Abstract
Superconducting metamaterials comprising rf Superconducting QUantum Interference Devices (SQUIDs) have been recently realized and investigated with respect to their tuneability, permeability, and dynamic multistability properties. These properties are a consequence of intrinsic nonlinearities due to the sensitivity of the superconducting state to external stimuli. SQUIDs, made of a superconducting ring interrupted by a Josephson junction, possess yet another source of nonlinearity, which makes them widely tuneable with an applied dc dlux. A model SQUID metamaterial, based on electric equivalent circuits, is used in the weak coupling approximation to demonstrate the dc flux tuneability, dynamic multistability, and nonlinear transmission in SQUID metamaterials comprising non-hysteretic SQUIDs. The model equations reproduce the experimentally observed tuneability patterns and predict tuneability with the power of an applied ac magnetic field. Moreover, the results indicate the opening of nonlinear frequency bands for energy transmission through SQUID metamaterials, for sufficiently strong ac fields.
Similar content being viewed by others
References
S.M. Anlage, J. Opt. 13, 024001 (2011)
In Special Issue: Focus on Superconducting Metamaterials, vol. 26, ed. by A.V. Ustinov, S. Anlage, A. Sanchez (Supercond. Sci. Technol. 2013)
D.R. Smith, J.B. Pendry, M.C.K. Wiltshire. Science 305(5685), 788 (2004)
V.M. Shalaev, Nat. Photonics 1, 41 (2007)
C.M. Soukoulis, M. Wegener, Nat. Photonics 5, 523 (2011)
I.V. Shadrivov, A.B. Kozyrev, D.W. van der Weide, Y.S. Kivshar, Appl. Phys. Lett. 93, 161903 (2008)
N.I. Zheludev, Science 328, 582 (2010)
N.I. Zheludev, Opt. Photonics News 22, 31 (2011)
M.C. Ricci, N. Orloff, S.M. Anlage, Appl. Phys. Lett. 87, 034102 (2005)
M.C. Ricci, H. Xu, R. Prozorov, A.P. Zhuravel, A.V. Ustinov, S.M. Anlage, IEEE Trans. Appl. Supercond. 17, 918 (2007)
H.T. Chen, H. Yang, R. Singh, J.F. OHara, A.K. Azad, A. Stuart, S.A. Trugman, Q.X. Jia, A.J. Taylor, Phys. Rev. Lett. 105, 247402 (2010)
B. Jin, C. Zhang, S. Engelbrecht, A. Pimenov, J. Wu, Q. Xu, C. Cao, J. Chen, W. Xu, Opt. Express 18, 17504 (2010)
V.A. Fedotov, A. Tsiatmas, J.H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, N.I. Zheludev, Opt. Express 18, 9015 (2010)
C. Kurter, P. Tassin, A.P. Zhuravel, L. Zhang, T. Koschny, A.V. Ustinov, C.M. Soukoulis, S.M. Anlage, Appl. Phys. Lett. 100, 121906 (2012)
R. Singh, J. Xiong, A.K. Azad, H. Yang, S.A. Trugman, Q.X. Jia, A.J. Taylor, H.T. Chen, Nanophotonics 1, 117–123 (2012)
R. Singh, J. Xiong, D.R. Chowdhury, H. Yang, A.K. Azad, S.A. Trugman, Q.X. Jia, A.J. Taylor, H.T. Chen, Proc. SPIE 8423, 84230Y (2012)
V. Savinov, V.A. Fedotov, S.M. Anlage, P.A.J. de Groot, N.I. Zheludev, Phys. Rev. Lett. 109, 243904 (2012)
P. Jung, S. Butz, S.V. Shitov, A.V. Ustinov, Appl. Phys. Lett. 102, 062601 (2013)
S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Opt. Express 29(19), 22540 (2013)
D. Zueco, C. Fernández-Juez, J. Yago, U. Naether, B. Peropadre, J.J. García-Ripoll, J.J. Mazo, Supercond. Sci. Technol. 26, 074006 (8pp) (2013)
B. Josephson, Phys. Lett. A 1, 251 (1962)
A. Barone, G. Patternó, Physics and Applications of the Josephson Effect (Wiley, New York, 1982)
K.K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, Philadelphia, 1986)
M. Trepanier, D. Zhang, O. Mukhanov, S.M. Anlage, arXiv:1308.1410 (2013)
P. Jung, S. Butz, M. Marthaler, M.V. Fistul, J. Leppäkangas, V.P. Koshelets, A.V. Ustinov, arXiv:1312.2937 (2013)
W.G. Jenks, S.S.H. Sadeghi, J.P.W. Jr, J. Phys. D: Appl. Phys. 30, 293 (1997)
D. Koelle, R. Kleiner, F. Ludwig, E. Dantsker, J. Clarke, Rev. Mod. Phys. 71, 631 (1999)
R. Kleiner, D. Koelle, F. Ludwig, J. Clarke, Proc. IEEE 92, 1534 (2004)
R.L. Fagaly, Rev. Sci. Instrum. 77, 101101 (2006)
C. Du, H. Chen, S. Li, Phys. Rev. B 74, 113105 (2006)
N. Lazarides, G.P. Tsironis, Appl. Phys. Lett. 16, 163501 (2007)
S. Butz, P. Jung, L.V. Filippenko, V.P. Koshelets, A.V. Ustinov, Supercond. Sci. Technol. 26, 094003 (2013)
