Abstract

We study the nonlinear optical response of a fishnet structure-metamaterial all-optical switching device that exhibits two near-infrared negative-index resonances. We study and compare the nonlinear optical response at both resonances and identify transient spectral features associated with the negative index resonance. We see a significantly stronger response at the longer wavelength resonance, but identical temporal dynamics at both resonances, providing insight into separately engineering the switching time and switching ratio of such a fishnet structure metamaterial all-optical switch. We also numerically reproduce the nonlinear behavior of our device using the Drude conductivity model and a finite integration technique over wide spectral and pump fluence ranges. Thereby, we show that beyond the linear properties of the device, the magnitude of the pump-probe response is completely described by only two material parameters. These results provide insight into engineering various aspects of the nonlinear response of fishnet structure metamaterials.

©2011 Optical Society of America

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  4. 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]
  5. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
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  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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  8. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  26. A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
    [Crossref] [PubMed]
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2011 (1)

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

2010 (1)

S. H. Lee, C. M. Park, Y. M. Seo, and C. K. Kim, “Reversed Doppler effect in double negative metamaterials,” Phys. Rev. B 81(24), 241102 (2010).
[Crossref]

2009 (9)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall angle induced bianisotropy in multiple layer negative index metamaterials,” Appl. Phys. Lett. 94(15), 153107 (2009).
[Crossref]

Z. Ku, J. Zhang, and S. R. J. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express 17(8), 6782–6789 (2009).
[Crossref] [PubMed]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. J. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B 26(12), B34–B38 (2009).
[Crossref]

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

2008 (1)

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008).
[Crossref] [PubMed]

2007 (3)

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

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

Z. Ku and S. R. J. Brueck, “Comparison of negative refractive index materials with circular, elliptical and rectangular holes,” Opt. Express 15(8), 4515–4522 (2007).
[Crossref] [PubMed]

2006 (2)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

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 (2)

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(13), 137404 (2005).
[Crossref] [PubMed]

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(13), 4922–4930 (2005).
[Crossref] [PubMed]

2003 (1)

T. Y. Choi, D. J. Hwang, and C. P. Grigoropoulos, “Ultrafast laser-induced crystallization of amorphous silicon films,” Opt. Eng. 42(11), 3383–3388 (2003).
[Crossref]

2000 (2)

K. Sokolowski-Tinten and D. Von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61(4), 2643–2650 (2000).
[Crossref]

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

1998 (1)

I. A. Shkrob and R. A. Crowell, “Ultrafast charge recombination in undoped amorphous hydrogenated silicon,” Phys. Rev. B 57(19), 12207–12218 (1998).
[Crossref]

1992 (2)

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

1990 (1)

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

1989 (1)

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Averitt, R. D.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Basov, D. N.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Bratkovsky, A. M.

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Brueck, S. R.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Brueck, S. R. J.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall angle induced bianisotropy in multiple layer negative index metamaterials,” Appl. Phys. Lett. 94(15), 153107 (2009).
[Crossref]

Z. Ku, J. Zhang, and S. R. J. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express 17(8), 6782–6789 (2009).
[Crossref] [PubMed]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. J. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B 26(12), B34–B38 (2009).
[Crossref]

Z. Ku and S. R. J. Brueck, “Comparison of negative refractive index materials with circular, elliptical and rectangular holes,” Opt. Express 15(8), 4515–4522 (2007).
[Crossref] [PubMed]

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(13), 4922–4930 (2005).
[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(13), 137404 (2005).
[Crossref] [PubMed]

Chae, B. G.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Chaturvedi, P.

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Cho, D. J.

Choi, T. Y.

T. Y. Choi, D. J. Hwang, and C. P. Grigoropoulos, “Ultrafast laser-induced crystallization of amorphous silicon films,” Opt. Eng. 42(11), 3383–3388 (2003).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Crowell, R. A.

I. A. Shkrob and R. A. Crowell, “Ultrafast charge recombination in undoped amorphous hydrogenated silicon,” Phys. Rev. B 57(19), 12207–12218 (1998).
[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]

Dani, K. M.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. J. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B 26(12), B34–B38 (2009).
[Crossref]

Davidson, B. N.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Di Ventra, M.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Driscoll, T.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Esser, A.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Fan, K.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Fan, W.

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(13), 137404 (2005).
[Crossref] [PubMed]

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(13), 4922–4930 (2005).
[Crossref] [PubMed]

Fauchet, P. M.

