Abstract

Dielectric and ohmic losses in metamaterials are known to limit their practical use. In this paper, an all-electronic approach for loss compensation in metamaterials is presented. Each unit cell of the meta-material is embedded with a cross-coupled transistor pair based negative differential resistance circuit to cancel these losses. Design, simulation and experimental results for Split Ring Resonator (SRR) metamaterials with and without loss compensation are presented. Results indicate that the quality factor (Q) of the SRR improves by over 400% at 1.6GHz, showing the effectiveness of the approach. The proposed technique is scalable over a broad frequency range and is limited only by the maximum operating frequency of transistors, which is reaching terahertz in today’s semiconductor technologies.

© 2012 OSA

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References

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  1. V. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  2. J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
    [CrossRef]
  3. J. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  4. Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
    [CrossRef]
  5. S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
    [CrossRef]
  6. C. Soukoulis and M. Wegener, “Optical metamaterials−more bulky and less lossy,” Science 330, 1633–1634 (2010).
    [CrossRef] [PubMed]
  7. B. Popa and S. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technol. Lett. 49, 2574–2577 (2007).
    [CrossRef]
  8. Y. Yuan, B. Popa, and S. Cummer, “Zero loss magnetic metamaterials using powered active unit cells,” Opt. Express 17, 16135–16143 (2009).
    [CrossRef] [PubMed]
  9. L. Jelinek and J. Machac, “An FET-based unit cell for an active magnetic metamaterial,” IEEE Antennas Wireless Propag. Lett. 10927–930 (2011).
    [CrossRef]
  10. F. Auzanneau and R. Ziolkowski, “Artificial composite materials consisting of nonlinearly loaded electrically small antennas: operational-amplifier-based circuits with applications to smart skins,” IEEE Trans. Antennas Propag. 47, 1330–1339 (1999).
    [CrossRef]
  11. S. Tretyakov, “Meta-materials with wideband negative permittivity and permeability,” Microwave and Opt. Technology Lett. 31, 163–165 (2001).
    [CrossRef]
  12. S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
    [CrossRef]
  13. A. Boardman, Y. Rapoport, N. King, and V. Malnev, “Creating stable gain in active metamaterials,” J. Opt. Soc. Am. B 24, A53–A61 (2007).
    [CrossRef]
  14. J. Craninckx and M. Steyaert, “A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,” IEEE J. Solid-State Circuits 32, 736–744 (1997).
    [CrossRef]
  15. B. Razavi, RF Microelectronics (Prentice Hall, 2011).
  16. J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.
  17. D. Shrekenhamer, S. Rout, A. Strikwerda, C. Bingham, R. Averitt, S. Sonkusale, and W. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19, 9968–9975 (2011).
    [CrossRef] [PubMed]
  18. D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
    [CrossRef]
  19. R. Shelby, D. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  20. B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators,” Opt. Express 16, 16058–16063 (2008).
    [CrossRef] [PubMed]
  21. A. Sedra and K. Smith, Microelectronic Circuits, vol. 1 (Oxford University Press, USA, 1998).
  22. D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
    [CrossRef]
  23. X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
    [CrossRef]
  24. W. Xu, W. J. Padilla, and S. Sonkusale, unpublished data.

2011 (3)

L. Jelinek and J. Machac, “An FET-based unit cell for an active magnetic metamaterial,” IEEE Antennas Wireless Propag. Lett. 10927–930 (2011).
[CrossRef]

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

D. Shrekenhamer, S. Rout, A. Strikwerda, C. Bingham, R. Averitt, S. Sonkusale, and W. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19, 9968–9975 (2011).
[CrossRef] [PubMed]

2010 (2)

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

C. Soukoulis and M. Wegener, “Optical metamaterials−more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (2)

A. Boardman, Y. Rapoport, N. King, and V. Malnev, “Creating stable gain in active metamaterials,” J. Opt. Soc. Am. B 24, A53–A61 (2007).
[CrossRef]

B. Popa and S. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technol. Lett. 49, 2574–2577 (2007).
[CrossRef]

2006 (1)

D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

2005 (1)

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

2004 (1)

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

2003 (1)

S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

2001 (2)

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

S. Tretyakov, “Meta-materials with wideband negative permittivity and permeability,” Microwave and Opt. Technology Lett. 31, 163–165 (2001).
[CrossRef]

2000 (1)

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

1999 (2)

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

F. Auzanneau and R. Ziolkowski, “Artificial composite materials consisting of nonlinearly loaded electrically small antennas: operational-amplifier-based circuits with applications to smart skins,” IEEE Trans. Antennas Propag. 47, 1330–1339 (1999).
[CrossRef]

1997 (1)

J. Craninckx and M. Steyaert, “A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,” IEEE J. Solid-State Circuits 32, 736–744 (1997).
[CrossRef]

1968 (1)

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

Albrecht, J.

