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.

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  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]

2010 (2)

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]

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]

2007 (2)

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

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

2004 (1)

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).

2003 (2)

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]

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]

2000 (2)

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]

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]

1999 (2)

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]

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]

1998 (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]

1971 (1)

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]

Avrutsky, I.

Biswas, R.

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]

Bolivar, P. H.

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]

de Maagt, P.

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]

Delgado, V.

Ebbesen, T. W.

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]

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

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]

Ederra, I.

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]

El-Kady, I.

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]

García de Abajo, F. J.

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

García Vidal, F. J.

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]

Garcia-Vidal, F. J.

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]

Genet, C.

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

Ghaemi, H. F.

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]

Gonzalo, R.

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]

Heitmann, D.

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]

Ho, K. M.

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]

Holker, M.

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]

Jelinek, L.

Kochergin, V.

Kuipers, L.

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]

Lezec, H. J.

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).

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]

Marqués, R.

Martín-Moreno, L.

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]

Pendry, J. B.

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]

Pierce, D. T.

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]

Porto, J. A.

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]

Reynolds, A. L.

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]

Rivas, J. G.

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]

Sarrazin, M.

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]

Schroter, U.

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]

Sigalas, M. M.

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]

Soukoulis, C. M.

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]

Spicers, W. E.

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]

Thio, T.

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).

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]

Vigneron, J. P.

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]

Wolff, P. A.

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]

Zhao, Y.

IEEE Trans. Microwave Theory Tech. (1)

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]

Nature (London) (2)

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]

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

Opt. Express (1)

Opt. Lett. (2)

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]

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).

Phys. Rev. B (3)

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]

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]

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]

Phys. Rev. E (1)

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]

Phys. Rev. Lett. (1)

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]

Rev. Mod. Phys. (2)

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

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]

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Figures (4)

Fig. 1
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.

Fig. 2
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.

Fig. 3
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.

Fig. 4
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.

Equations (11)

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E y = 1 + R + n = 1 N R n cos ( 2 n π y / a )
E y + = T + n = 1 N T n cos ( 2 n π y / a )
H x = Y 0 ( 1 + R ) + n = 1 N Y n R n cos ( 2 n π y / a )
H x + = Y 0 T n = 1 N Y n T n cos ( 2 n π y / a ) ,
[ E y , n + + E y , n E y , n + E y , n ] [ Z n ( 1 ) 0 0 Z n ( 2 ) ] [ H x , n + H x , n H x , n + + H x , n ] ,
Z n ( 1 ) = [ 1 + cos ( k z , n t ) ] i sin ( k z , n t ) Y d , n and Z n ( 2 ) = i sin ( k z , n t ) [ 1 + cos ( k z , n t ) ] Y d , n ,
a / 2 a / 2 A cos ( 2 m π y a ) dx = b / 2 b / 2 A cos ( 2 m π y a ) dx b / 2 b / 2 Adx = a / 2 a / 2 Adx ,
( 1 + Z n ( 1 ) Y n ) ( T n + R n ) = 2 ( 1 + R + T ) 2 Z 0 ( 1 ) Y 0 ( 1 R T ) ; n a / b
( 1 + Z n ( 2 ) Y n ) ( T n R n ) = 2 ( 1 R + T ) 2 Z 0 ( 2 ) Y 0 ( 1 + R T ) ; n a / b
1 Z s ( 1 ) Y 0 + ( 1 + Z s ( 1 ) Y 0 ) ( T + R ) + n = 1 N ( 1 + Z s ( 1 ) Y n ) ( T n + R n ) sinc ( bn π a ) = 0
1 + Z s ( 2 ) Y 0 + ( 1 + Z s ( 2 ) Y 0 ) ( T R ) + n = 1 N ( 1 + Z s ( 2 ) Y n ) ( T n + R n ) sinc ( bn π a ) = 0 ,

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