Abstract

Simulation results of near infrared (100- to 200-THz) fishnet-structure negative-index metamaterials (NIMs) with single and multiple functional layers exhibit bi-anisotropy - inhomogeneous asymmetry - due to the presence of a sidewall-angle. The influence of sidewall-angle resulting from realistic fabrication processes is investigated through the retrieved effective parameters by both a three-dimensional finite-difference time-domain (FDTD) method and a rigorous coupled wave analysis (RCWA).

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2008

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

J. Zhou, T. Koschny and C. M. Soukoulis, "An efficient way to reduce losses of left-handed metamaterials," Opt. Express 16, 11147-11152 (2008).
[CrossRef] [PubMed]

2007

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

G. Doling, M. Wegener and S. Linden, "Realization of three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef]

Z. Ku and S. R. J. Brueck, "Comparison of negative refractive index materials with circular, elliptical and rectangular holes," Opt. Express 15, 4515-4522 (2007).
[CrossRef] [PubMed]

2006

2005

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]

S. R. J. Brueck, "Optical and Interferometric Lithography - Nanotechnology Enablers," Proc. IEEE 93, 1704-1721 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005),
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

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

2002

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]

B. K. Minhas, W. Fan, K. Agi, S. R. J. Brueck and K. J. Malloy, "Metallic inductive and capacitive grids: theory and experiment," J. Opt. Soc. Am. A 19, 1352-1359 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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

1983

1981

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Agi, K.

Alexander, R.W.

Au Kong, J.

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bratkovsky, A. M.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Brueck, S. R. J.

Cai, W.

Chen, X.

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

Chettiar, U. K.

Doling, G.

Drachev, V. P.

Fan, W.

Fang, N.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Gaylord, T. K.

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Grzegorczyk, T. M.

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

Kildishev, A. V.

Kim, E.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Koschny, T.

Koschny, Th.

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

Ku, Z.

Linden, S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

G. Doling, M. Wegener and S. Linden, "Realization of three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef]

Liu, Y.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Long, L. L.

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]

Minhas, B. K.

Moharam, M. G.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Ordal, M. A.

Osgood, R. M.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy,R. M. Osgood and S. R. J. Brueck, "Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks," Opt. Express 14, 6778-6787 (2006).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Panoiu, N.-C.

Pendry, J. B.

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

Plet, C.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

Ponizovskaya, E.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Rill, M. S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

Sarychev, A. K.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002).
[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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[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 (2002).
[CrossRef]

Shen, Y. R.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[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 71, 036617 (2005).
[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]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

J. Zhou, T. Koschny and C. M. Soukoulis, "An efficient way to reduce losses of left-handed metamaterials," Opt. Express 16, 11147-11152 (2008).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, Th. Koschny and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials,"Phys. Rev. E 71, 036617 (2005).
[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]

Staude, I.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

Sun, C.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Thiel, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

Tong, W.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

von Freymann, G.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

Wang, S. Y.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Ward, C. A.

Wegener, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
[CrossRef] [PubMed]

G. Doling, M. Wegener and S. Linden, "Realization of three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef]

Williams, R. S.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Wu, B-I.

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

Wu, W.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Yu, Z.

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
[CrossRef]

Yuan, H.-K.

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy,R. M. Osgood and S. R. J. Brueck, "Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks," Opt. Express 14, 6778-6787 (2006).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
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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).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
[CrossRef] [PubMed]

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
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Zhou, J.

Appl. Opt.

Appl. Phys. A

W. Wu, E. Kim, E. Ponizovskaya, Y. Liu, Z. Yu, N. Fang, Y. R. Shen, A. M. Bratkovsky, W. Tong, C. Sun, X. Zhang, S. Y. Wang and R. S. Williams, "Optical metamaterials at near and mid-IR range fabricated by nanoimprint lithography,"Appl. Phys. A,  87, 143-150 (2007).
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Nat. Mater.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden and M. Wegener, "Photonic metamaterials by direct laser writing and silver chemical vapour deposition," Nat. Mater. 7, 543-546 (2008).
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Nature

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal and X. Zhang, "Three-Dimensional Optical Metamaterial with a Negative Refractive Index," Nature 455, 376-379 (2008).
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Opt. Express

Opt. Lett.