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008).
[Crossref] [PubMed]

Gorkunov, M.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Grigoropoulos, C. P.

T. Y. Choi, D. J. Hwang, and C. P. Grigoropoulos, “Ultrafast laser-induced crystallization of amorphous silicon films,” Opt. Eng. 42(11), 3383–3388 (2003).
[Crossref]

Hulin, D.

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

Hwang, D. J.

T. Y. Choi, D. J. Hwang, and C. P. Grigoropoulos, “Ultrafast laser-induced crystallization of amorphous silicon films,” Opt. Eng. 42(11), 3383–3388 (2003).
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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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Jokerst, N. M.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[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]

Kim, B. J.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Kim, C. K.

S. H. Lee, C. M. Park, Y. M. Seo, and C. K. Kim, “Reversed Doppler effect in double negative metamaterials,” Phys. Rev. B 81(24), 241102 (2010).
[Crossref]

Kim, E.

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Kim, H. T.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
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Kivshar, Y.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Ku, Z.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall angle induced bianisotropy in multiple layer negative index metamaterials,” Appl. Phys. Lett. 94(15), 153107 (2009).
[Crossref]

Z. Ku, J. Zhang, and S. R. J. Brueck, “Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls,” Opt. Express 17(8), 6782–6789 (2009).
[Crossref] [PubMed]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. J. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B 26(12), B34–B38 (2009).
[Crossref]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
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Z. Ku and S. R. J. Brueck, “Comparison of negative refractive index materials with circular, elliptical and rectangular holes,” Opt. Express 15(8), 4515–4522 (2007).
[Crossref] [PubMed]

Kurz, H.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Lapine, M.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Lee, S. C.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

Lee, S. H.

S. H. Lee, C. M. Park, Y. M. Seo, and C. K. Kim, “Reversed Doppler effect in double negative metamaterials,” Phys. Rev. B 81(24), 241102 (2010).
[Crossref]

Lee, Y. W.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Lucovsky, G.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Malloy, K. J.

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(13), 137404 (2005).
[Crossref] [PubMed]

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(13), 4922–4930 (2005).
[Crossref] [PubMed]

Marqués, R.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008).
[Crossref] [PubMed]

Mary, A.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008).
[Crossref] [PubMed]

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]

Mourchid, A.

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

Nemanich, R. J.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Nighan, W. L.

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

Osgood, R. M.

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(13), 137404 (2005).
[Crossref] [PubMed]

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(13), 4922–4930 (2005).
[Crossref] [PubMed]

Padilla, W. J.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Palit, S.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

Panoiu, N. C.

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(13), 137404 (2005).
[Crossref] [PubMed]

Panoiu, N.-C.

Park, C. M.

S. H. Lee, C. M. Park, Y. M. Seo, and C. K. Kim, “Reversed Doppler effect in double negative metamaterials,” Phys. Rev. B 81(24), 241102 (2010).
[Crossref]

Parsons, G. N.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

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]

Ponizovskaya, E.

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Powell, D.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Prasankumar, R. P.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008).
[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]

Seibert, K.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Seo, Y. M.

S. H. Lee, C. M. Park, Y. M. Seo, and C. K. Kim, “Reversed Doppler effect in double negative metamaterials,” Phys. Rev. B 81(24), 241102 (2010).
[Crossref]

Shadrivov, I.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

Shalaev, V. M.

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

Shen, Y. R.

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Shkrob, I. A.

I. A. Shkrob and R. A. Crowell, “Ultrafast charge recombination in undoped amorphous hydrogenated silicon,” Phys. Rev. B 57(19), 12207–12218 (1998).
[Crossref]

Smith, D. R.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science 325(5947), 1518–1521 (2009).
[Crossref] [PubMed]

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]

Sokolowski-Tinten, K.

K. Sokolowski-Tinten and D. Von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61(4), 2643–2650 (2000).
[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]

Strikwerda, A. C.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Tanguy, C.

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

Tao, H.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Taylor, A. J.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Upadhya, P. C.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Z. Ku, K. M. Dani, P. C. Upadhya, and S. R. J. Brueck, “Bianisotropic negative-index metamaterial embedded in a symmetric medium,” J. Opt. Soc. Am. B 26(12), B34–B38 (2009).
[Crossref]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Vanderhaghen, R.

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Von der Linde, D.

K. Sokolowski-Tinten and D. Von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61(4), 2643–2650 (2000).
[Crossref]

Wang, C.

