Abstract

This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked two-dimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.

© 2010 OSA

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
    [CrossRef]
  4. M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734–742 (2009).
    [CrossRef]
  5. S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
    [CrossRef]
  6. M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
    [CrossRef]
  7. I. R. Hooper and J. R. Sambles, “Some considerations on the transmissivity of thin metal films,” Opt. Express 16, 17249–17256 (2008).
    [CrossRef] [PubMed]
  8. C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
    [CrossRef]
  9. A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.
  10. 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]
  11. R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1991).
  12. B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, 2000).
    [CrossRef]
  13. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
    [CrossRef]
  14. R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
    [CrossRef]
  15. O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
    [CrossRef]
  16. F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
    [CrossRef]
  17. F. Medina, F. Mesa, and D. C. Skigin, “Extraordinary transmission through arrays of slits: a circuit theory model,” IEEE Trans. Microwave Theory Tech. 58, 105–115 (2010).
    [CrossRef]
  18. N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
    [CrossRef] [PubMed]
  19. A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
    [CrossRef]
  20. S. Tretyakov, Analytical modeling in applied electromagnetics, (Artech House, 2003).
  21. HFSS: High Frequency Structure Simulator based on the Finite Element Method, Ansoft Corporation, http://www.ansoft.com
  22. D. M. Pozar, Microwave Engineering, third edition, (Wiley, 2004).
  23. CST Microwave Studio CST GmbH, Darmstadt, Germany, 2008, http://www.cst.com.

2010 (1)

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

2009 (2)

M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734–742 (2009).
[CrossRef]

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

2008 (4)

I. R. Hooper and J. R. Sambles, “Some considerations on the transmissivity of thin metal films,” Opt. Express 16, 17249–17256 (2008).
[CrossRef] [PubMed]

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[CrossRef]

2005 (2)

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

2003 (1)

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[CrossRef]

1998 (3)

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (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]

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1967 (1)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

Alu, A.

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Bertolotti, M.

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[CrossRef]

Bloemer, M. J.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Bowden, C. M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Butler, C. A. M.

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1991).

Coquet, Ph.

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

Daniel, J. P.

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Ebbesen, T. W.

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]

Elson, J. M.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Engheta, N.

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Feng, S.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Gadsdon, M. R.

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]

Goussetis, G.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Granet, G.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Hibbins, A. P.

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

Hirose, N.

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

Hobson, P. A.

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

Hooper, I. R.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Kaipa, C. S. R.

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

Larciprete, M. C.

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[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]

Lioubtchenko, D.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Luukkonen, O.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Marqués, R.

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

Matsui, T.

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

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, 105–115 (2010).
[CrossRef]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

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, 105–115 (2010).
[CrossRef]

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[CrossRef]

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

Munk, B. A.

B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, 2000).
[CrossRef]

Overfelt, P. L.

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Padooru, Y. R.

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

Paoloni, S.

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[CrossRef]

Parsons, J.

M. R. Gadsdon, J. Parsons, and J. R. Sambles, “Electromagnetic resonances of a multilayer metal-dielectric stack,” J. Opt. Soc. Am. B 26, 734–742 (2009).
[CrossRef]

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

Pethel, A. S.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering, third edition, (Wiley, 2004).

Raisanen, A. V.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Sambles, J. R.

Sauleau, R.

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

Scalora, M.

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

Sibilia, C.

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[CrossRef]

Simovski, C.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[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, 105–115 (2010).
[CrossRef]

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]

Tretyakov, S.

S. Tretyakov, Analytical modeling in applied electromagnetics, (Artech House, 2003).

Tretyakov, S. A.

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[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]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yakovlev, A. B.

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

Young, M. E.

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

C. A. M. Butler, J. Parsons, J. R. Sambles, A. P. Hibbins, and P. A. Hobson, “Microwave transmissivity of a metamaterial-dielectric stack,” Appl. Phys. Lett. 95, 174101 (2009).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag. 56, 1624–1632 (2008).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

F. Medina, F. Mesa, and R. Marqués, “Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective,” IEEE Trans. Microwave Theory Tech. 56, 3108–3120 (2008).
[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, 105–115 (2010).
[CrossRef]

Infrared Phys. (1)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7, 37–55 (1967).
[CrossRef]

Int. J. Infrared and Millim. Waves (1)

R. Sauleau, Ph. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study of Fabry-Pérot cavities with metal mesh mirrors using equivalent circuit models. Comparison with experimental results in the 60 GHz band,” Int. J. Infrared and Millim. Waves 19, 1693–1710 (1998).
[CrossRef]

