Abstract

We propose a technique capable of designing fishnet metamaterials that have a negative refractive index (NRI) over a broad range in the visible and infrared. The technique relies on optimizing the shape and scale of the fishnet apertures as well as the depth of different layers of the composite. A metamaterial is obtained that exhibits an unbroken 552 nm bandwidth of NRI, covering the entire red and infrared regions. Moreover, two fishnet structures perforated with star-like holes are found to render refractive index negative in the yellow and green spectra.

© 2014 Optical Society of America

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2013

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

S. W. Zhou, X. Huang, Q. Li, and Y. M. Xie, Opt. Express 21, A285 (2013).
[CrossRef]

2012

2011

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

2010

S. W. Zhou, W. Li, and Q. Li, J. Comput. Phys. 229, 6915 (2010).
[CrossRef]

S. W. Zhou, W. Li, G. Y. Sun, and Q. Li, Opt. Express 18, 6693 (2010).
[CrossRef]

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[CrossRef]

2009

2008

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

2007

2006

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

2003

J. Gielis, Am. J. Bot. 90, 333 (2003).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

1997

R. Storn and K. Price, J. Global Optim. 11, 341 (1997).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1968

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Adam, P. M.

Alaeian, H.

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

Atre, A. C.

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Borneman, J.

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Cai, W.

Chen, Y. H.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[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, Science 314, 977 (2006).
[CrossRef]

Dickson, W.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Dionne, J. A.

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

Dolling, G.

Drachev, V.

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Drachev, V. P.

Garcia-Etxarri, A.

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

Garcia-Meca, C.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Gielis, J.

J. Gielis, Am. J. Bot. 90, 333 (2003).
[CrossRef]

Hedge, R.

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Huang, X.

Hurtado, J.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Kildishev, A.

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Kildishev, A. V.

Li, E. P.

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[CrossRef]

Li, Q.

S. W. Zhou, X. Huang, Q. Li, and Y. M. Xie, Opt. Express 21, A285 (2013).
[CrossRef]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

S. W. Zhou, W. Li, and Q. Li, J. Comput. Phys. 229, 6915 (2010).
[CrossRef]

S. W. Zhou, W. Li, G. Y. Sun, and Q. Li, Opt. Express 18, 6693 (2010).
[CrossRef]

Li, W.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

S. W. Zhou, W. Li, and Q. Li, J. Comput. Phys. 229, 6915 (2010).
[CrossRef]

S. W. Zhou, W. Li, G. Y. Sun, and Q. Li, Opt. Express 18, 6693 (2010).
[CrossRef]

Linden, S.

Macias, D.

Marti, J.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Martinez, A.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Mary, A.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[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, Science 314, 977 (2006).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Ni, X.

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Park, G. H.

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[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, Science 314, 977 (2006).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Price, K.

R. Storn and K. Price, J. Global Optim. 11, 341 (1997).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Rodriguez-Oliveros, R.

Ruiz-Cortes, V.

Sanchez-Gil, J. A.

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Shalaev, V.

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Soukoulis, C. M.

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Storn, R.

R. Storn and K. Price, J. Global Optim. 11, 341 (1997).
[CrossRef]

Sun, G. Y.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

S. W. Zhou, W. Li, G. Y. Sun, and Q. Li, Opt. Express 18, 6693 (2010).
[CrossRef]

Szabo, Z.

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Wegener, M.

Xiao, S.

Xie, Y. M.

Yuan, H. K.

Zayats, A. V.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Zhou, S. W.

S. W. Zhou, X. Huang, Q. Li, and Y. M. Xie, Opt. Express 21, A285 (2013).
[CrossRef]

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

S. W. Zhou, W. Li, G. Y. Sun, and Q. Li, Opt. Express 18, 6693 (2010).
[CrossRef]

S. W. Zhou, W. Li, and Q. Li, J. Comput. Phys. 229, 6915 (2010).
[CrossRef]

Acta Mater.

S. W. Zhou, W. Li, Y. H. Chen, G. Y. Sun, and Q. Li, Acta Mater. 59, 2624 (2011).
[CrossRef]

Adv. Opt. Mater.

A. C. Atre, A. Garcia-Etxarri, H. Alaeian, and J. A. Dionne, Adv. Opt. Mater. 1, 327 (2013).
[CrossRef]

Am. J. Bot.

J. Gielis, Am. J. Bot. 90, 333 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Z. Szabo, G. H. Park, R. Hedge, and E. P. Li, IEEE Trans. Microwave Theory Tech. 58, 2646 (2010).
[CrossRef]

J. Comput. Phys.

S. W. Zhou, W. Li, and Q. Li, J. Comput. Phys. 229, 6915 (2010).
[CrossRef]

J. Global Optim.

R. Storn and K. Price, J. Global Optim. 11, 341 (1997).
[CrossRef]

Nature

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, Phys. Rev. Lett. 106, 067402 (2011).
[CrossRef]

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Proc. IEEE

A. Kildishev, J. Borneman, X. Ni, V. Shalaev, and V. Drachev, Proc. IEEE 99, 1691 (2011).
[CrossRef]

Science

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Scheme of a double fishnet structure (gray stands for silver, purple for ITO, blue for MgF2 and green for air). (b) Unit cell used for simulation.

Fig. 2.
Fig. 2.

(a) Variety of complex shapes described by Gielis’ superformula. The patterns in xy plane for (b) structure B, (c) structure C, and (d) structure D.

Fig. 3.
Fig. 3.

(a), (d), (g) Magnitude of the simulated S parameters for structure B, C, and D. (b), (e), (h) Retrieved permeability and permittivity and (c), (f), (i) refractive index for structure B, C, and D.

Fig. 4.
Fig. 4.

Profile of the E field at the resonance frequency for structure D on (a) the xy plane with z=0, (b) the yz plane with x=0 and colorbar for Fig. 4(d), (c) the xy plane with z=d3/2, and (d) the profile of Ez on the xy plane with z=0.

Fig. 5.
Fig. 5.

NRI of four fishnet structures.

Tables (1)

Tables Icon

Table 1. Gielis’ Parameters and Index Features of the Optimized Structures in Comparison with Previous Work

Equations (1)

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

r(θ)=(|cos(mθ/4)/a|n2+|sin(mθ/4)/b|n3)1/n1.

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