Abstract

We report on a bistable light transmission through a bilayer “fish-scale” (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved that is nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light, which leads to destination of a multistable transmission.

© 2014 Optical Society of America

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    [CrossRef]
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  26. A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
    [CrossRef]
  27. A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
    [CrossRef]
  28. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]
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    [CrossRef]
  31. N. Lapshina, R. Noskov, and Yu. Kivshar, “Nanoradar based on nonlinear dimer nanoantenna,” Opt. Lett. 37, 3921–3923 (2012).
    [CrossRef]
  32. N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
    [CrossRef]

2013 (1)

N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
[CrossRef]

2012 (7)

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
[CrossRef]

N. Lapshina, R. Noskov, and Yu. Kivshar, “Nanoradar based on nonlinear dimer nanoantenna,” Opt. Lett. 37, 3921–3923 (2012).
[CrossRef]

M. Kitano, Y. Tamayama, and T. Nakanishi, “Coupled-resonator-based metamaterials,” IEICE Electron. Express 9, 512012 (2012).
[CrossRef]

V. R. Tuz, V. S. Butylkin, and S. L. Prosvirnin, “Enhancement of absorption bistability by trapping-light planar metamaterial,” J. Opt. 14, 045102 (2012).
[CrossRef]

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

X. Zhang, J. Gu, W. Cao, J. Han, A. Lakhtakia, and W. Zhang, “Bilayer-fish-scale ultrabroad terahertz bandpass filter,” Opt. Lett. 37, 906–908 (2012).
[CrossRef]

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

2011 (1)

V. R. Tuz and S. L. Prosvirnin, “All-optical switching in planar metamaterial with high structural symmetry,” Eur. Phys. J. Appl. Phys. 56, 30401 (2011).
[CrossRef]

2010 (8)

P. L. Mladyonov and S. L. Prosvirnin, “Wave diffraction by double-periodic gratings of continuous curvilinear metal strips placed on both sides of a dielectric layer,” Radio Phys. Radio Astron. 1, 309–320 (2010).

M. N. Kawakatsu, V. A. Dmitriev, and S. L. Prosvirnin, “Microwave frequency selective surfaces with high Q-factor resonance and polarization insensitivity,” J. Electromagn. Waves Appl. 24, 261–270 (2010).
[CrossRef]

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “Trapping of light by metal arrays,” J. Opt. 12, 045102 (2010).
[CrossRef]

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

V. R. Tuz, S. L. Prosvirnin, and L. A. Kochetova, “Optical bistability involving planar metamaterials with broken structural symmetry,” Phys. Rev. B 82, 233402 (2010).
[CrossRef]

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

2009 (2)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

2008 (3)

Y. S. Kivshar, “Nonlinear optics: the next decade,” Opt. Express 16, 22126–22128 (2008).
[CrossRef]

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators,” Opt. Express 16, 16058–16063 (2008).
[CrossRef]

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

2007 (1)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

2005 (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

2003 (1)

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

2002 (1)

S. L. Prosvirnin, S. A. Tretyakov, and P. L. Mladyonov, “Electromagnetic wave diffraction by planar periodic gratings of wavy metal strips,” J. Electromagn. Waves Appl. 16, 421–435 (2002).
[CrossRef]

1999 (1)

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Alexopolous, N.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Angelis, F. D.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Broas, R. F. J.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Butylkin, V. S.

V. R. Tuz, V. S. Butylkin, and S. L. Prosvirnin, “Enhancement of absorption bistability by trapping-light planar metamaterial,” J. Opt. 14, 045102 (2012).
[CrossRef]

Cao, W.

Constant, T. J.

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

Dmitriev, V.

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

Dmitriev, V. A.

M. N. Kawakatsu, V. A. Dmitriev, and S. L. Prosvirnin, “Microwave frequency selective surfaces with high Q-factor resonance and polarization insensitivity,” J. Electromagn. Waves Appl. 24, 261–270 (2010).
[CrossRef]

Fabrizio, E. D.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Fedotov, V. A.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Fu, Y. H.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

Galynsky, V. M.

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
[CrossRef]

Gholipour, B.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Gu, J.

Han, J.

Hewak, D. W.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Hibbins, A. P.

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

Huang, C. C.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Huang, D.

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010 (2010).
[CrossRef]

Iarko, E. O.

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “Trapping of light by metal arrays,” J. Opt. 12, 045102 (2010).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Kawakatsu, M. N.

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

M. N. Kawakatsu, V. A. Dmitriev, and S. L. Prosvirnin, “Microwave frequency selective surfaces with high Q-factor resonance and polarization insensitivity,” J. Electromagn. Waves Appl. 24, 261–270 (2010).
[CrossRef]

Khardikov, V. V.

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “Trapping of light by metal arrays,” J. Opt. 12, 045102 (2010).
[CrossRef]

Kitano, M.