Phys. Rev. B

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).
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Phys. Rev. E

X. Chen, B-I. Wu, J. Au Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005).

D. R. Smith, D. C. Vier, Th. Koschny and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials,"Phys. Rev. E 71, 036617 (2005).
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J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
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Figures (7)

Fig. 1.
Fig. 1.

(a). Schematic tilted view of the unit cell for 3 functional layered fishnet NIMs with SWA with geometrical parameters, the direction of polarization and propagation. Side view is shown in (b) with SWA.

Fig. 2.
Fig. 2.

S ij2 , where i, j = port 1, port 2 for one up to five functional layered fishnet NIMs with SWAs (0°, 4°, 10°, 16°, 20°) as a parameter using the CST simulator. (a) The transmission is independent of propagation direction (∣S 212 = ∣S 122). (b), (c) The reflectances (∣S 112, ∣S 222) depend on the direction of incident wave as a result of the sidewall-angle. (d) Reflectivity difference ∣S 222 − ∣S 112.

Fig. 3.
Fig. 3.

Real parts of the effective parameters (n, μ) for one- up to five-functional layered fishnet NIMs with SWAs (0°, 4°, 10°, 16°, 20°) using the modified retrieval equation. (a), (b) show Re[neff ] and Re[μeff ]. (c), (d) Minimum values and the wavelength at minimum values of real parts of effective refractive index and permeability. The five rows represent 1 FL up to 5 FLs, respectively.

Fig. 4.
Fig. 4.

Schematic depicting the electric and magnetic dipoles in an ideal fishnet structure (SWA = 0°) and a realistic fishnet structure with a fabrication-induced sidewall-angle (SWA ≠ 0°). (a) Electric/magnetic dipole induced by electric/magnetic field, respectively. (b) Electric dipole response, indicated by the two rightmost arrows, also induces a magnetic dipole (mE ) due to the unbalanced current distribution in the two plates. The magnetic dipole response, asymmetric current loop, also induces an electric dipole (PH ) in the metamaterial plane given by the vector sum of the two induced polarizations. The same coordinate system as Fig. 1 is followed.

Fig. 5.
Fig. 5.

Real and imaginary parts of the bi-anisotropic parameter (ξ) for one- up to five-functional layered fishnet NIMs with SWAs (0°, 4°, 10°, 16°, 20°).

Fig. 6.
Fig. 6.

y-component of current density at specific frequency (minimum value of real part of effective permeability) for 2, 3FLs with sidewall-angle 0°, 20° (a), (b) 2 FLs with sidewall-angle 0°, 20°. (c), (d) 3 FLs with sidewall-angle 0°, 20°.

Fig. 7.
Fig. 7.

The figure of merit (FOM = - Re(n)/Im(n)) of 1 to 5 functional layered NIMs as a function of the sidewall-angle.

Tables (1)

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Table 1. NIM geometrical parameters (all dimensions in nm)

Equations (3)

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

D ¯ = ε ˭ · E ¯ + ξ ˭ · H ¯ , B ¯ = μ ˭ · H ¯ + ζ ˭ · E ¯ ,
ε ˭ = ε 0 ( ε x 0 0 0 ε y 0 0 0 ε z ) , μ ˭ = μ 0 ( μ x 0 0 0 μ y 0 0 0 μ z ) , ξ ˭ = 1 c ( i 0 0 0 ξ 0 0 0 0 0 ) , ζ ˭ = 1 c ( 0 0 0 0 0 0 0 0 )
( D y B x ) = ( ε 0 ε y c c μ 0 μ x ) ( E y H x )

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