Abstract

We investigate a two-dimensional metamaterial template constructed from different pixels through a conservation law of effective indices: If the product of refractive indices along the principal axes is invariant for different anisotropic materials in a two-dimensional space, the product of indices of the effective medium remains constant after mixing these materials. Such effective media of constant indices product can be implemented using metamaterial structures. The orientation of the metamaterial structure in a single pixel controls the direction of the principal axis of the effective medium. Different pixels are assembled into an array to obtain reconfigurable anisotropy of the effective medium. These considerations would be useful for constructing reconfigurable metamaterials and transformation media with area-preserving maps.

© 2015 Optical Society of America

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References

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  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004).
    [Crossref] [PubMed]
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  3. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Annalen. Der. Physik. 24(7), 636–664 (1935).
    [Crossref]
  4. D. Polder and J. H. Van Santen, “The effective permeability of mixtures of solids,” Physica 12(5), 257–271 (1946).
    [Crossref]
  5. G. P. de Loor, “Dielectric properties of heterogeneous mixtures with a polar constituent,” Appl. Sci. Res. B. 11(3-4), 310–320 (1964).
    [Crossref]
  6. H. Looyenga, “Dielectric constants of heterogeneous mixtures,” Physica 31(3), 401–406 (1965).
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  7. A. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Rem. Sens. 26(4), 420–429 (1988).
    [Crossref]
  8. D. J. Bergman, “Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material,” Phys. Rev. Lett. 44(19), 1285–1287 (1980).
    [Crossref]
  9. G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization,” SIAM J. Math. Anal. 20(3), 608–623 (1989).
    [Crossref]
  10. G. Allaire, “Homogenization and two-scale convergence,” SIAM J. Math. Anal. 23(6), 1482–1518 (1992).
    [Crossref]
  11. S. Guenneau and F. Zolla, “Homogenization of Three-Dimensional Finite Photonic Crystals,” Progress In Electomagnetic Research. 27, 91–127 (2000).
    [Crossref]
  12. N. Wellander and G. Kristensson, “Homogenization of the Maxwell Equations at Fixed Frequency,” SIAM. J. Math. 64, 170 (2003).
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  16. T. C. Han, C. W. Qiu, J. W. Dong, X. H. Tang, and S. Zouhdi, “Homogeneous and isotropic bends to tunnel waves through multiple different/equal waveguides along arbitrary directions,” Opt. Express 19(14), 13020–13030 (2011).
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  17. Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
    [Crossref]
  18. H.-R. Wenk and P. Van Houtte, “Texture and anisotropy,” Rep. Prog. Phys. 67(8), 1367–1428 (2004).
    [Crossref]
  19. L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
    [Crossref]
  20. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
    [Crossref]
  21. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
    [Crossref]
  22. H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
    [Crossref]
  23. R. V. Craster and Y. V. Obnosov, “Four-Phase Checkerboard Composites,” SIAM J. Appl. Math. 61(6), 1839–1856 (2001).
    [Crossref]
  24. R. V. Craster and Y. V. Obnosov, “Checkerboard composites with separated phases,” J. Math. Phys. 42(11), 5379 (2001).
    [Crossref]
  25. G. W. Milton, “Proof of a conjecture on the conductivity of checkerboards,” J. Math. Phys. 42(10), 4873 (2001).
    [Crossref]
  26. F. Zolla and S. Guenneau, “Duality relation for the Maxwell system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2 Pt 2), 026610 (2003).
    [Crossref] [PubMed]
  27. S. Chakrabarti, S. A. Ramakrishna, and S. Guenneau, “Finite checkerboards of dissipative negative refractive index,” Opt. Express 14(26), 12950–12957 (2006).
    [Crossref] [PubMed]
  28. C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
    [Crossref] [PubMed]
  29. A. Castanié, J.-F. Mercier, S. Félix, and A. Maurel, “Generalized method for retrieving effective parameters of anisotropic metamaterials,” Opt. Express 22(24), 29937–29953 (2014).
    [Crossref] [PubMed]
  30. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
    [Crossref] [PubMed]
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2014 (2)

2013 (1)

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

2012 (1)

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

2011 (1)

2009 (1)

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

2008 (2)

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[Crossref]

L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[Crossref]

2006 (2)

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

S. Chakrabarti, S. A. Ramakrishna, and S. Guenneau, “Finite checkerboards of dissipative negative refractive index,” Opt. Express 14(26), 12950–12957 (2006).
[Crossref] [PubMed]

2004 (2)

H.-R. Wenk and P. Van Houtte, “Texture and anisotropy,” Rep. Prog. Phys. 67(8), 1367–1428 (2004).
[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

2003 (3)

N. Wellander and G. Kristensson, “Homogenization of the Maxwell Equations at Fixed Frequency,” SIAM. J. Math. 64, 170 (2003).