J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.

Auzanneau, F.

F. Auzanneau and R. Ziolkowski, “Artificial composite materials consisting of nonlinearly loaded electrically small antennas: operational-amplifier-based circuits with applications to smart skins,” IEEE Trans. Antennas Propag. 47, 1330–1339 (1999).
[CrossRef]

Averitt, R.

Bingham, C.

Boardman, A.

Bonic, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Cao, J.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Chang, T.

J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.

Chen, X.

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Craninckx, J.

J. Craninckx and M. Steyaert, “A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,” IEEE J. Solid-State Circuits 32, 736–744 (1997).
[CrossRef]

Cummer, S.

Y. Yuan, B. Popa, and S. Cummer, “Zero loss magnetic metamaterials using powered active unit cells,” Opt. Express 17, 16135–16143 (2009).
[CrossRef] [PubMed]

B. Popa and S. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technol. Lett. 49, 2574–2577 (2007).
[CrossRef]

Dong, Z.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Grzegorczyk, T.

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Holden, A.

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Hrabar, S.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Jelinek, L.

L. Jelinek and J. Machac, “An FET-based unit cell for an active magnetic metamaterial,” IEEE Antennas Wireless Propag. Lett. 10927–930 (2011).
[CrossRef]

King, N.

Kiricenko, A.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Kong, J.

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Koschny, T.

B. Wang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Nonlinear properties of split-ring resonators,” Opt. Express 16, 16058–16063 (2008).
[CrossRef] [PubMed]

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Krois, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

Li, T.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Liu, H.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Machac, J.

L. Jelinek and J. Machac, “An FET-based unit cell for an active magnetic metamaterial,” IEEE Antennas Wireless Propag. Lett. 10927–930 (2011).
[CrossRef]

Malnev, V.

Mock, J.

D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Pacheco, J.

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Padilla, W.

Padilla, W. J.

W. Xu, W. J. Padilla, and S. Sonkusale, unpublished data.

Pendry, J.

S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

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

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Popa, B.

Y. Yuan, B. Popa, and S. Cummer, “Zero loss magnetic metamaterials using powered active unit cells,” Opt. Express 17, 16135–16143 (2009).
[CrossRef] [PubMed]

B. Popa and S. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technol. Lett. 49, 2574–2577 (2007).
[CrossRef]

Ramakrishna, S.

S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

Rapoport, Y.

Razavi, B.

B. Razavi, RF Microelectronics (Prentice Hall, 2011).

Robbins, D.

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Rosker, M.

J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.

Rout, S.

Schultz, S.

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

Schurig, D.

D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Sedra, A.

A. Sedra and K. Smith, Microelectronic Circuits, vol. 1 (Oxford University Press, USA, 1998).

Shelby, R.

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

Shrekenhamer, D.

Smith, D.

D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

Smith, K.

A. Sedra and K. Smith, Microelectronic Circuits, vol. 1 (Oxford University Press, USA, 1998).

Sonkusale, S.

Soukoulis, C.

C. Soukoulis and M. Wegener, “Optical metamaterials−more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Soukoulis, C. M.

Stewart, W.

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

Steyaert, M.

J. Craninckx and M. Steyaert, “A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,” IEEE J. Solid-State Circuits 32, 736–744 (1997).
[CrossRef]

Strikwerda, A.

Tretyakov, S.

S. Tretyakov, “Meta-materials with wideband negative permittivity and permeability,” Microwave and Opt. Technology Lett. 31, 163–165 (2001).
[CrossRef]

Veselago, V.

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

Vier, D.

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Wallace, H.

J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.

Wang, B.

Wang, S.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Wegener, M.

