Abstract

We present experimental data on a one-dimensional super-conducting metamaterial that is tunable over a broad frequency band. The basic building block of this magnetic thin-film medium is a single-junction (rf-) superconducting quantum interference device (SQUID). Due to the nonlinear inductance of such an element, its resonance frequency is tunable in situ by applying a dc magnetic field. We demonstrate that this results in tunable effective parameters of our metamaterial consisting of 54 rf-SQUIDs. In order to obtain the effective magnetic permeability μr,eff from the measured data, we employ a technique that uses only the complex transmission coefficient S21.

© 2013 OSA

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  1. M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
    [CrossRef]
  2. M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
    [CrossRef]
  3. J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
    [CrossRef]
  4. J. Wu, B. Jin, Y. Xue, C. Zhang, H. Dai, L. Zhang, C. Cao, L. Kang, W. Xu, J. Chen, and P. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express19, 12021–12026 (2011).
    [CrossRef] [PubMed]
  5. N. Lazarides and G. P. Tsironis, “rf superconducting quantum interference device metamaterials,” Appl. Phys. Lett.90, 163501 (2007).
    [CrossRef]
  6. C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
    [CrossRef]
  7. A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial fim containing Josephson junction,” Optics Commun.283, 1633–1639 (2010).
    [CrossRef]
  8. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  9. P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
    [CrossRef]
  10. K. K. Likharev, Dynamics of Josephson Junctions(Gordon and Breach Science, 1991).
  11. M. Tinkham, Introduction to Superconductivity (2nd Edition) (Dover Publications Inc., 2004).
  12. S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
    [CrossRef]
  14. J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).
  15. D. M. Pozar, Microwave Engineering (2nd Edition) (John Wiley & Sons Inc., 1998) pp. 208–211
  16. J.-H. Yeh and S. M. Anlage, “In situ broadband cryogenic calibration for two-port superconducting microwave resonators”, Rev. Sci. Instrum.84, 034706 (2013).
    [CrossRef] [PubMed]

2013 (3)

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

J.-H. Yeh and S. M. Anlage, “In situ broadband cryogenic calibration for two-port superconducting microwave resonators”, Rev. Sci. Instrum.84, 034706 (2013).
[CrossRef] [PubMed]

2011 (1)

2010 (2)

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial fim containing Josephson junction,” Optics Commun.283, 1633–1639 (2010).
[CrossRef]

2008 (1)

C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
[CrossRef]

2007 (2)

N. Lazarides and G. P. Tsironis, “rf superconducting quantum interference device metamaterials,” Appl. Phys. Lett.90, 163501 (2007).
[CrossRef]

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

2005 (1)

M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
[CrossRef]

2000 (1)

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

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

Anlage, S. M.

J.-H. Yeh and S. M. Anlage, “In situ broadband cryogenic calibration for two-port superconducting microwave resonators”, Rev. Sci. Instrum.84, 034706 (2013).
[CrossRef] [PubMed]

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
[CrossRef]

Baker-Jarvis, J.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Butz, S.

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

Cao, C.

Cao, W.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Chen, H.

C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
[CrossRef]

Chen, H.-T.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Chen, J.

Dai, H.

Du, C.

C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
[CrossRef]

Filippenko, L. V.

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

Gabitov, I. R.

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial fim containing Josephson junction,” Optics Commun.283, 1633–1639 (2010).
[CrossRef]

Geyer, R. G.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Grosvenor, C. A.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Gu, J.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Han, J.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

He, M.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

Holloway, C. L.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Janezic, M. D.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Jin, B.

Johnk, R. T.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Jung, P.

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

Kabos, P.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Kang, L.

Koshelets, V. P.

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

Lazarides, N.

N. Lazarides and G. P. Tsironis, “rf superconducting quantum interference device metamaterials,” Appl. Phys. Lett.90, 163501 (2007).
[CrossRef]

Li, S.

C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
[CrossRef]

Likharev, K. K.

