 12, 234 (2004). [CrossRef] [PubMed]

]. The light is incident normal to the film surface and the transmittance is calculated from the obtained electromagnetic field distributions.

Fig. 1. (a). Schematic view of silver metallic hole array having periodicity ‘d’ with converging-diverging channels (CDC), (b) cross-sectional view of the CDC shape with aperture (A), thickness (t), slope or angle (θ) of CDC shape and gap at the throat (g).

3. Results and Discussion

Figure 2(a) shows the transmission spectrum for Ag MHAs having various aperture sizes. The transmission spectrum changes when the aperture size decreases. But, the magnitude of the transmission peak remains the same when the aperture size increases and this is unexpected according to the Bethe-Bouwkamp power law model [33

33. H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163 (1944). [CrossRef]

, 34

34. C. J. Bouwkamp, “On the Diffraction of Electromagnetic Waves by Small Circular Disks and Holes,” Philips Res. Rep. 5, 401 (1950).

]. According to this model the transmissivity for a single hole should vary with (A/λ)4, where ‘A’ is the aperture size and ‘λ’ is the wavelength of light. One possible reason is that the transmission through the holes might have reached saturation with respect to the open air fraction of the metallic film [35

35. 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]

]. The full width at half maximum (FWHM) of the transmission peaks becomes smaller when the aperture size decreases. The peak of the transmission has a blue-shift when the aperture size decreases, which is in agreement with the result reported by [35

35. 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]

]. Figure 2(b) shows the transmission spectrum for different MHAs having CDC shape or straight channel shape. For CDC shape smaller throat sizes ‘g’ are considered while the aperture size ‘A’ is fixed at 10 μm. It can be observed that the straight channel has a broader transmission peak. When the channel shape is changed to CDC then the transmittance peaks become narrower along with a blue-shift. The blue-shift is larger when the throat gets smaller. In addition the transmission on the red side of the peak decays faster for the CDC shape MHA with smaller throat when compared to the other cases. Also, it is to be noted that the transmission peak magnitudes do not decrease with the CDC shape.

Fig. 2. (a). Transmission spectrum for a silver metallic hole array with a straight channel shape having period ‘d’ = 19 μm, thickness ‘t’ = 2 μm and different aperture sizes ‘A’, (b) Transmission spectrum for silver metallic hole array with converging-diverging channel having period ‘d’ = 19 μm, thickness ‘t’ = 2 μm, aperture ‘A’ = 10 μm and different gaps at the throat ‘g’.

Figure 3(a) shows the transmittance of MHAs at λ = 20 μm for two different aperture sizes with varying ‘g’. For A = 10 μm the MHA with a straight channel (g = 10 μm) has higher transmission when compared to the CDC shape with different throat sizes. The transmission decreases exponentially with the decrease in the throat size and reaches ‘0’ value asymptotically. For A = 12 μm the transmission for the straight channel (g = 12 μm) is not the highest. But, the CDC shape with approximately g = 9.75 μm has near unity transmittance. Hence, it can be seen that when A = 12 μm the transmittance increases as the throat size reduces until it reaches a maximum transmission and then decreases exponentially with the decrease in the ‘g’. This suggests that the CDC shape with a particular ‘g’ aids the mediation of SPP mode coupling between the incident and transmitted surfaces. Similar kind of behavior was observed previously in gold metallic gratings having CDC shape [29

29. A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging-diverging channels,” Appl. Phys. Lett. 89, 131113 (2006). [CrossRef]

]. It is to be noted that the small variation in transmittance for A = 12 μm near the peak is due to the numerical calculations with different mesh densities.

Fig. 3. Transmittance at wavelength ‘A’ = 20 μm for silver metallic hole array with converging-diverging channel having period ‘d’ = 19 μm, thickness ‘t’ = 2 μm, different aperture sizes ‘A’ and varying gaps at the throat ‘g’.

