Abstract

After the prediction that strong enough optical activity may result in negative refraction and negative reflection, more and more artificial chiral metamaterials were designed and fabricated at difference frequency ranges from microwaves to optical waves. Therefore, a simple and robust method to retrieve the effective constitutive parameters for chiral metamaterials is urgently needed. Here, we analyze the wave propagation in chiral metamaterials and follow the regular retrieval procedure for ordinary metamaterials and apply it in chiral metamaterial slabs. Then based on the transfer matrix technique, the parameter retrieval is extended to treat samples with not only the substrate but also the top layers. After the parameter retrieval procedure, we take two examples to check our method and study how the substrate influences on the thin chiral metamaterials slabs. We find that the substrate may cause the homogeneous slab to be inhomogeneous, i.e. the reflections in forward and backward directions are different. However, the chiral metamaterial where the resonance element is embedded far away from the substrate is insensitive to the substrate.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  2. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
    [CrossRef]
  3. C. Monzon, and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
    [CrossRef] [PubMed]
  4. S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
    [CrossRef]
  5. V. Yannopapas, “Negative index of refraction in artificial chiral materials,” J. Phys. Condens. Matter 18, 6883–6890 (2006).
    [CrossRef]
  6. V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
    [CrossRef]
  7. C. Zhang, and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Appl. Phys. Lett. 91, 194101 (2007).
    [CrossRef]
  8. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
    [CrossRef]
  11. J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
    [CrossRef] [PubMed]
  12. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
    [CrossRef]
  13. E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
    [CrossRef] [PubMed]
  14. L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  24. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
    [CrossRef]
  25. Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
    [CrossRef] [PubMed]
  26. Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
    [CrossRef]
  27. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
    [CrossRef]
  28. 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, 026610 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  37. J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).
  38. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [CrossRef]
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2010

2009

V. Yannopapas, “Circular dichroism in planar nonchiral plasmonic metamaterials,” Opt. Lett. 34, 632–634 (2009).
[CrossRef] [PubMed]

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 1501–1503 (2009).
[CrossRef] [PubMed]

J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
[CrossRef] [PubMed]

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, 026610 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

2008

L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
[CrossRef]

D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design,” Opt. Express 16, 11822–11829 (2008).
[CrossRef] [PubMed]

2007

C. Zhang, and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32, 856–858 (2007).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

2006

V. Yannopapas, “Negative index of refraction in artificial chiral materials,” J. Phys. Condens. Matter 18, 6883–6890 (2006).
[CrossRef]

V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
[CrossRef]

2005

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

C. Monzon, and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

2004

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef] [PubMed]

2003

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

2002

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

1999

J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).

1937

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
[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, 026610 (2009).
[CrossRef]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Baena, J. D.

L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Chen, Y.

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Cui, T. J.

C. Zhang, and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

Decker, M.

Dong, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
[CrossRef] [PubMed]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

Economou, E. N.

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

Fedotov, V. A.

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
[CrossRef]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Forester, D. W.

C. Monzon, and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

Freymann, G. V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Gartstein, Y. N.

V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
[CrossRef]

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).

Ino, Y.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Jefimovs, K.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Jelinek, L.

L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Jylha, L.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

Kafesaki, M.

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

Kauranen, M.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

Klein, M. W.

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Koschny, Th.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

Kriegler, C. E.

Kuwata-Gonokami, M.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Kwon, D. H.

Li, J.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Li, Z.

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, 026610 (2009).
[CrossRef]

Linden, S.

Liu, X.-X.

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

Lu, X.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Markoš, P.

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Marques, R.

L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Maslovski, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

Mesa, F.

L. Jelinek, R. Marquěs, F. Mesa, and J. D. Baena, “Periodic arrangements of chiral scatterers providing negative refractive index bi-isotropic media,” Phys. Rev. B 77, 205110 (2008).
[CrossRef]

Monzon, C.

C. Monzon, and D. W. Forester, “Negative refraction and focusing of circularly polarized waves in optically active media,” Phys. Rev. Lett. 95, 123904 (2005).
[CrossRef] [PubMed]

Nefedov, I.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

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, 026610 (2009).
[CrossRef]

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Park, Y. S.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).

Plum, E.

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
[CrossRef]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).

Ruther, M.

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Saito, N.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Schwanecke, A. S.

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Shalaev, V. M.

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

Simovski, C.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, “Twisted split-ring-resonator photonic metamaterial with huge optical activity,” Opt. Lett. 35, 1593–1595 (2010).
[CrossRef] [PubMed]

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 1501–1503 (2009).
[CrossRef] [PubMed]

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Svirko, Y.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef] [PubMed]

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

Tsai, D. P.

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

Turunen, J.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Vallius, T.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Vier, D. C.

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

Wang, B.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

Wegener, M.

Werner, D. H.

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Yannopapas, V.

V. Yannopapas, “Circular dichroism in planar nonchiral plasmonic metamaterials,” Opt. Lett. 34, 632–634 (2009).
[CrossRef] [PubMed]

V. Yannopapas, “Negative index of refraction in artificial chiral materials,” J. Phys. Condens. Matter 18, 6883–6890 (2006).
[CrossRef]

Zakhidov, A. A.