F. Zolla and S. Guenneau, “Duality relation for the Maxwell system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2 Pt 2), 026610 (2003).
[Crossref] [PubMed]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

2001 (3)

R. V. Craster and Y. V. Obnosov, “Four-Phase Checkerboard Composites,” SIAM J. Appl. Math. 61(6), 1839–1856 (2001).
[Crossref]

R. V. Craster and Y. V. Obnosov, “Checkerboard composites with separated phases,” J. Math. Phys. 42(11), 5379 (2001).
[Crossref]

G. W. Milton, “Proof of a conjecture on the conductivity of checkerboards,” J. Math. Phys. 42(10), 4873 (2001).
[Crossref]

2000 (1)

S. Guenneau and F. Zolla, “Homogenization of Three-Dimensional Finite Photonic Crystals,” Progress In Electomagnetic Research. 27, 91–127 (2000).
[Crossref]

1992 (1)

G. Allaire, “Homogenization and two-scale convergence,” SIAM J. Math. Anal. 23(6), 1482–1518 (1992).
[Crossref]

1989 (1)

G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization,” SIAM J. Math. Anal. 20(3), 608–623 (1989).
[Crossref]

1988 (1)

A. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Rem. Sens. 26(4), 420–429 (1988).
[Crossref]

1980 (1)

D. J. Bergman, “Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material,” Phys. Rev. Lett. 44(19), 1285–1287 (1980).
[Crossref]

1965 (1)

H. Looyenga, “Dielectric constants of heterogeneous mixtures,” Physica 31(3), 401–406 (1965).
[Crossref]

1964 (1)

G. P. de Loor, “Dielectric properties of heterogeneous mixtures with a polar constituent,” Appl. Sci. Res. B. 11(3-4), 310–320 (1964).
[Crossref]

1946 (1)

D. Polder and J. H. Van Santen, “The effective permeability of mixtures of solids,” Physica 12(5), 257–271 (1946).
[Crossref]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Annalen. Der. Physik. 24(7), 636–664 (1935).
[Crossref]

1904 (1)

J. C. Maxwell Garnett, “Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 203(359-371), 385–420 (1904).
[Crossref]

Allaire, G.

G. Allaire, “Homogenization and two-scale convergence,” SIAM J. Math. Anal. 23(6), 1482–1518 (1992).
[Crossref]

Bergman, D. J.

D. J. Bergman, “Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material,” Phys. Rev. Lett. 44(19), 1285–1287 (1980).
[Crossref]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Annalen. Der. Physik. 24(7), 636–664 (1935).
[Crossref]

Castanié, A.

Chakrabarti, S.

Chan, C. T.

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[Crossref]

Chen, H. Y.

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[Crossref]

Craster, R. V.

R. V. Craster and Y. V. Obnosov, “Four-Phase Checkerboard Composites,” SIAM J. Appl. Math. 61(6), 1839–1856 (2001).
[Crossref]

R. V. Craster and Y. V. Obnosov, “Checkerboard composites with separated phases,” J. Math. Phys. 42(11), 5379 (2001).
[Crossref]

de Loor, G. P.

G. P. de Loor, “Dielectric properties of heterogeneous mixtures with a polar constituent,” Appl. Sci. Res. B. 11(3-4), 310–320 (1964).
[Crossref]

Della Giovampaola, C.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

Dong, J. W.

Engheta, N.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

Félix, S.

Gajic, R.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

Guenneau, S.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

S. Chakrabarti, S. A. Ramakrishna, and S. Guenneau, “Finite checkerboards of dissipative negative refractive index,” Opt. Express 14(26), 12950–12957 (2006).
[Crossref] [PubMed]

F. Zolla and S. Guenneau, “Duality relation for the Maxwell system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2 Pt 2), 026610 (2003).
[Crossref] [PubMed]

S. Guenneau and F. Zolla, “Homogenization of Three-Dimensional Finite Photonic Crystals,” Progress In Electomagnetic Research. 27, 91–127 (2000).
[Crossref]

S. Guenneau and J. Li, “Conservation law in anisotropic effective thin plates” (in preparation)

Han, T. C.

Hingerl, K.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

Isic, G.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

Jiang, X.

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

Kadic, M.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Kong, J. A.

A. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Rem. Sens. 26(4), 420–429 (1988).
[Crossref]

Kristensson, G.