Figure 4 shows the transmittance of different MHAs with respect to wavelength and aperture size ‘A’ or throat size ‘g’ (g = A - tan(θ)*t) where ‘θ’ [Fig. 1(b)] and the thickness are held fixed. Figure 4(a) shows the transmittance for MHAs with straight channel or θ = 0°. It can be seen that at a large aperture the transmittance is high at large wavelengths and decreases very slowly as the wavelength is reduced. But, when the aperture is small the transmittance is high at lower wavelengths and it decreases very sharply as the wavelength increases. Also, it can be noted from Fig. 4(a) is that the location of the transmittance peak spectrum changes linearly as the ‘A’ or ‘g’ decreases. In addition, the full width at half maximum (FWHM) of the transmittance peaks is large when the aperture is big and it becomes very narrow as the aperture is reduced. Similar kind of transmittance variation [Fig. 4(b)] is observed for the CDC MHA having θ = 50°. But, this time transmission suffers a cutoff aperture size where there is no transmittance below a particular aperture size. Furthermore the location of the transmittance peak spectrum with respect to the aperture or throat size is not exactly linear. When the ‘θ’ in CDC MHA increases to 65° [Fig. 4(c)] and 72° [Fig. 4(d)] the cut-off aperture for zero transmittance increases.

Fig. 4. Transmittance spectrum of silver metallic hole array with period ‘d’ = 19 μm, thickness ‘t’ = 2 μm for varying aperture sizes ‘A’ and hole channel shapes as (a) straight, (b) CDC shape with angle ‘θ’ = 50°, (c) CDC shape with angle ‘θ’ = 65°, and (d) CDC shape with angle ‘θ’ = 72°.

4. Conclusion

It has been shown that the transmission spectrum of metallic hole arrays (MHAs) with converging-diverging channel (CDC) changes with the gap at the throat. The transmission peaks are blue-shifted when the throat size is reduced. Whereas, MHAs with a straight channel and a large aperture have broad transmission peaks at longer wavelengths. But, when the aperture size decreases, the transmission peak shifts to a lower wavelength and become narrower. It is also shown that the transmittance can be increased when the MHA channel changes from straight to CDC. But, the transmittance of MHAs with CDC shape suffers a cutoff aperture size below which there will be no transmission. The cut-off aperture size increases as the angle (θ) of the CDC shape increases. Also, it has been shown that the transmittance of MHAs with straight channel does not change much with the thickness of the film. But, for the MHA with CDC shape the transmittance is very sensitive to the thickness of the film. The proposed CDC shape in MHAs could lead to extraordinary transmission at different wavelengths and can be used to develop THz filters. This could lead to a wide range of potential applications in integrated photonic circuits, tunable filters, near-field optics, imaging, nanolithography, and biological sensors.

Acknowledgments

Financial support from the US Air Force of Scientific Research (AFOSR) is greatly appreciated. This work was also supported in part by research grants from the US National Science Foundation. The authors appreciate the computer support from the Intel’s Higher Education Program.

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 (London) 351, 667, 1998. [CrossRef]

2.

Q. Cao and P. Lalanne, “Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits,” Phys. Rev. Lett. 88, 057403 (2002). [CrossRef] [PubMed]

3.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629 (2004). [CrossRef] [PubMed]

4.

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

5.

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

6.

H. Cao and A. Nahata, “Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures,” Opt. Express 12, 3664 (2004). [CrossRef] [PubMed]

7.

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]

8.

J. O’Hara, R. D. Averitt, and A. J. Taylor, “Terahertz surface plasmon polariton coupling on metallic gratings,” Opt. Express 12, 6397 (2004). [CrossRef] [PubMed]

9.

A. K. Azad, Y. Zhao, and W. Zhang, “Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array,” Appl. Phys. Lett. 86, 141102 (2005). [CrossRef]

10.

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

11.

C. Janke, J. Gómez Rivas, C. Schotsch, L. Beckmann, P. H. Bolivar, and H. Kurz, “Optimization of enhanced terahertz transmission through arrays of subwavelength apertures,” Phys. Rev. B 69, 205314 (2004). [CrossRef]

12.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847 (2004). [CrossRef] [PubMed]

13.

M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30, 1210 (2005). [CrossRef] [PubMed]

14.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong Polarization in the Optical Transmission through Elliptical Nanohole Arrays,” Phys. Rev. Lett. 92, 037401 (2004). [CrossRef] [PubMed]

15.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92, 183901 (2004). [CrossRef] [PubMed]

16.

J. A. Matteo, D. P. Fromm, Y. Yue, P. J. Schuck, W. E. Moerner, and L. Hesselink, “Spectral analysis of strongly enhanced visible light transmission through single C-shaped nanoapertures,” Appl. Phys. Lett. 85, 648 (2004). [CrossRef]

17.