K. K. Likharev, Dynamics of Josephson Junctions(Gordon and Breach Science, 1991).

Maimistov, A. I.

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial fim containing Josephson junction,” Optics Commun.283, 1633–1639 (2010).
[CrossRef]

Nemat-Nasser, S. C.

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

Orloff, N.

M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
[CrossRef]

Padilla, W. J.

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

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering (2nd Edition) (John Wiley & Sons Inc., 1998) pp. 208–211

Prozorov, R.

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

Ricci, M. C.

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
[CrossRef]

Riddle, B. F.

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

Schultz, S.

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

Shitov, S. V.

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

Singh, R.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Smith, D. R.

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

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

Tian, Z.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Tinkham, M.

M. Tinkham, Introduction to Superconductivity (2nd Edition) (Dover Publications Inc., 2004).

Tsironis, G. P.

N. Lazarides and G. P. Tsironis, “rf superconducting quantum interference device metamaterials,” Appl. Phys. Lett.90, 163501 (2007).
[CrossRef]

Ustinov, A. V.

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

Vier, D. C.

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

Wu, J.

Wu, P.

Xing, Q.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Xu, H.

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

Xu, W.

Xue, Y.

Yeh, J.-H.

J.-H. Yeh and S. M. Anlage, “In situ broadband cryogenic calibration for two-port superconducting microwave resonators”, Rev. Sci. Instrum.84, 034706 (2013).
[CrossRef] [PubMed]

Zhang, C.

Zhang, J. W.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Zhang, L.

Zhang, W.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

Zhuravel, A. P.

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

N. Lazarides and G. P. Tsironis, “rf superconducting quantum interference device metamaterials,” Appl. Phys. Lett.90, 163501 (2007).
[CrossRef]

P. Jung, S. Butz, S. V. Shitov, and A. V. Ustinov, “Low-loss tunable metamaterials using superconducting circuits with Josephson junctions,” Appl. Phys. Lett.102, 062601 (2013).
[CrossRef]

M. C. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett.87, 034102 (2005).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett.97, 071102 (2010).
[CrossRef]

IEEE Trans. Appl. Supercond. (1)

M. C. Ricci, H. Xu, R. Prozorov, A. P. Zhuravel, A. V. Ustinov, and S. M. Anlage, “Tunability of Superconducting Metamaterials,” IEEE Trans. Appl. Supercond.17, 918–921 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech.41, 2075–2084 (1999).
[CrossRef]

J. Phys.: Condens. Matter (1)

C. Du, H. Chen, and S. Li, “Stable and bistable SQUID metamaterials,” J. Phys.: Condens. Matter20, 345220 (2008).
[CrossRef]

Opt. Express (1)

Optics Commun. (1)

A. I. Maimistov and I. R. Gabitov, “Nonlinear response of a thin metamaterial fim containing Josephson junction,” Optics Commun.283, 1633–1639 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

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

Rev. Sci. Instrum. (1)

J.-H. Yeh and S. M. Anlage, “In situ broadband cryogenic calibration for two-port superconducting microwave resonators”, Rev. Sci. Instrum.84, 034706 (2013).
[CrossRef] [PubMed]

Supercond. Sci. Technol. (1)

S. Butz, P. Jung, L. V. Filippenko, V. P. Koshelets, and A. V. Ustinov, “Protecting SQUID metamaterials against stray magnetic field”, Supercond. Sci. Technol.26, 094003 (2013).
[CrossRef]

Other (4)

J. Baker-Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, “Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials,” NIST Technical Note1536 (Boulder, CO, USA), (2005).

D. M. Pozar, Microwave Engineering (2nd Edition) (John Wiley & Sons Inc., 1998) pp. 208–211

K. K. Likharev, Dynamics of Josephson Junctions(Gordon and Breach Science, 1991).

M. Tinkham, Introduction to Superconductivity (2nd Edition) (Dover Publications Inc., 2004).

Supplementary Material (1)

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