C. Soukoulis and M. Wegener, “Optical metamaterials−more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

Wu, B.

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Xu, W.

W. Xu, W. J. Padilla, and S. Sonkusale, unpublished data.

Yuan, Y.

Zhang, X.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Zhou, J.

Zhu, S.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Zhu, Z.

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

Ziolkowski, R.

F. Auzanneau and R. Ziolkowski, “Artificial composite materials consisting of nonlinearly loaded electrically small antennas: operational-amplifier-based circuits with applications to smart skins,” IEEE Trans. Antennas Propag. 47, 1330–1339 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

Z. Dong, H. Liu, T. Li, Z. Zhu, S. Wang, J. Cao, S. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96, 044104 (2010).
[CrossRef]

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett. 99, 254103 (2011).
[CrossRef]

D. Schurig, J. Mock, and D. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

L. Jelinek and J. Machac, “An FET-based unit cell for an active magnetic metamaterial,” IEEE Antennas Wireless Propag. Lett. 10927–930 (2011).
[CrossRef]

IEEE J. Solid-State Circuits (1)

J. Craninckx and M. Steyaert, “A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,” IEEE J. Solid-State Circuits 32, 736–744 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

F. Auzanneau and R. Ziolkowski, “Artificial composite materials consisting of nonlinearly loaded electrically small antennas: operational-amplifier-based circuits with applications to smart skins,” IEEE Trans. Antennas Propag. 47, 1330–1339 (1999).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
[CrossRef]

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

Microwave and Opt. Technology Lett. (1)

S. Tretyakov, “Meta-materials with wideband negative permittivity and permeability,” Microwave and Opt. Technology Lett. 31, 163–165 (2001).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

B. Popa and S. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technol. Lett. 49, 2574–2577 (2007).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (1)

S. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

Phys. Rev. E (2)

D. Smith, D. Vier, T. Koschny, and C. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

X. Chen, T. Grzegorczyk, B. Wu, J. Pacheco, and J. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (2)

C. Soukoulis and M. Wegener, “Optical metamaterials−more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

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

Sov. Phys. Usp. (1)

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

Other (4)

B. Razavi, RF Microelectronics (Prentice Hall, 2011).

J. Albrecht, M. Rosker, H. Wallace, and T. Chang, “THz electronics projects at DARPA: Transistors, TMICs, and amplifiers,” in “Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International,” (IEEE, 2010), pp. 1118–1121.

W. Xu, W. J. Padilla, and S. Sonkusale, unpublished data.

A. Sedra and K. Smith, Microelectronic Circuits, vol. 1 (Oxford University Press, USA, 1998).

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Figures (3)

Fig. 1
Fig. 1

(a) simplified equivalent circuit model: The SRR is modeled by an RLC parallel circuit, in which the R stands for the loss of the resonator. Negative Differential Resistance (NDR) circuit provides loss compensation that is bias tunable. (b) Implementation of active NDR circuit and its connection to SRR. Dimensions of SRR are in mm. w = 2, l1 = 16, l2 = 12, g = 1.5

Fig. 2
Fig. 2

(a) Simulated |S11| in dB of SRR with and without active loss compensation circuit (b) Measurement setup to measure the reflection. Area I shows the active NDR circuit implemented on the printed circuit board. Area II shows the SRR. Area III shows the loop antenna. The circuit in area I could be integrated into single chip in future, with dimensions much smaller than the size of each unit cell.

Fig. 3
Fig. 3

(a) Measured |S11| in dB of loop antenna by itself and SRR with and without embedded active NDR circuit. When the bias voltage Vbias is set to 0.350V, the current flowing in the active circuit is 3.6mA. The DC power supply voltage is 3.1V. (b) Retrieved complex permeability μ = μ′ + i · μ″ of SRR excited by plane wave and their Lorentz oscillation model. Osc. model 1 is the Lorentz oscillator model used to fit the μ curve of SRR without NDR circuit. Osc. model 2 is the Lorentz oscillator model used to fit the μ curve of SRR embedded with the NDR circuit.

Equations (1)

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μ = [ ( 1 + S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2 ] 1 / 2 × 1 k d arccos [ 1 2 S 21 ( 1 S 11 2 + S 21 2 ) ]

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