Abstract

A chiral optical negative-index metamaterial design of doubly periodic construction for the near-infrared spectrum is presented. The chirality is realized by incorporating sub-wavelength planar silver-alumina-silver resonators and arranging them in a left-handed helical (i.e., stair-step) configuration as a wave propagates through the metamaterial. An effective material parameter retrieval procedure is developed for general bi-isotropic metamaterials. A numerical design example is presented and the retrieved effective material parameters exhibiting a negative index of refraction are provided.

© 2008 Optical Society of America

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  1. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  4. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4930 (2005).
    [CrossRef] [PubMed]
  5. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 mm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  6. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813nm and single negative at 772nm," Opt. Lett. 32, 1671-1673 (2007).
    [CrossRef] [PubMed]
  7. J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
    [CrossRef] [PubMed]
  8. V. Yannopapas, "Negative index of refraction in artificial chiral materials," J. Phys.: Condens. Matter 18, 6883-6890 (2006).
    [CrossRef]
  9. Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
    [CrossRef]
  10. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
    [CrossRef] [PubMed]
  11. E. Plum, J. Dong, J. Zhou, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, "3D-chiral metamaterial showing artificial magnetic response and negative refraction," arXiv:0806.0823v1 (2008).
  12. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, "Giant optical gyrotropy due to electromagnetic coupling," Appl. Phys. Lett. 90, 223113 (2007).
    [CrossRef]
  13. 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]
  14. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  15. A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," Appl. Comput. Electrom. 22, 172-183 (2007).
  16. 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]
  17. D.-H. Kwon, P. L. Werner, and D. H. Werner, "Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation," Opt. Express 16, 11802-11807 (2008).
    [CrossRef] [PubMed]
  18. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE Press, Piscataway, NJ, 1998).
    [CrossRef]
  19. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  20. E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic Press, Boston, 1991).
  21. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
    [CrossRef]

2008 (1)

2007 (6)

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

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

A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," Appl. Comput. Electrom. 22, 172-183 (2007).

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 mm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813nm and single negative at 772nm," Opt. Lett. 32, 1671-1673 (2007).
[CrossRef] [PubMed]

2006 (2)

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

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

2005 (2)

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4930 (2005).
[CrossRef] [PubMed]

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]

2004 (1)

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

2002 (1)

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

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Bai, B.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

Brueck, S. R. J.

Cai, W.

Chen, Y.

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

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Decker, M.

Dolling, G.

Drachev, V. P.

Fan, W.

Fedotov, V. A.

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

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

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]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

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.

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.

Linden, S.

Malloy, K. J.

Markos, P.

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

Osgood, R. M.

Osipov, M.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

Panoiu, N. C.

Pendry, J. B.

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

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Plum, E.

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

Rogacheva, A. V.

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[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. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schwanecke, A. S.

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

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

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

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 mm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, 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.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

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]

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

Turunen, J.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

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.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

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]

Wegener, M.

Werner, D. H.

Werner, P. L.

Xiao, S.

Yannopapas, V.

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

Yuan, H.-K.

Zhang, S.

Zheludev, N.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

Zheludev, N. I.

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

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

Appl. Comput. Electrom. (1)

A. V. Kildishev and U. K. Chettiar, "Cascading optical negative index metamaterials," Appl. Comput. Electrom. 22, 172-183 (2007).

Appl. Phys. Lett. (2)

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

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

J. Phys.: Condens. Matter (1)

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007).
[CrossRef]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

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

Phys. Rev. Lett. (3)

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006).
[CrossRef] [PubMed]

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]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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

Other (4)

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE Press, Piscataway, NJ, 1998).
[CrossRef]

E. Plum, J. Dong, J. Zhou, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, "3D-chiral metamaterial showing artificial magnetic response and negative refraction," arXiv:0806.0823v1 (2008).

E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic Press, Boston, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

(Color online) A BI slab under illumination by a circularly-polarized plane wave.

Fig. 2.
Fig. 2.

(Color online) Construction of the unit cell of a doubly-periodic optical chiral meta-material: (a) A quadrant, (b) The spacer layer geometry of a quadrant, (c) The unit cell.

Fig. 3.
Fig. 3.

(Color online) The spectra and material parameters of the chiral optical metamaterial: (a) R ± and T ± (reflectance and transmittance), (b) z ±, (c) n ±, (d) κ, (e) ε ±, and (f)μ ±.

Equations (15)

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

D = ε E + ( χ + i κ ) μ 0 ε 0 H ,
B = ( χ i κ ) μ 0 ε 0 E + μ H ,
1 + r 0 ± = t 1 ± + r 1 ± ,
1 r 0 ± z 0 = t 1 ± z ± r 1 ± z .
t 1 ± e i k ± d + r 1 ± e i k d = t 2 ± ,
t 1 ± e i k ± d z ± r 1 ± e i k d z = t 2 ± z 2 .
e i k ± d = ( 1 r 0 + ) z 0 ± ( 1 + r 0 + ) z t 2+ ( 1 z 2 ± 1 z ) ,
e i k d = ( 1 r 0 ) z 0 ± ( 1 + r 0 ) z ± t 2− ( 1 z 2 ± 1 z ± ) ,
[ ( 1 + r 0 + ) ( 1 + r 0 ) t 2 + t 2 ] ( 1 z ± ) 2 + 2 ( r 0 ± r 0 ) z 0 ( 1 z ± ) ( 1 r 0 + ) ( 1 r 0 ) z 0 2 + t 2 + t 2 z 2 2 = 0 ,
cos k ± d = 1 2 [ ( 1 r 0 ± ) z 0 + ( 1 + r 0 ± ) z t 2 ± ( 1 z 2 + 1 z ) + ( 1 r 0 ) z 0 ( 1 + r 0 ) z t 2 ( 1 z 2 1 z ) ] .
z = z + z , n = ( n + + n ) z z + + z , χ = n z + z i 2 z , κ = n + n 2 .
E t x = x ̂ t x x + y ̂ t y x ,
E t y = x ̂ t x y + y ̂ t y y .
E t R = ( x ̂ · u ̂ R ) E t x + ( y ̂ · u ̂ R ) E t y = x ̂ t x x + i t x y 2 + y ̂ t y x + i t y y 2 = x ̂ t x x i t y x 2 + y ̂ t y x + i t x x 2 ,
E t L = ( x ̂ · u ̂ L ) E t x + ( y ̂ · u ̂ L ) E t y = x ̂ t x x i t x y 2 + y ̂ t y x i t y y 2 = x ̂ t x x + i t y x 2 + y ̂ t y x i t x x 2 .

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