M. Kitano, Y. Tamayama, and T. Nakanishi, “Coupled-resonator-based metamaterials,” IEICE Electron. Express 9, 512012 (2012).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar, “Nonlinear optics: the next decade,” Opt. Express 16, 22126–22128 (2008).
[CrossRef]

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

Kivshar, Yu.

Kivshar, Yu. S.

N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Knight, K.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Kochetova, L. A.

V. R. Tuz, S. L. Prosvirnin, and L. A. Kochetova, “Optical bistability involving planar metamaterials with broken structural symmetry,” Phys. Rev. B 82, 233402 (2010).
[CrossRef]

Koschny, T.

Kozyrev, A. B.

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

Lakhtakia, A.

Lapshina, N.

Lapshina, N. S.

N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
[CrossRef]

MacDonald, K. F.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Maslovski, S. I.

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Mladenov, P.

P. Mladenov, S. Prosvirnin, S. Tretyakov, and S. Zouhdi, “Planar arrays of wavy microstrip lines as thin resonant magnetic walls,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 2, pp. 1103–1106.

Mladyonov, P. L.

P. L. Mladyonov and S. L. Prosvirnin, “Wave diffraction by double-periodic gratings of continuous curvilinear metal strips placed on both sides of a dielectric layer,” Radio Phys. Radio Astron. 1, 309–320 (2010).

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

S. L. Prosvirnin, S. A. Tretyakov, and P. L. Mladyonov, “Electromagnetic wave diffraction by planar periodic gratings of wavy metal strips,” J. Electromagn. Waves Appl. 16, 421–435 (2002).
[CrossRef]

Nakanishi, T.

M. Kitano, Y. Tamayama, and T. Nakanishi, “Coupled-resonator-based metamaterials,” IEICE Electron. Express 9, 512012 (2012).
[CrossRef]

Noskov, R.

Noskov, R. E.

N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
[CrossRef]

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Novitsky, A. V.

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

Papasimakis, N.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

Poutrina, E.

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010 (2010).
[CrossRef]

Prosvirnin, S.

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in Advances in Electromagnetics of Complex Media and Metamaterials, S. Zouhdi and M. Arsalane, eds. (Kluwer, 2003), pp. 281–290.

P. Mladenov, S. Prosvirnin, S. Tretyakov, and S. Zouhdi, “Planar arrays of wavy microstrip lines as thin resonant magnetic walls,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 2, pp. 1103–1106.

Prosvirnin, S. L.

V. R. Tuz, V. S. Butylkin, and S. L. Prosvirnin, “Enhancement of absorption bistability by trapping-light planar metamaterial,” J. Opt. 14, 045102 (2012).
[CrossRef]

V. R. Tuz and S. L. Prosvirnin, “All-optical switching in planar metamaterial with high structural symmetry,” Eur. Phys. J. Appl. Phys. 56, 30401 (2011).
[CrossRef]

V. R. Tuz, S. L. Prosvirnin, and L. A. Kochetova, “Optical bistability involving planar metamaterials with broken structural symmetry,” Phys. Rev. B 82, 233402 (2010).
[CrossRef]

P. L. Mladyonov and S. L. Prosvirnin, “Wave diffraction by double-periodic gratings of continuous curvilinear metal strips placed on both sides of a dielectric layer,” Radio Phys. Radio Astron. 1, 309–320 (2010).

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “Trapping of light by metal arrays,” J. Opt. 12, 045102 (2010).
[CrossRef]

M. N. Kawakatsu, V. A. Dmitriev, and S. L. Prosvirnin, “Microwave frequency selective surfaces with high Q-factor resonance and polarization insensitivity,” J. Electromagn. Waves Appl. 24, 261–270 (2010).
[CrossRef]

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

S. L. Prosvirnin, S. A. Tretyakov, and P. L. Mladyonov, “Electromagnetic wave diffraction by planar periodic gratings of wavy metal strips,” J. Electromagn. Waves Appl. 16, 421–435 (2002).
[CrossRef]

Rance, H. J.

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Sambles, J. R.

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

Sámson, Z. L.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Smith, D. R.

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010 (2010).
[CrossRef]

Soukoulis, C. M.

Taflove, S. C. H. A.

S. C. H. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Tamayama, Y.

M. Kitano, Y. Tamayama, and T. Nakanishi, “Coupled-resonator-based metamaterials,” IEICE Electron. Express 9, 512012 (2012).
[CrossRef]

Tretyakov, S.

P. Mladenov, S. Prosvirnin, S. Tretyakov, and S. Zouhdi, “Planar arrays of wavy microstrip lines as thin resonant magnetic walls,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 2, pp. 1103–1106.

Tretyakov, S. A.