N. Wellander and G. Kristensson, “Homogenization of the Maxwell Equations at Fixed Frequency,” SIAM. J. Math. 64, 170 (2003).

Li, J.

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

S. Guenneau and J. Li, “Conservation law in anisotropic effective thin plates” (in preparation)

Liang, Z.

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

Looyenga, H.

H. Looyenga, “Dielectric constants of heterogeneous mixtures,” Physica 31(3), 401–406 (1965).
[Crossref]

Maurel, A.

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 203(359-371), 385–420 (1904).
[Crossref]

McManamon, P. F.

L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[Crossref]

Mercier, J.-F.

Miao, F.

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

Milton, G. W.

G. W. Milton, “Proof of a conjecture on the conductivity of checkerboards,” J. Math. Phys. 42(10), 4873 (2001).
[Crossref]

Nguetseng, G.

G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization,” SIAM J. Math. Anal. 20(3), 608–623 (1989).
[Crossref]

Obnosov, Y. V.

R. V. Craster and Y. V. Obnosov, “Checkerboard composites with separated phases,” J. Math. Phys. 42(11), 5379 (2001).
[Crossref]

R. V. Craster and Y. V. Obnosov, “Four-Phase Checkerboard Composites,” SIAM J. Appl. Math. 61(6), 1839–1856 (2001).
[Crossref]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

Polder, D.

D. Polder and J. H. Van Santen, “The effective permeability of mixtures of solids,” Physica 12(5), 257–271 (1946).
[Crossref]

Qiu, C. W.

Ramakrishna, S. A.

S. Chakrabarti, S. A. Ramakrishna, and S. Guenneau, “Finite checkerboards of dissipative negative refractive index,” Opt. Express 14(26), 12950–12957 (2006).
[Crossref] [PubMed]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

Ros, P. J.

L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[Crossref]

Salandrino, A.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

Schittny, R.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Shi, L.

L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[Crossref]

Sihvola, A. H.

A. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Rem. Sens. 26(4), 420–429 (1988).
[Crossref]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

Tang, X. H.

Van Houtte, P.

H.-R. Wenk and P. Van Houtte, “Texture and anisotropy,” Rep. Prog. Phys. 67(8), 1367–1428 (2004).
[Crossref]

Van Santen, J. H.

D. Polder and J. H. Van Santen, “The effective permeability of mixtures of solids,” Physica 12(5), 257–271 (1946).
[Crossref]

Vasic, B.

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

Wegener, M.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on Transformation Thermodynamics: Molding the Flow of Heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Wellander, N.

N. Wellander and G. Kristensson, “Homogenization of the Maxwell Equations at Fixed Frequency,” SIAM. J. Math. 64, 170 (2003).

Wenk, H.-R.

H.-R. Wenk and P. Van Houtte, “Texture and anisotropy,” Rep. Prog. Phys. 67(8), 1367–1428 (2004).
[Crossref]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

Zolla, F.

F. Zolla and S. Guenneau, “Duality relation for the Maxwell system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2 Pt 2), 026610 (2003).
[Crossref] [PubMed]

S. Guenneau and F. Zolla, “Homogenization of Three-Dimensional Finite Photonic Crystals,” Progress In Electomagnetic Research. 27, 91–127 (2000).
[Crossref]

Zouhdi, S.

Annalen. Der. Physik. (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Annalen. Der. Physik. 24(7), 636–664 (1935).
[Crossref]

Appl. Sci. Res. B. (1)

G. P. de Loor, “Dielectric properties of heterogeneous mixtures with a polar constituent,” Appl. Sci. Res. B. 11(3-4), 310–320 (1964).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (1)

A. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Rem. Sens. 26(4), 420–429 (1988).
[Crossref]

J. Appl. Phys. (1)

L. Shi, P. F. McManamon, and P. J. Ros, “Liquid crystal optical phase plate with a variable in-plane gradient,” J. Appl. Phys. 104(3), 033109 (2008).
[Crossref]

J. Math. Phys. (2)

R. V. Craster and Y. V. Obnosov, “Checkerboard composites with separated phases,” J. Math. Phys. 42(11), 5379 (2001).
[Crossref]

G. W. Milton, “Proof of a conjecture on the conductivity of checkerboards,” J. Math. Phys. 42(10), 4873 (2001).
[Crossref]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the Near Field,” J. Mod. Opt. 50(9), 1419–1430 (2003).
[Crossref]

Nat. Mater. (1)

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

New J. Phys. (1)