A. Esser, K. Seibert, H. Kurz, G. N. Parsons, C. Wang, B. N. Davidson, G. Lucovsky, and R. J. Nemanich, “Ultrafast recombination and trapping in amorphous silicon,” Phys. Rev. B Condens. Matter 41(5), 2879–2884 (1990).
[Crossref] [PubMed]

Wang, F.

Wang, S.

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Wang, S. Y.

Williams, R. S.

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Wu, W.

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Xia, D.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

Yu, Z.

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhang, J.

Zhang, S.

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(13), 4922–4930 (2005).
[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(13), 137404 (2005).
[Crossref] [PubMed]

Zhang, X.

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S. Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Adv. Mater. (Deerfield Beach Fla.) (1)

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, “Nanostructures and functional materials fabricated by interferometric lithography,” Adv. Mater. (Deerfield Beach Fla.) 23(2), 147–179 (2011).
[Crossref]

Appl. Phys. Lett. (3)

Z. Ku and S. R. J. Brueck, “Experimental demonstration of sidewall angle induced bianisotropy in multiple layer negative index metamaterials,” Appl. Phys. Lett. 94(15), 153107 (2009).
[Crossref]

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marqués, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Wang, and R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91(17), 173105 (2007).
[Crossref]

J. Non-Cryst. Solids (3)

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

A. Mourchid, R. Vanderhaghen, D. Hulin, C. Tanguy, and P. M. Fauchet, “Femtosecond optical spectroscopy in a-Si:H and its alloys,” J. Non-Cryst. Solids 114, 582–584 (1989).
[Crossref]

P. M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, and W. L. Nighan., “The properties of free carriers in amorphous silicon,” J. Non-Cryst. Solids 141, 76–87 (1992).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Schematic view of fishnet structure-metamterial device. Geometrical parameters of elliptical negative-index metamaterial: p = 345 nm; ax = 119 nm; ay = 81 nm; and θ (sidewall-angle) = 18°. The device consists of 28 nm thick Ag; 68 nm thick α-Si; and 28 nm thick Ag. The direction of polarization for the incoming light is parallel to the narrower stripe width between apertures. Inset: Top view scanning electron microscope (SEM) image.

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Fig. 2
Fig. 2 (a) Measured normal incidence transmission spectra (FTIR) for both polarizations (E || and E ⊥). The simulated transmission curves are obtained using a finite integration technique, where the metamaterial parameters are adjusted to give the best fit to the measured transmission. (b) Real parts of the effective refractive index and permeability using the best-fit parameters obtained from (a).

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Fig. 3
Fig. 3 Ultrafast pump-probe setup. The frequency doubled signal pulse from a near-IR OPA provides the 590 nm visible pump pulse. The idler pulse from a visible OPA (930-2300 nm) is tuned to study the response around each resonance.

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Fig. 4
Fig. 4 Time-resolved pump-probe response versus probe wavelength. (a) Response near the (1,1) resonance (b) Response near the (1,0) resonance. At both resonances and for all probe wavelengths, the time-resolved traces show a triple exponential decay with a fast ~600 fs component, a few ps component and a slow component that lasts for nanoseconds. At both resonances, at zero pump-probe delay we see ΔT/T > 0 (ΔT/T < 0) for probe wavelengths just longer (shorter) that the negative index resonance.

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Fig. 5
Fig. 5 Dual-band negative index resonance in a single metamaterial device. (a) We see the characteristic pump-probe response of a negative index resonance in a metamaterial device, thereby allowing us to clearly identify two negative index resonances in our device. The simulated transmission through the device on photoexcitation around the (b) (1,1) resonance and (c) (1,0) resonance demonstrate that ΔT/T > 0 (ΔT/T < 0) for wavelengths just longer (shorter) than the negative index resonance.

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Fig. 6
Fig. 6 SR versus pump fluence. We see a nonlinear scaling of the SR versus pump fluence at both the resonances. This is indicative of the nonlinear dependence of the effective parameters of the metamaterial on its constituent elements. Inset: The normalized plots show that the scaling is identical for both the resonances, thereby demonstrating experimentally the common physical origin of the nonlinear response at both the resonances, i.e. the change in metamaterial properties is due to the photoexcitation of carriers in the α-Si.

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Equations (1)

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n p h o t o e x c i t e d   α − S i = [ n α − S i 2 − ω p 2 ω ( ω + i γ ) ] 1 2

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