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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 14 — Jul. 4, 2011
  • pp: 13612–13617
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Extraordinary transmission through dielectric screens with 1D sub-wavelength metallic inclusions

V. Delgado, R. Marqués, and L. Jelinek  »View Author Affiliations


Optics Express, Vol. 19, Issue 14, pp. 13612-13617 (2011)
http://dx.doi.org/10.1364/OE.19.013612


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Abstract

Extraordinary optical transmission (EOT) through dielectric screens periodically loaded with sub-wavelength 1D discontinuities, such as apertures or metallic insets is analyzed. The results of the analysis and computational electromagnetic simulations show that the transmission is higher for for metallic inclusions than for empty slits. This effect confirms that EOT is a quite general property of weakly transparent periodic diffraction screens and opens the door to optically induced EOT in photo-conductive semiconductor screens.

© 2011 OSA

1. Introduction

The first reports on extraordinary optical transmission (EOT) through metallic screens periodically perforated by sub-wavelength holes or slits [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 (London) 391, 667–669 (1998). [CrossRef]

, 2

2. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

] stimulated many subsequent experimental and theoretical studies of this effect. The reader is referred to the excellent reviews by C. Genet et al. [3

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

], F. J. García de Abajo [4

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

] or F.J. García Vidal et al. [5

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

] in order to have a complete overview of the topic. Soon after the seminal work of Ebbesen was published, it was reported that EOT also appears in periodically corrugated thin metal films without apertures [6

6. U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60(7), 4992–4999 (1999). [CrossRef]

, 7

7. I. Avrutsky, Y. Zhao, and V. Kochergin , “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25(9), 595–597 (2000). [CrossRef]

], and in non-metallic dielectric screens with apertures [8

8. M. Sarrazin and J. P. Vigneron, “Optical properties of tungsten thin films perforated with a bidimensional array of subwavelength holes,” Phys. Rev. E 68, 016603 (2003). [CrossRef]

, 9

9. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Lett. 12(16), 3629–3651 (2004).

]. Therefore, it seems that nor the metallic nature of the screen nor the presence of apertures are essential for the presence of EOT. On the contrary, it seems that EOT will appear, for the appropriate light polarization, when: (i) There is some periodic modulation of the electrical properties of the screen and (ii) there is some weak coupling mechanism between both surfaces of the screen.

Following this ansatz, we will study EOT through high permittivity thin dielectric screens, which will provide the required weak coupling between both sides of the screen. Our analysis and numerical simulations will show that dielectric screens periodically loaded either with apertures or with metallic inclusions may present EOT in the vicinity of Wood’s anomaly. Surprisingly, transmittance will be higher for metallic inclusions than for apertures.

2. Theory

Fig. 1 Front and side views of the unit cell of the analyzed structures. Due to the polarization of the incident wave and due to periodicity, upper and lower planes of the unit cell are virtual perfect conducting plates (PEC).Therefore, the structures are equivalent to a symmetrical metallo-dielectric discontinuity in a parallel-plate waveguide. (a) and (b): Front and side views of the unit cell of a dielectric screen with apertures. (c): Side view of the unit cell of a dielectric screen with metallic insets.

3. Results

Fig. 2 Transmittance through a zirconium-tin-titanate (ε = 92.7(1 + 0.005i)) screen of thickness t = 0.12 mm, periodically perforated by an array of parallel slits of periodicity a = 3 mm and width b = a/6, which can be either empty or filled by a PEC. Solid lines are our results computed from Eqs. (8)(11). Dashed lines are results from CST. Upper scale shows the ratio f/f w, where f w is the frequency corresponding to Wood’s anomaly f w = c/a.

In the THz range of frequencies most metals behave as PEC. Thus, transmittances through the same diffraction screen, but with the slits filled with a PEC, was analyzed. The results of this analysis, also shown in Fig. 2, illustrate how EOT can be induced by metallic inclusions in low-loss, high permittivity, thin dielectric screens operating in the THz frequency range and below. Surprisingly, transmittance is higher with metallic inclusions than with apertures.

Similar results are shown at infrared frequencies in Fig. 3 for screens of amorphous silicon (a-Si), periodically loaded with silver inclussions. In this analysis, the metallic inclusions were modeled using standard Drude theory with the constants already used in [13

13. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in three-dimensional metallic lattices,” Phys. Rev. B 62, 15299–15302 (2000). [CrossRef]

] for silver. The results of Fig. 3 show that the increase of transmittance in a-Si screens loaded with metallic insets is much higher than the corresponding increase of transmittance due to the presence of open slits in the screen, which is actually very weak.

Fig. 3 Transmittance through an a-Si screen periodically perforated by an array of parallel slits which can be either empty or filled with silver. Solid lines are our results computed from Eqs. (8)(11). In (a), the periodicity of the array is a = 3 μm, the thickness of the slab is t = 200 nm and the permittivity of a-Si is ε = 11.8(1+0.007i) [12]. In (b) a = 1.55 μm, t = 100 nm and the permittivity of a-Si is ε = 12.4(1 + 0.016i). In both cases the width of the slits/inclusions is b = a/4. Dashed lines are results from CST. Upper scale shows the ratio f / f w, where f w is the frequency corresponding to Wood’s anomaly f w = c/a.