Z. Liang, X. Jiang, F. Miao, S. Guenneau, and J. Li, “Transformation media with variable optical axes,” New J. Phys. 14(10), 103042 (2012).
[Crossref]

Opt. Express (3)

Philos. Trans. R. Soc. Lond. B Biol. Sci. (1)

J. C. Maxwell Garnett, “Colours in Metal Glasses and in Metallic Films,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 203(359-371), 385–420 (1904).
[Crossref]

Phys. Rev. B (3)

B. Vasic, G. Isic, R. Gajic, and K. Hingerl, “Coordinate transformation based design of confined metamaterial structures,” Phys. Rev. B 79(8), 085103 (2009).
[Crossref]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

H. Y. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78(5), 054204 (2008).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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Figures (6)

Fig. 1
Fig. 1 The local annex problem obtained from the homogenization process in a 2D periodic structure with a square unit cell. Permittivity ε(r) denotes distribution of materials in the domain. Arrows Ε 0 represent the constant electric field applied to the background. Periodic boundary conditions are applied.
Fig. 2
Fig. 2 Homogenization of effective media for a square array of circular inclusions (parameters described in text). Inset is the sketch of mixture. Elliptical equifrequency contours denote anisotropy in different domains and arrows indicate individual directions of optical axis.
Fig. 3
Fig. 3 A reconfigurable effective medium implemented by metamaterial atoms. Structure a1 denotes the homogeneous anisotropic media c with a circular disk geometry, which can be considered as the effective media of the circular disk structure a2 which is composed by air c' of the same size with double perfect electric conductor (PEC) bars inside. Structures b1 and b2 are the corresponding structures embedded in an isotropic background in matching the principal indices product.
Fig. 4
Fig. 4 Reconfigurable effective medium with microstructure in getting a constant index product. It is a pixel. The effective parameters are shown in a). Solid lines are for the homogenized model shown in b) while the discrete symbols are for the model with structures shown in c). θ c represents the rotation of optical axis of homogeneous medium in the disc as well as the rotation of the bars. Detailed dimensions are discussed in the text.
Fig. 5
Fig. 5 Effective medium of constant indices product of a bilayer superlattice structure constructed from basic pixels in Fig. 4. Solid lines are results for the homogenized cylinder model shown in b). Discrete symbols are the results for the model with double bars shown in c).
Fig. 6
Fig. 6 Effective medium of constant indices product of a checkerboard superlattice structure constructed from basic pixels in Fig. 4. Solid lines are results for the homogenized model shown in b). Discrete symbols are the results for the model with double bars shown in c).

Equations (22)

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(ε(r)E(r))=0,
E( r )= E V( r ) D( r )= D +×U( r ) D( r )=ε( r )E( r )
D = εE = ε eff E .
E a D b = E a D b ,
E a ε eff E b = E a ε E b = E b ε eff E a .
E a × E b = E a × E b z ^ D a × D b = z ^ D a × D b .
z ^ E a × E b detε = z ^ D a × D b = z ^ D a × D b = z ^ E a × E b det ε eff = z ^ E a × E b det ε eff .
det ε eff =detε if detε=constant.
ε A =( ε α A 0 0 ε β A ).
ε α eff ε B ε α eff + ε B =f ε α A ε B ε α A + ε B .
ε β eff ε B ε β eff + ε B =f ε β A ε B ε β A + ε B .
ε α eff ε β eff = ( ε B ) 2 if ε α A ε β A = ( ε B ) 2 .
γ eff 1 γ eff +1 f γ A 1 γ A +1 .
ε I =( ε xx I ε xy I ε xy I ε yy I )=R( θ I )( ε α I 0 0 ε β I )R ( θ I ) T .
R( θ I )=( cos θ I sin θ I sin θ I cos θ I ).
( D x I D y I )= ε I .( E x I E y I )=( ε xx I ε xy I ε xy I ε yy I )( E x I E y I ).
E x A = E x B = E x , D y A = D y B = D y .
( D x E y )= f A ( D x A E y A )+ f B ( D x B E y B )
( D x D y )= ε eff .( E x E y )=( ε xx eff ε xy eff ε xy eff ε yy eff )( E x E y )
ε xx eff = f A ε xx A + f B ε xx B f A f B ( ε xy A ε xy B ) 2 f B ε yy A + f A ε yy B , ε xy eff ε yy eff = f A ε xy A ε yy A + f B ε xy B ε yy B , 1 ε yy eff = f A ε yy A + f B ε yy B
det ε eff =det ε A =det ε B if ε α A ε β A = ε α B ε β B
γ+ 1 γ = Tr( ε ) detε

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