Abstract

Extraordinary Optical Transmission of TM waves impinging at oblique incidence on metallic or high permittivity dielectric screens with a periodic distribution of 1D slits or any other kind of 1D defects is analyzed. Generalized waveguide theory altogether with the surface impedance concept are used for modeling such phenomena. A numerical analysis based on the mode matching technique proves to be an efficient tool for the characterization of these structures for any angle of incidence and slit or defect apertures.

© 2011 OSA

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References

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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. E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (2003).
    [CrossRef]
  3. A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
    [CrossRef]
  4. 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(15), 6779–6782 (1998).
    [CrossRef]
  5. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
    [CrossRef] [PubMed]
  6. 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]
  7. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [CrossRef] [PubMed]
  8. R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17(7), 5571–5579 (2009).
    [CrossRef] [PubMed]
  9. V. Delgado, R. Marqués, and L. Jelinek, “Analytical theory of extraordinary optical transmission through realistic metallic screens,” Opt. Express 18(7), 6506–6515 (2010).
    [CrossRef] [PubMed]
  10. V. Delgado, R. Marqués, and L. Jelinek, “Extraordinary transmission through dielectric screens with 1D sub-wavelength metallic inclusions,” Opt. Express 19(14), 13612–13617 (2011).
    [CrossRef] [PubMed]
  11. J. D. Jackson, Classical Electrodynamics, 3rd Ed. (John Wiley & Sons, Inc., 1998)
  12. 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]
  13. F. J. García-Vidal and L. Martín Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
    [CrossRef]
  14. M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  15. F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
    [CrossRef]
  16. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983).
    [CrossRef] [PubMed]
  17. 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]

2011

2010

V. Delgado, R. Marqués, and L. Jelinek, “Analytical theory of extraordinary optical transmission through realistic metallic screens,” Opt. Express 18(7), 6506–6515 (2010).
[CrossRef] [PubMed]

F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
[CrossRef]

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

2009

2004

2003

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (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]

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]

2002

F. J. García-Vidal and L. Martín Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[CrossRef]

1999

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

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]

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(15), 6779–6782 (1998).
[CrossRef]

1983

Alexander, R. W.

Altug, H.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Artar, A.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Beruete, M.

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]

Bravo-Abad, J.

Campillo, I.

Connor, J. H.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[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.

Dereux, A.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (2003).
[CrossRef]

Devaux, E.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (2003).
[CrossRef]

Dolado, J. S.

Ebbesen, T. W.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (2003).
[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]

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(15), 6779–6782 (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]

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]

García-Vidal, F. J.

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

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

F. J. García-Vidal and L. Martín Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Geisbert, T. W.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Ghaemi, H. F.

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(15), 6779–6782 (1998).
[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]

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]

Grupp, D. E.

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(15), 6779–6782 (1998).
[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]

Huang, M.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd Ed. (John Wiley & Sons, Inc., 1998)

Jelinek, L.

Kamohara, O.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Lezec, H. J.

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]

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(15), 6779–6782 (1998).
[CrossRef]

Long, L. L.

Marqués, R.

Martín Moreno, L.

F. J. García-Vidal and L. Martín Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Martín-Moreno, L.

Medina, F.

F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
[CrossRef]

R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17(7), 5571–5579 (2009).
[CrossRef] [PubMed]

Mesa, F.

F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
[CrossRef]

R. Marqués, F. Mesa, L. Jelinek, and F. Medina, “Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes,” Opt. Express 17(7), 5571–5579 (2009).
[CrossRef] [PubMed]

Ordal, M. A.

Pendry, J. B.

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

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]

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]

Skigin, D. C.

F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
[CrossRef]

Sorolla, M.

Thio, T.

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]

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(15), 6779–6782 (1998).
[CrossRef]

Treacy, M. M. J.

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[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]

Ward, C. A.

Weeber, J.-C.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (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]

Yanik, A. A.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via micro-gratings,” Appl. Phys. Lett. 83, 4936 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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]

F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58(1), 105–115 (2010).
[CrossRef]

Nano Lett.

A. A. Yanik, M. Huang, O. Kamohara, A. Artar, T. W. Geisbert, J. H. Connor, and H. Altug, “An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media,” Nano Lett. 10, 4962–4969 (2010).
[CrossRef]

Nature (London)

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]

Opt. Express

Opt. Lett.

Phys. Rev. B

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(15), 6779–6782 (1998).
[CrossRef]

F. J. García-Vidal and L. Martín Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[CrossRef]

Phys. Rev. E

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.

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]

Science

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

Other

J. D. Jackson, Classical Electrodynamics, 3rd Ed. (John Wiley & Sons, Inc., 1998)

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Figures (8)

Fig. 1
Fig. 1

Front (a) and side (b) view of the screen with a periodic distribution of slits. Unit cell of the structure (c) with the incident TM wave. The impinging wave imposes periodic boundary conditions with a constant phase shift Δϕ = ky,0a along y.

Fig. 2
Fig. 2

Transmission through an array of slits in a lossy copper screen (σ = 59.6×106S/m) at normal incidence and different sizes of the slits. Periodicity is a = 300μm and thickness of the screen is t = a/20. Continuous lines correspond to mode matching model, dashed lines to CST simulations and dot-dashed lines to our previous numerical model [9].