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

S. L. Prosvirnin, S. A. Tretyakov, and P. L. Mladyonov, “Electromagnetic wave diffraction by planar periodic gratings of wavy metal strips,” J. Electromagn. Waves Appl. 16, 421–435 (2002).
[CrossRef]

Tsai, D. P.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

Tsarev, M. V.

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Tuz, V.

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

Tuz, V. R.

V. R. Tuz, V. S. Butylkin, and S. L. Prosvirnin, “Enhancement of absorption bistability by trapping-light planar metamaterial,” J. Opt. 14, 045102 (2012).
[CrossRef]

V. R. Tuz and S. L. Prosvirnin, “All-optical switching in planar metamaterial with high structural symmetry,” Eur. Phys. J. Appl. Phys. 56, 30401 (2011).
[CrossRef]

V. R. Tuz, S. L. Prosvirnin, and L. A. Kochetova, “Optical bistability involving planar metamaterials with broken structural symmetry,” Phys. Rev. B 82, 233402 (2010).
[CrossRef]

van der Weide, D. W.

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

Wang, B.

Yablonovitch, E.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Yatsenko, V. V.

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

Zhang, L.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

Zhang, W.

Zhang, X.

Zharov, A. A.

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Zheludev, N. I.

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

Zhou, J.

Zhukovsky, S. V.

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
[CrossRef]

Zouhdi, S.

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

P. Mladenov, S. Prosvirnin, S. Tretyakov, and S. Zouhdi, “Planar arrays of wavy microstrip lines as thin resonant magnetic walls,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 2, pp. 1103–1106.

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in Advances in Electromagnetics of Complex Media and Metamaterials, S. Zouhdi and M. Arsalane, eds. (Kluwer, 2003), pp. 281–290.

Adv. Electromagn. (1)

V. Dmitriev, V. Tuz, S. Prosvirnin, and M. N. Kawakatsu, “Electromagnetic controllable surfaces based on trapped-mode effect,” Adv. Electromagn. 1, 89–95 (2012).
[CrossRef]

Appl. Phys. Lett. (3)

Z. L. Sámson, K. F. MacDonald, F. D. Angelis, B. Gholipour, K. Knight, C. C. Huang, E. D. Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96, 143105 (2010).
[CrossRef]

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[CrossRef]

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94, 211902 (2009).
[CrossRef]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

V. R. Tuz and S. L. Prosvirnin, “All-optical switching in planar metamaterial with high structural symmetry,” Eur. Phys. J. Appl. Phys. 56, 30401 (2011).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

V. V. Yatsenko, S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhdi, “Plane-wave reflection from double arrays of small magnetoelectric scatterers,” IEEE Trans. Antennas Propag. 51, 2–11 (2003).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theor. Tech. 47, 2059–2074 (1999).
[CrossRef]

IEICE Electron. Express (1)

M. Kitano, Y. Tamayama, and T. Nakanishi, “Coupled-resonator-based metamaterials,” IEICE Electron. Express 9, 512012 (2012).
[CrossRef]

J. Appl. Phys. (1)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

J. Electromagn. Waves Appl. (2)

S. L. Prosvirnin, S. A. Tretyakov, and P. L. Mladyonov, “Electromagnetic wave diffraction by planar periodic gratings of wavy metal strips,” J. Electromagn. Waves Appl. 16, 421–435 (2002).
[CrossRef]

M. N. Kawakatsu, V. A. Dmitriev, and S. L. Prosvirnin, “Microwave frequency selective surfaces with high Q-factor resonance and polarization insensitivity,” J. Electromagn. Waves Appl. 24, 261–270 (2010).
[CrossRef]

J. Opt. (2)

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “Trapping of light by metal arrays,” J. Opt. 12, 045102 (2010).
[CrossRef]

V. R. Tuz, V. S. Butylkin, and S. L. Prosvirnin, “Enhancement of absorption bistability by trapping-light planar metamaterial,” J. Opt. 14, 045102 (2012).
[CrossRef]

JETP Lett. (1)

N. S. Lapshina, R. E. Noskov, and Yu. S. Kivshar, “Nonlinear nanoantenna with self-tunable scattering pattern,” JETP Lett. 96, 759–764 (2013).
[CrossRef]

New J. Phys. (1)

E. Poutrina, D. Huang, and D. R. Smith, “Analysis of nonlinear electromagnetic metamaterials,” New J. Phys. 12, 093010 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (3)

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: microscopic Lorentz-theory approach,” Phys. Rev. B 86, 075138 (2012).
[CrossRef]

H. J. Rance, T. J. Constant, A. P. Hibbins, and J. R. Sambles, “Surface waves at microwave frequencies excited on a zigzag metasurface,” Phys. Rev. B 86, 125144 (2012).
[CrossRef]

V. R. Tuz, S. L. Prosvirnin, and L. A. Kochetova, “Optical bistability involving planar metamaterials with broken structural symmetry,” Phys. Rev. B 82, 233402 (2010).
[CrossRef]

Phys. Rev. E (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E 72, 056613 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef]

Radio Phys. Radio Astron. (1)

P. L. Mladyonov and S. L. Prosvirnin, “Wave diffraction by double-periodic gratings of continuous curvilinear metal strips placed on both sides of a dielectric layer,” Radio Phys. Radio Astron. 1, 309–320 (2010).

