Abstract

In this work, we propose an efficient approach to compensate for the commonly observed substrate-induced bianisotropy that occurs in on-wafer optical metamaterials at normal incidence. First, the consequence of placing a finite thickness substrate underneath a metamaterial is analyzed, indicating that the induced bianisotropy is a near-field effect. The properties of metamaterials sandwiched between an infinitely thick substrate and a finite-thickness superstrate with different permittivity and thickness values are then investigated. It is demonstrated from full-wave simulations that by adding an ultrathin superstrate with a judicious choice of its thickness and permittivity value, the substrate-induced bianisotropy of the system can be suppressed and even eliminated. In addition to the extracted nonlocal effective medium parameters, the induced electric and magnetic dipole moments calculated from the volumetric microscopic fields are also presented, validating that the magnetoelectric coupling compensation is a real physical phenomenon. This study will benefit future optical metamaterial design and implementation strategies as well as the corresponding fabrication and characterization methodologies.

© 2013 OSA

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  33. R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express18(14), 14553–14567 (2010).
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2012 (4)

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun3, 870 (2012).
[CrossRef] [PubMed]

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

2011 (7)

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

M. Albooyeh and C. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt.13(10), 105102 (2011).
[CrossRef]

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011).
[CrossRef] [PubMed]

2010 (4)

D. A. Powell and Y. S. Kivshar, “Substrate-induced bianisotropy in metamaterials,” Appl. Phys. Lett.97(9), 091106 (2010).
[CrossRef]

D. Ö. Güney, Th. Koschny, and C. M. Soukoulis, “Intra-connected 3D isotropic bulk negative index photonic metamaterial,” Opt. Express18(12), 12348–12353 (2010).
[CrossRef] [PubMed]

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
[CrossRef]

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express18(14), 14553–14567 (2010).
[CrossRef] [PubMed]

2009 (7)

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(2), 026610 (2009).
[CrossRef] [PubMed]

C. García-Meca, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett.34(10), 1603–1605 (2009).
[CrossRef] [PubMed]

J. A. Bossard, S. Yun, D. H. Werner, and T. S. Mayer, “Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms,” Opt. Express17(17), 14771–14779 (2009).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B80(3), 035109 (2009).
[CrossRef]

Z. Ku, J. Zhang, and S. R. J. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express17(8), 6782–6789 (2009).
[CrossRef] [PubMed]

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall-angle induced bi-anisotropy in multiple-layer negative-index metamaterials,” Appl. Phys. Lett.94(15), 153107 (2009).
[CrossRef]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B26(12), B34–B38 (2009).
[CrossRef]

2008 (4)

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101(10), 103902 (2008).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express16(18), 13773–13780 (2008).
[CrossRef] [PubMed]

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

2007 (2)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B75(19), 195111 (2007).
[CrossRef]

2006 (2)

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett.88(4), 041109 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

2003 (1)

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
[CrossRef]

2002 (1)

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B65(14), 144440 (2002).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Albooyeh, M.

M. Albooyeh and C. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt.13(10), 105102 (2011).
[CrossRef]

Alù, A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun3, 870 (2012).
[CrossRef] [PubMed]

Andryieuski, A.

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

Aydin, K.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(2), 026610 (2009).
[CrossRef] [PubMed]

Azad, A. K.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Bahou, M.

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun3, 870 (2012).
[CrossRef] [PubMed]

Borneman, J. D.

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

Bossard, J. A.

Brueck, S. R.

Brueck, S. R. J.

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall-angle induced bi-anisotropy in multiple-layer negative-index metamaterials,” Appl. Phys. Lett.94(15), 153107 (2009).
[CrossRef]

Z. Ku, J. Zhang, and S. R. J. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express17(8), 6782–6789 (2009).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Chen, A.

Chen, H. S.

Chen, H.-T.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Cheng, X. X.

Chin, J. Y.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Cui, T. J.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Dani, K. M.

Dickson, W.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Drachev, V. P.

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

García-Meca, C.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

C. García-Meca, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett.34(10), 1603–1605 (2009).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101(10), 103902 (2008).
[CrossRef] [PubMed]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Giessen, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

Gregory, M. D.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

Gu, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Gu, P. D.

Güney, D. Ö.

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

Ha, S.

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

Han, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Heussler, S. P.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Hou, L. L.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Hurtado, J.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
[CrossRef]

Jandhyala, V.

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
[CrossRef]

Jian, L. K.

Jiang, Z. H.

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
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[CrossRef]

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J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B80(3), 035109 (2009).
[CrossRef]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

Kalaiselvi, S. M. P.

Kildishev, A. V.

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

Kivshar, Y. S.

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

D. A. Powell and Y. S. Kivshar, “Substrate-induced bianisotropy in metamaterials,” Appl. Phys. Lett.97(9), 091106 (2010).
[CrossRef]

Kong, J. A.