Fig. 3
Fig. 3

Transmission through an array of slits in a lossy copper screen (σ = 59.6×106S/m) for different angles of incidence and Wood’s anomalies resonances. Periodicity is a = 300μm, size of slits is b = a/4 and thickness of the screen is t = a/20. Continuous lines correspond to mode matching model and dashed lines to CST simulations.

Fig. 4
Fig. 4

Transmission through an array of slits in a silver screen (ωp = 2π × 2175THz and fc = 1.26 × fc = 1.26 × 2π × 4.35 THz) for different angles of incidence and Wood’s anomalies resonances. Periodicity is a = 1μm, size of slits is b = a/4 and thickness of the screen is t = a/20. Continuous lines correspond to mode matching model and dashed lines to CST simulations.

Fig. 5
Fig. 5

Transmission through an array of slits in a zirconium-tin-titanate (ɛ = 92.7(1 + 0.005i) [17]) screen for different angles of incidence and Wood’s anomalies resonances. Periodicity is a = 3mm, size of slits is b = a/6 and thickness of the screen is t = a/25. Continuous lines correspond to mode matching model and dashed lines to CST simulations.

Fig. 6
Fig. 6

Transmission through an array of PEC inclusions in a zirconium-tin-titanate (ɛ = 92.7(1 + 0.005i) [17]) screen for different angles of incidence and Wood’s anomalies resonances. Periodicity is a = 3mm, size of the inclusions is b = a/6 and thickness of the screen is t = a/25. Continuous lines correspond to mode matching model and dashed lines to CST simulations.

Fig. 7
Fig. 7

Propagating component of the real part of the Poynting vector at the frequencies of the EOT peaks for the lossy copper screen analyzed in Fig.2. In (a) EOT is associated to the divergence of the TM−2 mode and in (b) to the divergence of the TM−4 mode. Angle of incidence is θ = 20° in both cases.

Fig. 8
Fig. 8

Propagating component of the real part of the Poynting vector at the frequencies of the EOT peaks for the zirconium-tin-titanate screen analyzed in Figs. 5 and 6. In (a) the slits are empty and in (b) filled with PEC. Angle of incidence is θ = 20° and EOT is associated to the divergence of the TM−2 mode in both cases.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E y ( 1 ) ( z = t / 2 ) = ( 1 + R ) exp [ i k y , 0 y ] + n = N n 0 N R n exp [ i ( k y , 0 + 2 n π a ) y ] ,
E y ( 2 ) ( z = t / 2 ) = S 0 + + S 0 exp [ i k z , 0 ( w ) t ] + m = 1 M ( S m + + S m exp [ i k z , m ( w ) t ] ) cos ( m π b ( y + b / 2 ) ) ,
E y ( 2 ) ( z = t / 2 ) = S 0 + exp [ i k z , 0 ( w ) t ] + S 0 + m = 1 M ( S m + exp [ i k z , m ( w ) t ] + S m ) cos ( m π b ( y + b / 2 ) ) ,
E y ( 3 ) ( z = t / 2 ) = T exp [ i k y , 0 y ] + n = N n 0 N T n exp [ i ( k y , 0 + 2 n π a ) y ] ,
k z , m ( w ) = ɛ r k 0 2 ( m π b ) 2
E y ( 1 ) ( z = t / 2 ) = E y ( 2 ) ( z = t / 2 ) E y ( 2 ) ( z = t / 2 ) = E y ( 3 ) ( z = t / 2 ) H x ( 1 ) ( z = t / 2 ) = H x ( 2 ) ( z = t / 2 ) H x ( 2 ) ( z = t / 2 ) = H x ( 3 ) ( z = t / 2 ) } for | y | b / 2 ,
[ E y , n ( 3 ) + E y , n ( 1 ) E y , n ( 3 ) E y , n ( 1 ) ] [ Z n ( 1 ) 0 0 Z n ( 2 ) ] [ H x , n ( 3 ) H x , n ( 1 ) H x , n ( 3 ) + H x , n ( 1 ) ] for b / 2 | y | a / 2 ,
Z n ( 1 ) = [ 1 + cos ( k z , n ( s ) t ) ] i sin ( k z , n ( s ) t ) Y s , n and Z n ( 2 ) = i sin ( k z , n ( s ) t ) [ 1 + cos ( k z , n ( s ) t ) ] Y s , n ,
k z , n ( s ) = ɛ s k 0 2 ( 2 n π a ) 2 and Y s , n = ω ɛ s ɛ 0 k z , n ( s )
cos [ m π b ( y + b / 2 ) ] , m = 1 , .. , M ;
exp [ i ( k y , 0 + 2 n π a ) y ] , n = N , , 0 , N ;
ɛ s i σ ω ɛ 0 ,
ɛ s ɛ 0 ( 1 ω p 2 ω ( ω i f c ) ) ,
f w , n = { n c a ( 1 sin ( θ ) ) for n > 0 | n | c a ( 1 + sin ( θ ) ) for n < 0

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