, Volume 13, Issue 5, pp 1711–1719 | Cite as

Analysis of Stacked Structures Composed of Arrays of Thick Slits: an Accurate Analytical Circuit Model

  • Saeedeh Barzegar-PariziEmail author


In this paper, a stacked structure composed of periodic arrays of one-dimensional thick slits embedded in a conventional dielectric medium is investigated in the subwavelength regime. Arrays of thick slits are known to support extraordinary transmission resonances. When periodically embedded in multilayered structures, they demonstrate band gap properties, which can produce flat passband regions in some structures, applicable to filter designs. In addition, by adjusting the parameters of the structures, they can be designed to create epsilon-near-zero and negative permittivity metamaterials. The analysis is carried out based on a simple and accurate analytical solution. The employed circuit model includes a transmission line corresponding to the slits, terminated by two surface admittances at the interfaces. The surface admittances assume the role of the diffractive modes and dominate the limitations of the usual analytical surface admittances obtained through heuristic approaches. A Π network of lumped elements equivalent to this circuit model is introduced in the present paper. This network helps to find the source of extraordinary resonances. Finally, the electromagnetic wave transmission through the stacked structure is studied and the effects of the thickness of the slits and dielectric slabs on the transmission spectra are analyzed. The results are compared to those obtained by full wave simulations, showing good agreement.


Array of thick slits Circuit model Stacked structure 


  1. 1.
    Molero C, Rodrıguez-Berral R, Mesa F, Medina F, Yakovlev AB (2016) Wideband analytical equivalent circuit for one-dimensional periodic stacked arrays. Phys Rev E 93(1):013306. CrossRefPubMedGoogle Scholar
  2. 2.
    Barzegar-Parizi S (2016) Study of backward waves in multilayered structures composed of graphene microribbons. J Appl Phys 119(19):193105. CrossRefGoogle Scholar
  3. 3.
    Kaipa CSR, Yakovlev AB, Medina F, Mesa F, Butler CAM, Hibbins AP (2010) Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes. Opt Express 18(13):13309–13320. CrossRefPubMedGoogle Scholar
  4. 4.
    Padooru YR, Yakovlev AB, Kaipa CS, Hanson GW, Medina F, Mesa F (2013) Dual capacitive-inductive nature of periodic graphene patches: transmission characteristics at low-terahertz frequencies. Phys Rev B 87(11):115401. CrossRefGoogle Scholar
  5. 5.
    Barzegar-Parizi S, Tavakol MR, Khavasi A (2017) Deriving surface impedance for 2-D arrays of graphene patches using a variational method. IEEE J Quantum Electron 53:7000106CrossRefGoogle Scholar
  6. 6.
    Li M, Behdad N (2013) Frequency selective surfaces for pulsed high-power microwave applications. IEEE Trans Antennas Propagat 61:677–687CrossRefGoogle Scholar
  7. 7.
    Arik K, Abdollahramezani S, Farajollahi S, Khavasi A, Rejaei B (2016) Design of mid-infrared ultra-wideband metallic absorber based on circuit theory. Opt Commun 381:309–313. CrossRefGoogle Scholar
  8. 8.
    Luukkonen O, Simovski C, Granet G, Goussetis G, Lioubtchenko D, Raisanen AV, Tretyakov SA (2008) Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches. IEEE Trans Antennas Propag 56(6):1624–1632. CrossRefGoogle Scholar
  9. 9.
    Medina F, Mesa F, Skigin DC (2010) Extraordinary transmission through arrays of slits: a circuit theory model. IEEE Trans Microw Theory Tech 58(1):105–115. CrossRefGoogle Scholar
  10. 10.
    Yang R, Rodríguez-Berral R, Medina F, Hao Y (2011) Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens. J Appl Phys 109(10):103107. CrossRefGoogle Scholar
  11. 11.
    Yarmoghaddam E, Shirmanesh GK, Khavasi A, Mehrany K (2014) Circuit model for periodic array of slits with multiple propagating diffracted orders. IEEE Trans Antennas Propagat 62(8):4041–4048. CrossRefGoogle Scholar
  12. 12.
    Medina F, Mesa F, Marqués R (2008) Extraordinary transmission through arrays of electrically small holes from a circuit theory perspective. IEEE Trans Microw Theory Tech 56(12):3108–3120. CrossRefGoogle Scholar
  13. 13.
    Shirmanesh GK, Yarmoghaddam E, Khavasi A, Mehrany K (2015) Circuit model in design of THz transparent electrodes based on two-dimensional arrays of metallic square holes. IEEE Trans Terahertz Sci Technol 5:655–656CrossRefGoogle Scholar
  14. 14.
    Garcia-Vidal FJ, Martin-Moreno L, Pendry JB (2005) Surfaces with holes in them: new plasmonic metamaterials. J Opt Pure Appl Opt 7(2):S97–S101. CrossRefGoogle Scholar
  15. 15.
    D’Aguanno G, Mattiucci N, Alù A, Argyropoulos C, Foreman JV, Bloemer MJ (2012) Thermal emission from a metamaterial wire medium slab. Opt Exp 20(9):9784–9789. CrossRefGoogle Scholar
  16. 16.
    Rodriguez-Berral R, Medina F, Mesa F, García-Vigueras M (2012) Quasi-analytical modeling of transmission/reflection in strip/slit gratings loaded with dielectric slabs. IEEE Trans Microw Theory Tech 60(3):405–418. CrossRefGoogle Scholar
  17. 17.
    Rodrguez-Berral R, Medina F, Mesa F (2010) Circuit model for a periodic array of slits sandwiched between two dielectric slabs. Appl Phys Lett 96(16):161104. CrossRefGoogle Scholar
  18. 18.
    Barzegar-Parizi S, Rejaei B, Khavasi A (2015) Analytical circuit model for periodic arrays of graphene disks. IEEE J Quantum Electron 51:7000507CrossRefGoogle Scholar
  19. 19.
    Woo DW, Muhn SJ, Park WS (2012) Simple analytical model of propagation through thick periodic slot. IEEE Trans Antennas Propagat 60(11):5329–5335. CrossRefGoogle Scholar
  20. 20.
    Shirmanesh GK, Khavasi A, Mehrany K (2015) Accurate effective medium theory for arrays of metallic nanowire. J Opt 17(2):025104. CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringSirjan University of TechnologySirjanIran

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