V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
[CrossRef]

Zhang, C.

C. Zhang, and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

Zhang, S.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zhang, W.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102, 023901 (2009).
[CrossRef] [PubMed]

Zhao, R.

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, “Twisted split-ring-resonator photonic metamaterial with huge optical activity,” Opt. Lett. 35, 1593–1595 (2010).
[CrossRef] [PubMed]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

Zheludev, N. I.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
[CrossRef]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

Zhou, J.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 1501–1503 (2009).
[CrossRef] [PubMed]

J. Dong, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17, 14172–14179 (2009).
[CrossRef] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

Appl. Phys. Lett.

C. Zhang, and T. J. Cui, “Negative reflections of electromagnetic waves in a strong chiral medium,” Appl. Phys. Lett. 91, 194101 (2007).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93, 191911 (2008).
[CrossRef]

B. Wang, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Nonplanar chiral metamaterials with negative index,” Appl. Phys. Lett. 94, 151112 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, A. S. Schwanecke, Y. Chen, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90, 223113 (2007).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

J. B. Pendry, A. J. Holden, and D. J. Robbins, “andW. J. Stewart,“ Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).

J. Electromagn. Waves Appl.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, “Waves and energy in chiral nihility,” J. Electromagn. Waves Appl. 17, 695–706 (2003).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

B. Wang, J. Zhou, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A, Pure Appl. Opt. 11, 114003 (2009).
[CrossRef]

J. Phys. Condens. Matter

V. Yannopapas, “Negative index of refraction in artificial chiral materials,” J. Phys. Condens. Matter 18, 6883–6890 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

S. Tretyakov, A. Sihvola, and L. Jylha, “Backward-wave regime and negative refraction in chiral composites,” Photonics Nanostruct. Fundam. Appl. 3, 107 (2005).
[CrossRef]

Phys. Rev. B

V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, “Negative refraction in gyrotropic media,” Phys. Rev. B 73, 045114 (2006).
[CrossRef]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, Th. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[CrossRef]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79, 121104 (2009).
[CrossRef]

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[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 036617 (2005).
[CrossRef]

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, 026610 (2009).
[CrossRef]

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 016608 (2004).
[CrossRef]

Phys. Rev. Lett.

Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

R. Zhao, J. Zhou, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Repulsive Casimir force in chiral metamaterials,” Phys. Rev. Lett. 103, 103602 (2009).
[CrossRef] [PubMed]

E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102, 113902 (2009).
[CrossRef] [PubMed]

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Other

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (2nd ed., Pergamon Press, Oxford, 1984), §104, p.362–367.

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A. Serdyukov,  et al., Electromagnetics of Bi-anisotropic Materials: Theory and Applications (Gordon and Breach Science Publishers, Amsterdam, 2001).

Some people [see, for instance, A. Lakhtakia et al., “Reflection of plane waves at planar achiral-chiral interfaces: independence of the reflected polarization state from the incident polarization state,” J. Opt. Soc. Am. A 7, 1654 (1990).] use the Drude-Born-Fedorov relations: D = ε (B + β∇ ×E), B = μ(H + β∇ ×H), where β characterizes the strength of the chirality. They can be brought to the same form. The transformations between the parameters of the two systems are given in Ref. 26.
[CrossRef]

CST MICROWAVE STUDIO (CST MWS) is a specialist tool for the 3D EM simulation of high frequency components, http://www.cst.com/Content/Products/MWS/Overview.aspx.

P. Markoš, and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).

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Figures (6)

Fig. 1.
Fig. 1.

Schematics of the transmission and reflection coefficient of a standalone CMM slab.

Fig. 2.
Fig. 2.

(a)–(c) are the Schematics of the twisted-crosses CMM slab. (a) free standing, (b) with substrate and top layer, and (c) with substrate only. The amplititudes, (d)–(f), and the phases, (g)–(i), are also shown correspondingly. The prime (′) denotes that the wave is incident from the opposite direction.

Fig. 3.
Fig. 3.

The retrieval parameters ε, μ, κ, n , n +, η, and θ for CMM slabs. (Left) freestanding, (Middle) with substrate and top layer, and (Right) with substrate only.These results were extracted using (19).

Fig. 4.
Fig. 4.

Schmetics of the four-folded rotated Ω-particle CMM. The inner and outer radius of the loop are r = 5µm and R = 5.5µm. The length of each straight wire is L = 8.08µm. d = 0.5µm. a = 32µm. b = 12µm. Each Ω-particle locates at the center of each quarter of the unit cell. The silver Ω-particle is embeded in the polyimide with ε = 2.5 and loss tangent δ = 0.03. The silver is charactored by the Drude model with the surface plasmon ωp = 13.66 × 1015 rad/s and the collision frequency ωc = 2.73 × 1013 rad/s.

Fig. 5.
Fig. 5.