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Other (5)

S. C. H. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

P. Mladenov, S. Prosvirnin, S. Tretyakov, and S. Zouhdi, “Planar arrays of wavy microstrip lines as thin resonant magnetic walls,” in IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 2, pp. 1103–1106.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in Advances in Electromagnetics of Complex Media and Metamaterials, S. Zouhdi and M. Arsalane, eds. (Kluwer, 2003), pp. 281–290.

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Figures (8)

Fig. 1.
Fig. 1.

Fragment of a planar bilayer fish-scale metamaterial and its unit cell.

Fig. 2.
Fig. 2.

Surface current distribution along the strips placed on the upper and bottom sides of the substrate in the bilayer fish-scale metamaterial.

Fig. 3.
Fig. 3.

Frequency dependences of the transmission coefficient magnitude for different values of the substrate thickness (linear regime); ε=3, 2w/d=0.05, Δ/d=0.25.

Fig. 4.
Fig. 4.

Frequency dependences (æ=d/λ) of (a) the inner field intensity and (b) the transmission coefficient magnitude for different values of the incident field magnitude (nonlinear regime); h/d=0.2, ε1=3, ε2=0.005cm2kW1. Other parameters are the same as in Fig. 3.

Fig. 5.
Fig. 5.

(a) Frequency dependency of the effective dielectric permittivity εeff of the homogenized layer with the thickness h/d=0.2 and (b) the corresponding transmission spectrum.

Fig. 6.
Fig. 6.

Bistability curves for stationary levels of (a) transmission, (b) reflection, and (c) normalized intensity in the middle of the layer.

Fig. 7.
Fig. 7.

Bistability curves for stationary levels of transmission calculated starting from (a) the low magnitude level and from (b) the high one. The letters “S” and “F” denote the starting and final values of magnitude variation.

Fig. 8.
Fig. 8.

(a), (c) Profiles of the incident, transmitted, and reflected pulses for the full pulse and the half of it, respectively. (b), (d) The bistability curves calculated from the data of panels (a) and (c). The letters “S” and “F” denote the starting and final values of magnitude variation.

Equations (18)

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

E⃗inc=p⃗A0exp(ik⃗incr⃗),
E⃗=E⃗d+E⃗s.
14π2m,n={E⃗1t(J⃗1,J⃗2)}(κ⃗)exp[i(κ⃗k⃗inc)ρ⃗mniκ⃗ρ⃗]dκ⃗+E⃗1td(ρ⃗)=0,z=0,14π2m,n={E⃗2t(J⃗1,J⃗2)}(κ⃗)exp[i(κ⃗k⃗inc)ρ⃗mniκ⃗ρ⃗]dκ⃗+E⃗2td(ρ⃗)=0,z=h,
E⃗s=α,β=a⃗αβexp{i[κ⃗αβρ⃗+γ(κ⃗αβ)z]},z0,E⃗s=α,β=b⃗αβexp{i[κ⃗αβρ⃗γ(κ⃗αβ)(z+h)]},zh,
J=J(æ,ε),R=R(æ,ε),T=T(æ,ε).
J¯=A˜FJ¯(æ,ε1+ε2(Iin(J¯))),
R=R(æ,ε1+ε2(Iin(A0))),T=T(æ,ε1+ε2(Iin(A0))).
εeff(æ)=ε+α1æ12ε1/εæ2iγ1æ+α2æ22ε1/εæ2iγ2æ,
d2Pkdt2+γkdPkdt+ε1εωk2Pk=αkE,k=1,2,
d2pkdτ2+ηkdpkdτ+ζkpk=αkA(t),k=1,2,
pkl+1=[pkl(2ζkΔτ2)+pkl1(1+ηkΔτ/2)+αkΔτ2Al]/(1+ηkΔτ/2),k=1,2.
2Ez2=1c22Dt2,
Ajl+1=[a1εjl1Ajl1+b1Aj+1l+b2Aj1l+(fεjlg)AjlRjl]/a2εjl+1.
Rjl=k=12[a2pjl+1+a1pjl1fpjl]k.
mξ¨+mγξ˙=eEmω02ξβmξ¨.
ξ=eE/m(1+β)ω02/(1+β)ω2iωγ/(1+β).
εm=1+4πPmE=1+ωp2ωr2ω2iωγr,
εeff(æ)=Vdε+VmεmVd+Vmε+α1æ12ε1/εæ2iγ1æ+α2æ22ε1/εæ2iγ2æ,

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