N. Lazarides, G.P. Tsironis, M. Eleftheriou, Nonlinear Phenom. Complex Syst. 11, 250 (2008)
G.P. Tsironis, N. Lazarides, M. Eleftheriou, PIERS Online 5, 26 (2009)
N. Lazarides, G.P. Tsironis, Proc. SPIE 8423, 84231K (2012)
W. Wernsdorfer, Supercond. Sci. Technol. 22, 064013 (2009)
J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M.X. He, J.W. Zhang, J. Han, H. Chen, W. Zhang, Appl. Phys. Lett. 97, 071102 (2010)
C.H. Zhang, J.B. Wu, B.B. Jin, Z.M. Ji, L. Kang, W.W. Xu, J. Chen, M. Tonouchi, P.H. Wu, Opt. Express 20(1), 42 (2011)
J.B. Wu, B.B. Jin, J. Wan, L. Liang, Y.G. Zhang, T. Jia, C.H. Cao, L. Kang, W.W. Xu, J. Chen, P.H. Wu, Appl. Phys. Lett. 99, 161113 (2011)
C.H. Zhang, J.B. Wu, B.B. Jin, Z.M. Ji, L. Kang, W.W. Xu, J. Chen, M. Tonouchi, P.H. Wu, Opt. Express 20(1), 42 (2012)
C.H. Zhang, J.H.B.B. Jin, I. Kawayama, H. Murakami, X. Jia, L. Liang, L. Kang, J. Chen, P. Wu, M. Tonouchi, New J. Phys. 15, 055017 (2013)
B.B. Jin, C.H. Zhang, J. Han, I. Kawayama, H. Murakami, J.B. Wu, L. Kang, J. Chen, P.H. Wu, M. Tonouchi, Appl. Phys. Lett. 102, 081121 (2013)
A. Pimenov, A. Loidl, P. Przyslupski, B. Dabrowski, Phys. Rev. Lett. 95, 247009 (2005)
A.G. Kussow, A. Akyurtlu, A. Semichaevsky, N. Angkawisittpan, Phys. Rev. B 76, 195123 (2007)
N. Limberopoulos, A. Akyurtlu, K. Higginson, A.G. Kussow, C.D. Merritt, Appl. Phys. Lett. 95, 023306 (2009)
A.L. Rakhmanov, V.A. Yampolskii, J.A. Fan, F. Capasso, F. Nori, Phys. Rev. B 81(7), 075101 (2010)
V.A. Golick, D.V. Kadygrob, V.A. Yampolskii, A.L. Rakhmanov, B.A. Ivanov, F. Nori, Phys. Rev. Lett. 104, 187003 (2010)
C. Kurter, P. Tassin, L. Zhang, T. Koschny, A.P. Zhuravel, A.V. Ustinov, S.M. Anlage, C.M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011)
J. Prat-Camps, A. Sanchez, C. Navau, Supercond. Sci. Technol. 26, 074001 (2013)
M.A. Castellanos-Beltran, K.D. Irwin, G.C. Hilton, L.R. Vale, K.W. Lehnert, Nat. Phys. 4, 928 (2008)
F. Magnus, B. Wood, J. Moore, K. Morrison, G. Perkins, J. Fyson, M.C.K. Wiltshire, D. Caplini, L.F. Cohen, J.B. Pendry, Nat. Mater. 7, 295 (2008)
C. Navau, D.X. Chen, A. Sanchez, N. Del-Valle, Appl. Phys. Lett. 94(24), 242501 (2009)
Y. Mawatari, C. Navau, A. Sanchez, Phys. Rev. B 85, 134524 (2012)
Y. Mawatari, Supercond. Sci. Technol. 26, 074005 (2013)
C. Kurter, J. Abrahams, S.M. Anlage, Appl. Phys. Lett. 96, 253504 (2010)
B.G. Ghamsari, J. Abrahams, S. Remillard, S.M. Anlage, Appl. Phys. Lett. 102(1), 013503 (2013)
J. Wu, B. Jin, Y. Xue, C. Zhang, H. Dai, L. Zhang, C. Cao, L. Kang, W. Xu, J. Chen, P. Wu, Opt. Express 19, 12021 (2011)
A. Tsiatmas, V.A. Fedotov, F.J.G. de Abajo, N.I. Zheludev, New J. Phys. 14, 115006 (2012)
J. Zuo, R. Liu, Y. Zhou, Y. Li, Y. Wang, Sci. China Phys. Mech. Astron. 55(2), 224 (2012)
A.M. Zagoskin, J. Opt. 14, 114011 (2012)
S.I. Mukhin, M.V. Fistul, Supercond. Sci. Technol. 26, 084003 (2013)
R.D. Wilson, M.J. Everitt, S. Savelev, A.M. Zagoskin, Supercond. Sci. Technol. 26, 084005 (2013)
P. Macha, G. Oelsner, J.M. Reiner, M. Marthaler, S. André, G. Schön, U. Hübner, H.G. Meyer, E. Il’ichev, A.V. Ustinov, arXiv:1309.5268v1 (2013)
N. Lazarides, G.P. Tsironis, Supercond. Sci. Technol. 26, 084006 (2013)
N. Lazarides, V. Paltoglou, G.P. Tsironis, Int. J. Bifurcation Chaos 21, 2147 (2011)
N. Lazarides, G.P. Tsironis, Phys. Lett. A 374, 2179 (2010)
Y. Huang, W.F. McColl, J. Phys. A: Math. Gen. 30, 7919 (1997)
Acknowledgments
This work was partially supported by the European Union’s Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under Grant Agreement No. 316165 and by the Thales Project MACOMSYS, cofinanced by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tsironis, G.P., Lazarides, N. & Margaris, I. Wide-band tuneability, nonlinear transmission, and dynamic multistability in SQUID metamaterials. Appl. Phys. A 117, 579–588 (2014). https://doi.org/10.1007/s00339-014-8706-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00339-014-8706-7