Abstract

Ultrathin metamaterial layers are modeled by a homogeneous bi-anisotropic film to represent various kinds of broken symmetries in photonic nanostructures, and specifically in optical metamaterials and metasurfaces. Two algorithms were developed to obtain the electromagnetic (EM) wave response from a metasurface (direct solver) or the metasurface parameters from the EM wave response (inverse solver) for a bi-anisotropic, subwavelength-thick nanostructured film. The algorithm is applied to two different metasurfaces to retrieve their effective homogeneous bi-anisotropic parameters. The effective layer of the same physical thickness is shown to produce the same response to plane wave excitation as the original metasurface.

© 2013 OSA

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2012 (4)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
[CrossRef] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[CrossRef] [PubMed]

Z. H. Zhu, C. C. Guo, K. Liu, W. M. Ye, X. D. Yuan, B. Yang, and T. Ma, “Metallic nanofilm half-wave plate based on magnetic plasmon resonance,” Opt. Lett. 37(4), 698–700 (2012).
[CrossRef] [PubMed]

2011 (7)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[CrossRef]

N. Engheta, “Antenna-guided light,” Science 334(6054), 317–318 (2011).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (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. IEEE 99(10), 1691–1700 (2011).
[CrossRef]

A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[CrossRef]

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[CrossRef]

2008 (3)

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(16), 11822–11829 (2008).
[CrossRef] [PubMed]

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008).
[CrossRef] [PubMed]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

2007 (2)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

2006 (1)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

2002 (1)

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Alù, A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[CrossRef] [PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[CrossRef]

A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[CrossRef]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[CrossRef]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[CrossRef] [PubMed]

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (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. IEEE 99(10), 1691–1700 (2011).
[CrossRef]

Cai, W.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Capasso, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Chan, C. T.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Chettiar, U. K.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (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. IEEE 99(10), 1691–1700 (2011).
[CrossRef]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Drezet, A.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008).
[CrossRef] [PubMed]

Ebbesen, T. W.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008).
[CrossRef] [PubMed]

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, “Antenna-guided light,” Science 334(6054), 317–318 (2011).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Genet, C.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008).
[CrossRef] [PubMed]

Genevet, P.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Guo, C. C.

Hao, J.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Jiang, T.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kats, M. A.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
[CrossRef] [PubMed]

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. IEEE 99(10), 1691–1700 (2011).
[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(16), 11822–11829 (2008).
[CrossRef] [PubMed]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Kong, J. A.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Kwon, D.-H.

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Liu, K.

Luukkonen, O.

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[CrossRef]

Ma, T.

Markoš, P.

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Maslovski, S. I.

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
[CrossRef] [PubMed]

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. IEEE 99(10), 1691–1700 (2011).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Ran, L.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Schultz, S.

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
[CrossRef] [PubMed]

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. IEEE 99(10), 1691–1700 (2011).
[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(16), 11822–11829 (2008).
[CrossRef] [PubMed]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Smith, D.

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Soukoulis, C.

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Tretyakov, S. A.

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[CrossRef]

Werner, D. H.

Xiao, S.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Yang, B.

Ye, W. M.

Yu, N.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Yuan, H. K.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Yuan, X. D.

Yuan, Y.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Zhao, Y.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[CrossRef] [PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[CrossRef]

Zhou, L.

J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

Zhu, Z. H.

IEEE Antennas Wirel. Propag. Lett. (1)

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[CrossRef]

MRS Bull. (1)

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull. 33(10), 921–926 (2008).
[CrossRef]

Nano Lett. (1)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[CrossRef] [PubMed]

Nat. Commun. (1)

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[CrossRef] [PubMed]

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

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A. Alù, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83(8), 081102 (2011).
[CrossRef]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
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D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[CrossRef]

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J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007).
[CrossRef] [PubMed]

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Proc. IEEE (1)

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. IEEE 99(10), 1691–1700 (2011).
[CrossRef]

Science (6)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

N. Engheta, “Antenna-guided light,” Science 334(6054), 317–318 (2011).
[CrossRef] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427–427 (2012).
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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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Figures (4)

Fig. 1
Fig. 1

Demonstration of co-polarized and cross-polarized reflection and transmission coefficients for an x-polarized input plane wave from the front size. The incident wave is indicated in blue, and the reflected and transmitted waves are in red. The direction of (E) and (H) fields are shown by arrows.