X. L. Shi, L. Hesselink, and R. L. Thornton, “Ultrahigh light transmission through a C-shaped nanoaperture,” Opt. Lett. 28, 1320 (2003). [CrossRef] [PubMed]

18.

Y. H. Ye, D. Y. Jeong, and Q. M. Zhang, “Fabrication of strain tunable infrared frequency selective surfaces on electrostrictive poly(vinylidene fluoride-trifluoroethylene) copolymer films using a stencil mask method,” Appl. Phys. Lett. 85, 654 (2004). [CrossRef]

19.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays,” Phys. Rev. Lett. 94, 033902 (2005). [CrossRef] [PubMed]

20.

K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes,” Phys. Rev. Lett. 92, 183901 (2004). [CrossRef] [PubMed]

21.

Q-j. Wang, J-q. Ki, C-p. Huang, C. Zhang, and Y-y Zhu, “Enhanced optical transmission through metal films with rotation-symmetrical hole arrays,” Appl. Phys. Lett. 87, 091105 (2005). [CrossRef]

22.

K. Nishio and H. Masuda, “Dependence of optical properties of ordered metal hole array on refractive index of surrounding medium,” Electrochem. Solid-State Lett. 7, H27 (2004). [CrossRef]

23.

C. L. Pan, C. F. Hsieh, R. P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Opt. Express 13, 3921 (2005). [CrossRef] [PubMed]

24.

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 (2002). [CrossRef]

25.

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

26.

D. Korobkin, Y. A. Urzhumov, B. Neuner III, C. Zorman, Z. Zhang, I. D. Mayergoyz, and G. Shvets, “Mid-infrared metamaterial based on perforated SiC membrane: engineering optical response using surface phonon polaritions,” Appl. Phys. A , 88, 605 (2007). [CrossRef]

27.

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express , 14, 5664 (2006). [CrossRef] [PubMed]

28.

H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photonics Nanostruct. Fundam. Appl. 4, 123 (2006). [CrossRef]

29.

A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging-diverging channels,” Appl. Phys. Lett. 89, 131113 (2006). [CrossRef]

30.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

31.

COMSOL 3.2a Reference Manual, version 3.2 ed. (Comsol AB, 2005).

32.

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, “Comprehensive FDTD modelling of photonic crystal waveguide components,” Opt. Express 12, 234 (2004). [CrossRef] [PubMed]

33.

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163 (1944). [CrossRef]

34.

C. J. Bouwkamp, “On the Diffraction of Electromagnetic Waves by Small Circular Disks and Holes,” Philips Res. Rep. 5, 401 (1950).

35.

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]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1220) Diffraction and gratings : Apertures
(120.2440) Instrumentation, measurement, and metrology : Filters
(120.7000) Instrumentation, measurement, and metrology : Transmission
(240.6680) Optics at surfaces : Surface plasmons
(040.2235) Detectors : Far infrared or terahertz

ToC Category:
Diffraction and Gratings

History
Original Manuscript: September 13, 2007
Revised Manuscript: October 18, 2007
Manuscript Accepted: October 19, 2007
Published: October 22, 2007

Virtual Issues
Vol. 2, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Arvind Battula, Yalin Lu, R. J. Knize, Kitt Reinhardt, and Shaochen Chen, "Tunable transmission at 100 THz through a metallic hole array with a varying hole channel shape," Opt. Express 15, 14629-14635 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-15-22-14629