It is well known that EOT can be associated to the excitation of weakly coupled leaky surface waves at both sides of the screen. In standard EOT, these surface waves are coupled through the apertures perforated in the screen. In low-loss dielectric screens, this coupling is ensured by the screen itself, and the role of the metallic inclusions is merely to allow for the excitation of the surface waves. In order to support this interpretation, we show in Fig. 4 the electric field distribution at both sides of the screen in the configuration of Fig. 3 at the frequency of maximum transmission. A clear standing wave pattern corresponding to the simultaneous excitation of two surface waves traveling at opposite directions along each side of the screen can be appreciated in both cases. These field distributions are very similar to those found in simulations of metallic screens at optical frequencies, thus confirming that the excitation of coupled surface waves with wavelengths close to the periodicity is the physical mechanism behind EOT in dielectric screens with conductive insets.

Fig. 4 Normalized electric field distribution (absolute value) at both sides of the screen for the configuration analyzed in Fig. 2 with empty slits (upper figure) and slits filled by PEC (lower figure). Calculations were made using CST, and correspond to the frequency of maximum transmission in both cases. Green color corresponds to low field values and red color to maximum field value.

4. Conclusion

An analytical model for EOT through high permittivity 1D dielectric screens periodically loaded with open slits or metallic inclusions has been provided and validated with full wave electromagnetic simulations. Analytical and numerical results show that EOT through high permittivity dielectric screens loaded with a periodic distribution of metallic inclusions is higher than for the corresponding screens with empty slits.

Regions with a high density of free electrons can be induced in most semiconductors by using lasers of the appropriate wavelength. Thus, we feel that the reported effect opens the door to the design of photo-induced EOT in semiconductor screens at THz and infrared frequencies.

Acknowledgments

This work has been supported by the Spanish Ministerio de Educación y Ciencia and European Union FEDER funds (project No. CSD2008-00066), by the Czech Grant Agency (project No. 102/09/0314), and by the Czech Technical University in Prague (project No. SGS10/271/OHK3/3T/13).

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) 391, 667–669 (1998). [CrossRef]

2.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

3.

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

4.

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

5.

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

6.

U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60(7), 4992–4999 (1999). [CrossRef]

7.

I. Avrutsky, Y. Zhao, and V. Kochergin , “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25(9), 595–597 (2000). [CrossRef]

8.

M. Sarrazin and J. P. Vigneron, “Optical properties of tungsten thin films perforated with a bidimensional array of subwavelength holes,” Phys. Rev. E 68, 016603 (2003). [CrossRef]

9.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Lett. 12(16), 3629–3651 (2004).

10.

V. Delgado, R. Marqués, and L. Jelinek, “Analytical theory of extraordinary optical transmission through realistic metallic screens,” Opt. Express 18, 6506–6515 (2010). [CrossRef] [PubMed]

11.

P. H. Bolivar, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Tech. 51(4), 1062–1066 (2003). [CrossRef]

12.

D. T. Pierce and W. E. Spicers, “Electronic structure of amorphous Si from photoemission and optical studies,” Phys. Rev. B 5, 3017–3029 (1971). [CrossRef]

13.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in three-dimensional metallic lattices,” Phys. Rev. B 62, 15299–15302 (2000). [CrossRef]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1960) Diffraction and gratings : Diffraction theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 22, 2011
Revised Manuscript: June 2, 2011
Manuscript Accepted: June 3, 2011
Published: June 29, 2011

Citation
V. Delgado, R. Marqués, and L. Jelinek, "Extraordinary transmission through dielectric screens with 1D sub-wavelength metallic inclusions," Opt. Express 19, 13612-13617 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13612


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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) 391, 667–669 (1998). [CrossRef]
  2. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]
  3. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature (London) 445, 39–46 (2007). [CrossRef]
  4. F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]
  5. F. J. García Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010). [CrossRef]
  6. U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60(7), 4992–4999 (1999). [CrossRef]
  7. I. Avrutsky, Y. Zhao, and V. Kochergin , “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25(9), 595–597 (2000). [CrossRef]
  8. M. Sarrazin and J. P. Vigneron, “Optical properties of tungsten thin films perforated with a bidimensional array of subwavelength holes,” Phys. Rev. E 68, 016603 (2003). [CrossRef]
  9. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Lett. 12(16), 3629–3651 (2004).
  10. V. Delgado, R. Marqués, and L. Jelinek, “Analytical theory of extraordinary optical transmission through realistic metallic screens,” Opt. Express 18, 6506–6515 (2010). [CrossRef] [PubMed]
  11. P. H. Bolivar, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Tech. 51(4), 1062–1066 (2003). [CrossRef]
  12. D. T. Pierce and W. E. Spicers, “Electronic structure of amorphous Si from photoemission and optical studies,” Phys. Rev. B 5, 3017–3029 (1971). [CrossRef]
  13. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Photonic band gaps in three-dimensional metallic lattices,” Phys. Rev. B 62, 15299–15302 (2000). [CrossRef]

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