Koschny, T.

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express18(14), 14553–14567 (2010).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B80(3), 035109 (2009).
[CrossRef]

Koschny, Th.

Kriegler, C. E.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
[CrossRef]

Ku, Z.

Kuga, Y.

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
[CrossRef]

Lalanne, P.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011).
[CrossRef] [PubMed]

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A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

Lee, S.-W.

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
[CrossRef]

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Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(2), 026610 (2009).
[CrossRef] [PubMed]

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C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Liu, G.

Liu, H. T.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011).
[CrossRef] [PubMed]

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N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

Liu, R. P.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Liu, X.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Liu, Z.

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Mahmood, S.

Maier, S. A.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Maniam, S. M.

Marques, R.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B65(14), 144440 (2002).
[CrossRef]

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C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

C. García-Meca, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett.34(10), 1603–1605 (2009).
[CrossRef] [PubMed]

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C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

C. García-Meca, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett.34(10), 1603–1605 (2009).
[CrossRef] [PubMed]

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A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101(10), 103902 (2008).
[CrossRef] [PubMed]

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A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101(10), 103902 (2008).
[CrossRef] [PubMed]

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S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
[CrossRef] [PubMed]

J. A. Bossard, S. Yun, D. H. Werner, and T. S. Mayer, “Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms,” Opt. Express17(17), 14771–14779 (2009).
[CrossRef] [PubMed]

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R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B65(14), 144440 (2002).
[CrossRef]

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D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett.88(4), 041109 (2006).
[CrossRef]

Moser, H. O.

Ni, X.

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

Ortuño, R.

Osgood, M. R.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Ozbay, E.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(2), 026610 (2009).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Powell, D. A.

D. A. Powell and Y. S. Kivshar, “Substrate-induced bianisotropy in metamaterials,” Appl. Phys. Lett.97(9), 091106 (2010).
[CrossRef]

Qi, L. X.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Rafii-El-Idrissi, R.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B65(14), 144440 (2002).
[CrossRef]

Rill, M. S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
[CrossRef]

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J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

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A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101(10), 103902 (2008).
[CrossRef] [PubMed]

Rodríguez-Fortuño, F. J.

Sauvan, C.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett.88(4), 041109 (2006).
[CrossRef]

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
[CrossRef]

Shalaev, V. M.

A. V. Kildishev, J. D. Borneman, X. Ni, V. M. Shalaev, and V. P. Drachev, “Bianisotropic effective parameters of optical metamagnetics and negative-index materials,” Proc. IEEE99(10), 1691–1700 (2011).
[CrossRef]

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M. Albooyeh and C. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt.13(10), 105102 (2011).
[CrossRef]

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C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B75(19), 195111 (2007).
[CrossRef]

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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett.88(4), 041109 (2006).
[CrossRef]

Soukoulis, C.

J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B80(3), 035109 (2009).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

D. Ö. Güney, Th. Koschny, and C. M. Soukoulis, “Intra-connected 3D isotropic bulk negative index photonic metamaterial,” Opt. Express18(12), 12348–12353 (2010).
[CrossRef] [PubMed]

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express18(14), 14553–14567 (2010).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Sukhorukov, A. A.

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, “Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B86(3), 035127 (2012).
[CrossRef]

Taylor, A. J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Toor, F.

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
[CrossRef] [PubMed]

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C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B75(19), 195111 (2007).
[CrossRef]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Upadhya, P. C.

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Wen, L.

Werner, D. H.

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
[CrossRef] [PubMed]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

J. A. Bossard, S. Yun, D. H. Werner, and T. S. Mayer, “Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms,” Opt. Express17(17), 14771–14779 (2009).
[CrossRef] [PubMed]

Wu, B. I.

Xu, F. Y.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

Xu, Q.

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

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J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107(4), 043903 (2011).
[CrossRef] [PubMed]

Yang, X. M.

L. L. Hou, J. Y. Chin, X. M. Yang, L. X. Qi, R. P. Liu, F. Y. Xu, and T. J. Cui, “Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model,” J. Appl. Phys.103(6), 064904 (2008).
[CrossRef]

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S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
[CrossRef] [PubMed]

Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano5(6), 4641–4647 (2011).
[CrossRef] [PubMed]

J. A. Bossard, S. Yun, D. H. Werner, and T. S. Mayer, “Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms,” Opt. Express17(17), 14771–14779 (2009).
[CrossRef] [PubMed]

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C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
[CrossRef] [PubMed]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, J.

Zhang, S.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, M. R. Osgood, and S. R. J. Brueck, “Demonstration of near-infrared negative-index materials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Zhang, W.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

Zhang, X.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat Commun3, 1151 (2012).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhao, R.