Fig. 2
Fig. 2

The unit cell of the two nanostructures used as examples for the homogenization algorithm. A top view is presented for each to describe the x and y directions.

Fig. 3
Fig. 3

(a) Effective slab parameters of the V-antenna structure. (b) Spectral phasor of reflection and transmission coefficients using FEM and effective Bi-anisotropic layer model. For all of them, the lower end point corresponds to 1 µm and the upper end point corresponds to 3 µm.

Fig. 4
Fig. 4

Retrieval results of the two rod structure.

Tables (1)

Tables Icon

Table 1 Complex reflection and transmission coefficients

Equations (29)

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( D B )=( ε 0 ε c 1 ξ c 1 ζ μ 0 μ )( E H )
×( H E )=ιω( ε 0 ε c 1 ξ c 1 ζ μ 0 μ )( E H )
d dz V=ιAV
V( z )= e ιAz V| z=0
T=UP U 1 ,
E 2 = T 11 E 1 + T 12 H 1 and H 2 = T 21 E 1 + T 22 H 1 ,
, S 21 x = M 1 + I x + M 1 S 11 x , z 2 1 n S 21 x = M 2 + I x + M 2 S 11 x ,
S 11 x = [ M 2 z 2 1 n M 1 ] 1 [ z 2 1 n M 1 + M 2 + ] I x
S 21 x = [ ( M 1 ) 1 z 2 1 ( M 2 ) 1 n ] 1 [ ( M 1 ) 1 M 1 + ( M 2 ) 1 M 2 + ] I x
S 11 y = [ M 2 z 2 1 n M 1 ] 1 [ z 2 1 n M 1 + M 2 + ] I y ,
S 21 y = [ ( M 1 ) 1 z 2 1 ( M 2 ) 1 n ] 1 [ ( M 1 ) 1 M 1 + ( M 2 ) 1 M 2 + ] I y
I x + S 22 x = M 1 S 12 x , z 2 1 n( S 22 x I x )= M 2 S 12 x ,
S 22 x = [ z 2 1 ( M 2 ) 1 n ( M 1 ) 1 ] 1 [ ( M 1 ) 1 + z 2 1 ( M 2 ) 1 n ] I x
S 12 x =2 [ M 1 + z 2 n M 2 ] 1 I x
S 22 y = [ z 2 1 ( M 2 ) 1 n ( M 1 ) 1 ] 1 [ ( M 1 ) 1 + z 2 1 ( M 2 ) 1 n ] I y
S 12 y =2 [ M 1 + z 2 n M 2 ] 1 I y
V 2 =T V 1
V 2 =( S 21 x S 21 y I x + S 22 x I y + S 22 y z 2 1 n S 21 x z 2 1 n S 21 y z 2 1 ( S 22 x I x ) z 2 1 ( S 22 y I y ) ), V 1 =( I x + S 11 x I y + S 11 y S 12 x S 12 y z 1 1 n( I x S 11 x ) z 1 1 n( I y S 11 y ) z 1 1 n S 12 x z 1 1 n S 12 y ).
A= 1 ιl ln( V 2 V 1 1 ).
( ε 0 ε c 1 ξ c 1 ζ μ 0 μ )= 1 ιωl N 1 ln( V 2 V 1 1 ).
V 1 =( ( 1+r )I tI ( 1r z 0 )n t z 0 n ), V 2 =( tI ( 1+r )I t z 0 n ( 1r z 0 )n )
T= V 2 V 1 1 =( ( 1( r 2 t 2 ) 2t )I ( z 0 ( ( 1+r ) 2 t 2 ) 2t )n ( ( 1r ) 2 t 2 2 z 0 t )n ( 1( r 2 t 2 ) 2t )I )
( p 2 ( 1( r 2 t 2 ) t )p+1 ) 2 =0
e ikl + e ikl = 1( r 2 t 2 ) t
cos( kl )= 1( r 2 t 2 ) 2t
U=( 1 1 0 0 0 0 1 1 0 0 z 1 z 1 z 1 z 1 0 0 ) U 1 = 1 2 ( 1 0 0 z 1 0 0 z 0 1 z 0 0 1 z 0 )
z= z 0 ( 1+r ) 2 t 2 ( 1r ) 2 t 2 .
( ε 0 ε c 1 ξ c 1 ζ μ 0 μ )= k ω N 1 Udiag( 1,1,1,1 ) U 1 = k ω ( z 1 I 0 0 zI )
ε= k ωz , μ= ωk z

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