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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 (London) 351, 667, 1998. [CrossRef]
  2. Q. Cao and P. Lalanne, "Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 88, 057403 (2002). [CrossRef] [PubMed]
  3. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629 (2004). [CrossRef] [PubMed]
  4. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39 (2007). [CrossRef]
  5. D. Qu, D. Grischkowsky, and W. Zhang, "Terahertz transmission properties of thin, subwavelength metallic hole arrays," Opt. Lett. 29, 896 (2004). [CrossRef] [PubMed]
  6. H. Cao and A. Nahata, "Influence of aperture shape on the transmission properties of a periodic array of subwavelength apertures," Opt. Express 12, 3664 (2004). [CrossRef] [PubMed]
  7. 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]
  8. J. O’Hara, R. D. Averitt, and A. J. Taylor, "Terahertz surface plasmon polariton coupling on metallic gratings," Opt. Express 12, 6397 (2004). [CrossRef] [PubMed]
  9. A. K. Azad, Y. Zhao, and W. Zhang, "Transmission properties of terahertz pulses through an ultrathin subwavelength silicon hole array," Appl. Phys. Lett. 86, 141102 (2005). [CrossRef]
  10. J. Gómez Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003). [CrossRef]
  11. C. Janke, J. Gómez Rivas, C. Schotsch, L. Beckmann, P. H. Bolivar, and H. Kurz, "Optimization of enhanced terahertz transmission through arrays of subwavelength apertures," Phys. Rev. B 69, 205314 (2004). [CrossRef]
  12. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847 (2004). [CrossRef] [PubMed]
  13. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa and E. Sano "Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays," Opt. Lett. 30, 1210 (2005). [CrossRef] [PubMed]
  14. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong Polarization in the Optical Transmission through Elliptical Nanohole Arrays," Phys. Rev. Lett. 92, 037401 (2004). [CrossRef] [PubMed]
  15. K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 92, 183901 (2004). [CrossRef] [PubMed]
  16. J. A. Matteo, D. P. Fromm, Y. Yue, P. J. Schuck, W. E. Moerner, and L. Hesselink, "Spectral analysis of strongly enhanced visible light transmission through single C-shaped nanoapertures," Appl. Phys. Lett. 85, 648 (2004). [CrossRef]
  17. X. L. Shi, L. Hesselink, and R. L. Thornton, "Ultrahigh light transmission through a C-shaped nanoaperture," Opt. Lett. 28, 1320 (2003). [CrossRef] [PubMed]
  18. Y. H. Ye, D. Y. Jeong, and Q. M. Zhang, "Fabrication of strain tunable infrared frequency selective surfaces on electrostrictive poly(vinylidene fluoride-trifluoroethylene) copolymer films using a stencil mask method," Appl. Phys. Lett. 85, 654 (2004). [CrossRef]
  19. W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, "Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays," Phys. Rev. Lett. 94, 033902 (2005). [CrossRef] [PubMed]
  20. K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst and L. Kuipers, "Strong Influence of Hole Shape on Extraordinary Transmission through Periodic Arrays of Subwavelength Holes," Phys. Rev. Lett. 92, 183901 (2004). [CrossRef] [PubMed]
  21. Q-j. Wang, J-q. Ki, C-p. Huang, C. Zhang and Y-y Zhu, "Enhanced optical transmission through metal films with rotation-symmetrical hole arrays," Appl. Phys. Lett. 87, 091105 (2005). [CrossRef]
  22. K. Nishio and H. Masuda, "Dependence of optical properties of ordered metal hole array on refractive index of surrounding medium," Electrochem. Solid-State Lett. 7, H27 (2004). [CrossRef]
  23. C. L. Pan, C. F. Hsieh, R. P. Pan, M. Tanaka, F. Miyamaru, M. Tani and M. Hangyo, "Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal," Opt. Express 13, 3921 (2005). [CrossRef] [PubMed]
  24. 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 (2002). [CrossRef]
  25. A. Z. Azad, and W. Zhang, "Resonant terahertz transmission in subwavelength metallic hole arrays of sub-skin-depth thickness," Opt. Lett. 30, 2945 (2005). [CrossRef] [PubMed]
  26. D. Korobkin, Y. A. Urzhumov, B. NeunerIII, C. Zorman, Z. Zhang, I. D. Mayergoyz, and G. Shvets, "Mid-infrared metamaterial based on perforated SiC membrane: engineering optical response using surface phonon polaritions," Appl. Phys. A,  88, 605 (2007). [CrossRef]
  27. J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express,  14, 5664 (2006). [CrossRef] [PubMed]
  28. H. Daninthe, S. Foteinopoulou, C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photonics Nanostruct. Fundam. Appl. 4, 123 (2006). [CrossRef]
  29. A. Battula, and S. C. Chen, "Extraordinary transmission in a narrow energy band for metallic gratings with converging-diverging channels," Appl. Phys. Lett. 89, 131113 (2006). [CrossRef]
  30. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  31. COMSOL 3.2a Reference Manual, version 3.2 ed. (Comsol AB, 2005).
  32. A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234 (2004). [CrossRef] [PubMed]
  33. H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163 (1944). [CrossRef]
  34. C. J. Bouwkamp, "On the Diffraction of Electromagnetic Waves by Small Circular Disks and Holes," Philips Res. Rep. 5, 401 (1950).
  35. 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]

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