Zhao, Y.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat Commun3, 870 (2012).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B80(3), 035109 (2009).
[CrossRef]

ACS Nano (2)

S. Yun, Z. H. Jiang, Q. Xu, Z. Liu, D. H. Werner, and T. S. Mayer, “Low-loss impedance-matched optical metamaterials with zero-phase delay,” ACS Nano6(5), 4475–4482 (2012).
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Adv. Mater. (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007).
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Appl. Phys. Lett. (3)

D. A. Powell and Y. S. Kivshar, “Substrate-induced bianisotropy in metamaterials,” Appl. Phys. Lett.97(9), 091106 (2010).
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D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett.88(4), 041109 (2006).
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IEEE J. Sel. Top. Quantum Electron. (1)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 367–375 (2010).
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IEEE Trans. Antenn. Propag. (1)

A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory,” IEEE Trans. Antenn. Propag.51(10), 2550–2557 (2003).
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IEEE Trans. Microw. Theory Tech. (1)

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J. Appl. Phys. (1)

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J. Opt. (1)

M. Albooyeh and C. Simovski, “Substrate-induced bianisotropy in plasmonic grids,” J. Opt.13(10), 105102 (2011).
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Nat Commun (2)

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C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

Nature (1)

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C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett.106(6), 067402 (2011).
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Proc. IEEE (1)

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Science (1)

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Figures (5)

Fig. 1
Fig. 1

(a) A multilayer fishnet metamaterial sandwiched between a superstrate and a substrate with finite thickness. Beneath the substrate and above the superstrate are the bottom and top half-spaces, respectively. (b) The unit cell geometry of the multilayer fishnet nanostructure composed of Ag and SiO2. The dimensions are px = 600, py = 600, wx = 72, wy = 336, ta = 15, td = 20 (all in nanometers). (c) Retrieved bianisotropic effective medium parameters for the free-standing fishnet displayed in (b). (d) Evolution of the real part of the effective index as a function of the number of functional layers (N) for the free-standing fishnet in (b).

Fig. 2
Fig. 2

(a) Scattering parameters of the multilayer fishnet alone on an infinite substrate. (b) Retrieved effective permittivity, permeability and magnetoelectric coupling parameter corresponding to (a). (c) Extracted scattering parameters of the multilayer fishnet alone on a 5μm thick substrate. (d) Retrieved effective permittivity, permeability and magnetoelectric coupling parameter corresponding to (c). (e) Evolution of the maximum real and imaginary parts of the retrieved magnetoelectric coupling parameter as a function of the thickness of the SiO2 substrate. The point on the right edge of the plot corresponds to the semi-infinite substrate case.

Fig. 3
Fig. 3

(a) Magnitudes of the induced electric (p) and magnetic (m) dipole moments in the free-standing multilayer fishnet under an electric (e) or magnetic (m) excitation. (b) Magnitudes of the induced electric (p) and magnetic (m) dipole moments in the multilayer fishnet on a semi-infinite substrate under an electric (e) or magnetic (m) excitation.

Fig. 4
Fig. 4

(a) Evolution of the maximum real and imaginary parts of the retrieved magnetoelectric coupling parameter as a function of the superstrate thickness with a permittivity of 2.25. The point on the right edge of the plot corresponds to the semi-infinite SiO2 superstrate case. (b) Retrieved magnetoelectric coupling parameter for the fishnet on a semi-infinite SiO2 substrate and the fishnet underneath a 200nm SiO2 superstrate. (c) Magnitudes of the induced electric (p) and magnetic (m) dipole moments in the multilayer fishnet sandwiched between a semi-infinite substrate and a 200nm superstrate under an electric (e) or magnetic (m) excitation.

Fig. 5
Fig. 5

(a) Evolution of the maximum real and imaginary parts of the retrieved magnetoelectric coupling parameter as a function of the superstrate thickness with a permittivity of 1.75 and 2.75, respectively. The point on the right edge of the plot corresponds to the infinite substrate case. (b) Optimum superstrate thickness as a function of the permittivity value of the superstrate.

Equations (6)

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T tot =[ T 11 T 12 T 21 T 22 ]= 1 S 21 [ 1 S 22 S 11 | T tot | ],
T tot =( T bhs )( T sub )( T MM )( T sup )( T ths ),
T MM = ( T sub ) 1 ( T bhs ) 1 ( T tot ) ( T ths ) 1 ( T sup ) 1 ,
S MM =[ S 11 S 12 S 21 S 22 ]= 1 T 11 [ T 21 | T MM | 1 T 12 ].
T slab = 1 2 [ 1+ ε s 1 ε s 1 ε s 1+ ε s ].[ e i ε s k 0 d 1 1 e i ε s k 0 d ]. 1 2 ε s [ ε s +1 ε s 1 ε s 1 ε s +1 ]
p x = v ( ε d(m) 1) E x d 3 a,   m y =  iω 2 v ( ε d(m) 1) n × E x d 3 a,

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