(a)–(d) are the simulation results of the amplitude and the phase of the reflection and transmission for the four-folded rotated Ω-particle CMM slabs. They are extracted using (19). R′ is the reflection for the incident wave from the opposite direction. (e)–(j) show the optical parameters ε, μ, and κ. Re/Im denotes the real/imaginary part of the value. The subscripts s and f denotes the retrieval results from the numerical simulation and the fitting results using Eqs. (29) respectively. The left is with substrate (n=1.27) only and the right is for the free standing sample.

Fig. 6.
Fig. 6.

Schematics of the single right-handed (left) and left-handed (right) Ω-particle resonators.

Equations (44)

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( D B ) = ( ε 0 ε i κ c 0 i κ c 0 μ 0 μ ) ( E H ) ,
k × H = ω D , k × E = ω B ,
k × ( k × E ) = k 0 2 ( ε μ κ 2 ) E 2 i κ k 0 ( k × E ) ,
E ± ( z ) = ( x ̂ ± i y ̂ ) E 0 e ikz ,
k ± = k 0 ( n ± κ ) ,
n ± = n ± κ .
θ = 1 2 [ arg ( T + ) arg ( T ) ] ,
η = 1 2 tan 1 ( T + 2 T 2 T + 2 + T 2 ) .
1 + R = T ± + R ,
1 R = T ± R Z ,
T ± e ik ± d + R e ik d = T ± ,
T ± e ik ± d R e ik d Z = T ± ,
T ± = 4 Z e ink 0 d e ± i κ k 0 d ( 1 + Z ) 2 ( 1 Z ) 2 e 2 ink 0 d ,
R = ( 1 Z 2 ) ( e 2 ink 0 d 1 ) ( 1 + Z ) 2 ( 1 Z ) 2 e 2 ink 0 d .
Z = ± ( 1 + R ) 2 T + T ( 1 R ) 2 T + T ,
n ± = i k 0 d { ln [ 1 T ± ( 1 Z 1 Z + 1 R ) ] ± 2 m π } ,
Re ( Z ) 0 , Im ( n ) 0 ,
T = 4 Z e ink 0 d ( 1 + Z ) 2 ( 1 Z ) 2 e 2 ink 0 d ,
R = ( 1 Z 2 ) ( e 2 ink 0 d 1 ) ( 1 + Z ) 2 ( 1 Z ) 2 e 2 ink 0 d .
κ = i 2 k 0 d ln ( T + T ) = i 2 k 0 d ln ( T + e i ϕ + T e i ϕ ) ,
Re ( κ ) = ϕ + ϕ + 2 m π 2 k 0 d ,
Im ( κ ) = ln T ln T + 2 k 0 d ,
S = ( r t t r ) ; M = ( t r r t r t r t 1 t ) ,
M total = M substrate M CMM M toplayer .
M = [ Z + 1 2 Z Z 1 2 Z Z 1 2 Z Z + 1 2 Z ] [ e ink 0 d 0 0 e ink 0 d ] [ 1 + Z 2 1 Z 2 1 Z 2 1 + Z 2 ] ,
M CMM = M substrate 1 M total M toplayer 1 .
R av = RR ,
U = 2 l E 0 ± μ 0 S H ̇ 0 ,
L I ̇ + q C + R I = U , I = q ̇ .
( ω 2 i ω γ + ω 0 2 ) q = α E 0 ± i ω β H 0 ,
q = α ω 2 i ω γ + ω 0 2 E 0 ± i ω β ω 2 i ω γ + ω 0 2 H 0 .
p = α 1 ω 0 2 ω 2 i ω γ E 0 + ± i ω β 1 ω 0 2 ω 2 i ω γ H 0 ,
m = i ω α A ω 0 2 ω 2 i ω γ E 0 + ω 2 β A ω 0 2 ω 2 i ω γ H 0 ,
P = N V 0 α l ω 0 2 ω 2 i ω γ E + N V 0 ± i ω β l ω 0 2 ω 2 i ω γ H ,
M = N V 0 i ω α A ω 0 2 ω 2 i ω γ E + N V 0 ω 2 β A ω 0 2 ω 2 i ω γ H .
D = ε 0 E + α l N V 0 ω 0 2 ω 2 i ω γ E + ± i ω β l N V 0 ω 0 2 ω 2 i ω γ H ,
B = μ 0 H + i μ 0 ω α A N V 0 ω 0 2 ω 2 i ω γ E + ω 2 μ 0 β A N V 0 ω 0 2 ω 2 i ω γ H .
ε = 1 + α l N V 0 ε 0 ω 0 2 ω 2 i ω γ ,
μ = 1 + ω 2 β A N V 0 ω 0 2 ω 2 i ω γ ,
κ = ± ω β l c 0 N V 0 ω 0 2 ω 2 i ω γ = ± ω μ 0 c 0 α A N V 0 ω 0 2 ω 2 i ω γ .
ε = ε b + Ω ε ω 0 2 ω 0 2 ω 2 i ω γ ,
μ = μ b + Ω μ ω 2 ω 0 2 ω 2 i ω γ ,
κ = Ω κ ω 0 ω ω 0 2 ω 2 i ω γ ,
Ω κ 2 = Ω ε Ω μ ,

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