J. Appl. Phys. (2)

M. C. Larciprete, C. Sibilia, S. Paoloni, and M. Bertolotti, “Accessing the optical limiting properties of metallodielectric photonic band gap structures,” J. Appl. Phys. 93, 5113–5017 (2003).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, “Transparent, metallodielectric, one-dimensional, photonic band-gap structures,” J. Appl. Phys. 83, 2377–2383 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (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]

Opt. Express (1)

Phys. Rev. B (2)

S. Feng, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistorsExtraordinary transmission through arrays of,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

Other (7)

R. E. Collin, Field Theory of Guided Waves (IEEE Press, 1991).

B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, 2000).
[CrossRef]

A. B. Yakovlev, C. S. R. Kaipa, Y. R. Padooru, F. Medina, and F. Mesa, “Dynamic and circuit theory models for the analysis of sub-wavelength transmission through patterned screens,” in 3rd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, (London, UK, 2009), pp. 671–673.

S. Tretyakov, Analytical modeling in applied electromagnetics, (Artech House, 2003).

HFSS: High Frequency Structure Simulator based on the Finite Element Method, Ansoft Corporation, http://www.ansoft.com

D. M. Pozar, Microwave Engineering, third edition, (Wiley, 2004).

CST Microwave Studio CST GmbH, Darmstadt, Germany, 2008, http://www.cst.com.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Exploded schematic (the air gaps between layers are not real) of the five stacked copper grids separated by dielectric slabs used in the experiments reported in [8]. This is an example of the type of structure for which the model in this paper is suitable. (b) Top view of each metal mesh.

Fig. 2.
Fig. 2.

(a) Transverse unit cell of the 2-D periodic structure corresponding to the analysis of the normal incidence of a y-polarized uniform plane wave on the structure shown in Fig. 1 (pec stands for perfect electric conductor, and pmc stands for perfect magnetic conductor). (b) Equivalent circuit for the electrically small unit cell (λg meaningfully smaller than the wavelength in the dielectric medium surrounding the grids); Z 0 and β 0 are the characteristic impedance and propagation constant of the air-filled region (input and output waveguides); Zd and βd are the same parameters for the dielectric-filled region (real for lossless dielectric and complex for lossy material). (c) Unit cell for the circuit based analysis of an infinite periodic structure.

Fig. 3.
Fig. 3.

Transmissivity (|T|2) of the stacked grids structure experimentally and numerically studied in [8]. HFSS (FEM model, FEM standing for finite elements method) and circuit simulations (analytical data) are obtained for the following parameters [with the notation used in Fig. 1]: λg = 5.0mm, wm = 0.15mm, td = 6.35mm, tm = 18µm; metal is copper and the dielectric is characterized by εr = 3 and tan δ = 0.0018. The four resonant modes in the first band are labeled as A, B, C, and D in the increasing order of frequency.

Fig. 4.
Fig. 4.

Field distributions for the four resonance modes of the four open and coupled Fabry-Pérot cavities that can be associated to each of the dielectric slabs in the stacked structure in Fig. 1. The numerical (HFSS, red curves) and analytical (circuit model, blue curves) results show a very good agreement.

Fig. 5.
Fig. 5.

Field distributions for the first and last resonance peaks (within the first transmission band, which has nine peaks) of a 9 slabs (10 grids) structure. Dimensions of the grids and individual slabs are the same as in Fig. 4. Dielectrics and metals are the same as well.

Fig. 6.
Fig. 6.

Brillouin diagram for the first transmission band of an infinite periodic structure (1-D photonic crystal) with the same unit cell as that used in the finite structure considered in Table 1. Numerical results were generated using the commercial software CST [23].

Tables (1)

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Table 1. Frequencies of lower (f LB) and upper (f UB) band edges with respect to the number of layers.

Equations (6)

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β 0 = ω c ; β d = ε r ( 1 j tan δ ) β 0
Z 0 = μ 0 ε 0 ; Z d = μ 0 ε 0 1 ε r ( 1 j tan δ )
Z g = j ω L g ; L g = η 0 λ g 2 π c ln [ csc ( π w m 2 λ g ) ]
cosh ( γ t d ) = cos ( k d t d ) + j Z d 2 Z g sin ( k d t d )
cosh ( γ t d ) = 1
cosh ( γ t d ) cos ( k d t d ) + j Z d 2 Z g sin ( k d t d ) = 1 .

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