Abstract

We report the design and experimental measurement of a powered active magnetic metamaterial with tunable permeability. The unit cell is based on the combination of an embedded radiofrequency amplifier and a tunable phase shifter, which together control the response of the medium. The measurements show that a negative permeability metamaterial with zero loss or even gain can be achieved through an array of such metamaterial cells. This kind of active metamaterial can find use in applications that are performance limited due to material losses.

© 2009 Optical Society of America

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    [PubMed]
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    [PubMed]
  3. Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).
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    [PubMed]
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    [PubMed]
  6. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
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    [PubMed]
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  12. B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).
  13. P. Kinsler, "Refractive index and wave vector in passive and active media," Phys. Rev. A 79, 023839 (2009).
  14. B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).
  15. Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
    [PubMed]
  16. H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006).
    [PubMed]
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  20. T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).
  21. D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
  22. H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006).
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    [PubMed]
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  25. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
  26. C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).
  27. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
  28. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm," Opt. Lett. 32, 1671-1673 (2007).
    [PubMed]
  29. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
  30. M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).
  31. H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)
  32. B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

2009 (4)

2008 (3)

B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).

R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

2007 (8)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm," Opt. Lett. 32, 1671-1673 (2007).
[PubMed]

2006 (9)

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006).
[PubMed]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[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, 977-980 (2006).
[PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

2005 (1)

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

2004 (2)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

O. Reynet and O. Acher, "Voltage controlled metamaterial," Appl. Phys. Lett. 84, 1198-1200 (2004).

2003 (1)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

2002 (2)

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).

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

2001 (1)

S. A. Tretyakov, "Meta-materials with wideband negative permittivity and permeability," Microwave Opt. Technology Lett. 31, 163-165 (2001).

2000 (1)

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

Acher, O.

O. Reynet and O. Acher, "Voltage controlled metamaterial," Appl. Phys. Lett. 84, 1198-1200 (2004).

Bai, Y.

Beigang, R.

Boardman, A. D.

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

Burokur, S. N.

Cai, W.

Chen, H.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006).
[PubMed]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

Chen, H.-T.

H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006).
[PubMed]

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

Chettiar, U. K.

Cummer, S. A.

B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).

T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

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, 977-980 (2006).
[PubMed]

B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

de Lustrac, A.

Drachev, V. P.

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Fang, A.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).

Forchel, A.

Gorkunov, M. V.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

Gredeskul, S. A.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Hand, T.

T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).

Heinrich, J.

Hfling, S.

Huangfu, J.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

Imhof, C.

Jiang, Q.

Jiang, T.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

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, 977-980 (2006).
[PubMed]

Kant, B.

Kildishev, A. V.

King, N.

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

Kinsler, P.

P. Kinsler, "Refractive index and wave vector in passive and active media," Phys. Rev. A 79, 023839 (2009).

Kivshar, Y. S.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

Kong, J. A.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006).
[PubMed]

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

Koschny, T.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

Koschny, Th.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).

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

Lgel, B.

Luo, Y.

Malnev, V. N.

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

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).

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, 977-980 (2006).
[PubMed]

Mu, M.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

Nistad, B.

B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

Padilla, W. J.

H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006).
[PubMed]

Paul, O.

Pendry, J.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

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, 977-980 (2006).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[PubMed]

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

Popa, B. I.

B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

Powell, D. A.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

Rahm, M.

Ran, L.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006).
[PubMed]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

Rapoport, Y. G.

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

Reynet, O.

O. Reynet and O. Acher, "Voltage controlled metamaterial," Appl. Phys. Lett. 84, 1198-1200 (2004).

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Schultz, S.

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).

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[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, 977-980 (2006).
[PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

Sellier, A.

Shadrivov, I. V.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

Shalaev, V. M.

Shen, L.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

Simovski, C. R.

C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).

Skaar, J.

B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

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, 977-980 (2006).
[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).

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

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).

Solymar, L.

R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).

Soukoulis, C. M.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).

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

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

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).

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, 977-980 (2006).
[PubMed]

Syms, R. R. A.

R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Tretyakov, S. A.

C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).

S. A. Tretyakov, "Meta-materials with wideband negative permittivity and permeability," Microwave Opt. Technology Lett. 31, 163-165 (2001).

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).

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Wang, D.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

Wegener, M.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).

Wolff, S.

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

Wu, B.-I.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

Xiao, S.

Young, I. R.

R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).

Yuan, H.-K.

Yuan, Y.

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006).
[PubMed]

Zengerle, R.

Zhang, B.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

Zhang, J.

Appl. Phys. Lett. (3)

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).

O. Reynet and O. Acher, "Voltage controlled metamaterial," Appl. Phys. Lett. 84, 1198-1200 (2004).

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).

IEEE Ant. Wireless Propag. Lett. (1)

T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).

J. Appl. Phys. (1)

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)

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

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).

Metamaterials (1)

R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).

Microwave Opt. Technol. Lett. (1)

B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).

Microwave Opt. Technology Lett. (1)

S. A. Tretyakov, "Meta-materials with wideband negative permittivity and permeability," Microwave Opt. Technology Lett. 31, 163-165 (2001).

Nature (1)

H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006).
[PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (2)

P. Kinsler, "Refractive index and wave vector in passive and active media," Phys. Rev. A 79, 023839 (2009).

Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).

Phys. Rev. B (3)

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).

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).

C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).

Phys. Rev. E (7)

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

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).

B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).

Phys. Rev. Lett. (3)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007).
[PubMed]

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

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
[PubMed]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[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, 977-980 (2006).
[PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) (a) Photograph of the constructed unit cell for the powered active magnetic metamaterial with individual components labeled. (b) A schematic of a single unit cell (solid) and three unit cells (dashed) inside the waveguide in the measurements. The incident magnetic field is perpendicular to the planes containing the loops, and volume under test to which all extracted effective parameters apply is bounded by the dashed lines.

Fig. 2.
Fig. 2.

(Color online) The subset of retrieved permeabilities (measured) for the unit cell: (a) the real part, and (b) the imaginary part.

Fig. 3.
Fig. 3.

(Color online) The retrieved permeability for the two cases: (a) Vb =4.5V, and (b) Vb =12V, where Vb is the DC voltage supply on the phase shifter.

Fig. 4.
Fig. 4.

(Color online) The retrieved permeability, permittivity, and the calculated total power loss in the case of Vb =4.5V. Dashed lines denote the zero-imaginary-permeability frequencies, and solid lines denote the frequencies at which the unit cell is lossless.

Fig. 5.
Fig. 5.

(Color online) Retrieved permeability for (a) the three unit cells measured individually, and (b) an array of these three cells. Expected permeability from susceptibility adding of the individually measured unit cells is also shown in (b) for comparison.

Equations (2)

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

B = μ0 (H+M)
μr = 1 + MH = 1 + MeH ,

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