Journal of Optics

, Volume 47, Issue 4, pp 437–444 | Cite as

Effect of resistance on effective parameter of LCR-circuit Metamaterials

  • Jing Huang
  • Mingxiang Gui
Research Article


A microparticle resonance model, describing the interaction between an LCR circuit coupled with a bipole, is established for the accurate simulation of Metamaterials. The quantum dynamic descriptions of both an LCR circuit and a bipole are harmonic oscillators. The coupling effect will induce a frequency (the resonance frequency) shift, thereby affecting the resonance occurrence of LCR-circuit Metamaterials. Resistance R has effects on the resonance frequency and effective parameters of Metamaterials, but its scale varying does not cause a fluctuation except in some situations, such as R2 or 1/R2 is the same quantity order of inductance L (\(R^{2} \ge 1 /L\) for the cases of parallel and series connections of R with L and C, respectively. The use of temperature adjustment (altering R) to adjust the LCR-circuit resonance frequency is proposed for the realization of a tunable Metamaterial.


Resonance frequency Harmonic oscillators Tunable Metamaterial 


  1. 1.
    A. Poddubny, I. Iorsh, P. Belov, Y. Kivshar, Hyperbolic metamaterials. Nat. Photonics 7, 948–957 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    Z. Jacob, J.-Y. Kim, G. Naik, A. Boltasseva, E. Narimanov, V. Shalaev, Engineering photonic density of states using metamaterials. Appl. Phys. B 100, 215–218 (2010)ADSCrossRefGoogle Scholar
  3. 3.
    H.N.S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, V.M. Menon, Topological transitions in metamaterials. Science 336, 205–209 (2012)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    A.V. Chebykin, A.A. Orlov, C.R. Simovski, Y.S. Kivshar, P.A. Belov, Nonlocal effective parameters of multilayered metal-dielectric metamaterials. Phys. Rev. B 86, 115420 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    A.V. Chebykin, A.A. Orlov, A.V. Vozianova, S.I. Maslovski, Y.S. Kivshar, P.A. Belov, Nonlocal effective medium model for multilayered metal-dielectric metamaterials. Phys. Rev. B 84, 115438 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    V.P. Drachev, V.A. Podolskiy, A.V. Kildishev, Hyperbolic metamaterials: new physics behind a classical problem. Opt. Express 21, 15048–15064 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    C.L. Cortes, W. Newman, S. Molesky, Z. Jacob, Quantum nanophotonics using hyperbolic metamaterials. J. Opt. 14, 063001 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Guo, Z. Jacob, Thermal hyperbolic metamaterials. Opt. Express 21, 15014–15019 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    C.L. Cortes, Z. Jacob, Photonic analog of a van Hove singularity in metamaterials. Phys. Rev. B 88, 045407 (2013)ADSCrossRefGoogle Scholar
  10. 10.
    C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, F. Lederer, Validity of effective material parameters for optical fishnet metamaterials. Phys. Rev. B 81, 035320 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, F. Lederer, A. Lavrinenko, Homogenization of resonant chiral metamaterials. Phys. Rev. B 82, 235107 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    W. Sun, S.B. Wang, J. Ng, L. Zhou, C.T. Chan, Analytic derivation of electrostrictive tensors and their application to optical force density calculations. Phys. Rev. B 91, 235439 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    G.T. Papadakis, P. Yeh, H.A. Atwater, Retrieval of material parameters for uniaxial metamaterials. Phys. Rev. B 91, 155406 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    J. Kim, V.P. Drachev, Z. Jacob, G.V. Naik, A. Boltasseva, E.E. Narimanov, V.M. Shalaev, Improving the radiative decay rate for dye molecules with hyperbolic metamaterials. Opt. Express 20, 8100–8116 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    Pilkyung Moon, Mikito Koshino, Electronic properties of graphene/hexagonal–boron–nitride moire superlattice. Phys. Rev. B 90, 155406 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    A.D. Raki, A.B. Djurisic, J.M. Elazar, M.L. Majewski, Optical properties of metallic films for vertical-cavity opto-electronic devices. Appl. Opt. 37, 5271–5283 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    J.H. Simmons, K.S. Potter, Optical Materials (Academic, San Diego, 2000)Google Scholar
  18. 18.
    J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 2008)zbMATHGoogle Scholar
  19. 19.
    V.A. Markel, Can the imaginary part of permeability be negative? Phys. Rev. E78, 026608 (2008)ADSGoogle Scholar
  20. 20.
    T. Koschny, P. Marko, D.R. Smith, C.M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Phys. Rev. E 68, 065602(R) (2003)ADSCrossRefGoogle Scholar
  21. 21.
    Detlef Lehmann, Mathematical Method of Many-Body Quantum Field Theory (CRC Press, London, 2004)Google Scholar
  22. 22.
    Jakub Sorocki, Ilona Piekarz, Krzysztof Wincza, Slawomir Gruszczynski, Right/left-handed transmission lines based on coupled transmission line sections and their application towards bandpass filters. IEEE Trans. Microw. Theory Technol. 63, 384–396 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    P. Alitalo, S. Maslovski, S. Tretyakovc, Three-dimensional isotropic perfect lens based on LC-loaded transmission lines. J. Appl. Phys. 99, 064912 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    T. Niemczyk, F. Deppe, H. Huebl, E.P. Menzel, F. Hocke, M.J. Schwarz, J.J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, R. Gross, Beyond the Jaynes–Cummings model: circuit QED in the ultrastrong coupling regime. Nat. Phys. 6, 772–776 (2010)CrossRefGoogle Scholar
  25. 25.
    D. Zueco, C. Fernandez-Juez, J. Yago, U. Naether, B. Peropadre, J.J. Garcıa-Ripoll, J.J. Mazo, From Josephson junction metamaterials to tunable pseudo-cavities. Supercond. Sci. Technol. 26, 074006 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    D. Lehmann, Mathematical Method of Many-Body Quantum Field Theory (CRC Press, London, 2004)Google Scholar
  27. 27.
    P.A. Belov, C.R. Simovski, Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald–Oseen extinction principle. Phys. Rev. B 73, 045102 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    R.W. Boyd, Nonlinear Optics, 2nd edn. (Academic, London, 2012)Google Scholar
  29. 29.
    A.B. Kozyrev, H. Kim, A. Karbassi, D.W. van der Weide, Wave propagation in nonlinear left-handed transmission line media. Appl. Phys. Lett. 87, 121109 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    A. Rose, D.R. Smith, Broadly tunable quasi-phase -matching in nonlinear metamaterials. Phys. Rev. A 84, 013823 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    N.N. Rosanov, N.V. Vysotina, A.N. Shatsev, A.S. Desyatnikov, Y.S. Kivshar, Knotted solitons in nonlinear magnetic metamaterials. Phys. Rev. Lett. 108, 133902 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    Alec Rose, Da Huang, David R. Smith, Controlling the second harmonic in a phase-matched negative-index meta-materia. Phys. Rev. Lett. 107, 063902 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    K. Du, Q. Li, W. Zhang, Y. Yang, M. Qiu, Wavelength and thermal distribution selectable microbolometers based on metamaterial absorbers. IEEE Photonics J. 7, 6800908 (2015)Google Scholar
  34. 34.
    D. Zhang, The design of copper resistance temperature sensor. J. Liaoning Teach. Coll. 10, 4 (2008)Google Scholar
  35. 35.
    D.A. Powell, I.V. Shadrivov, Y.S. Kivshar, Self-tuning mechanisms of nonlinear split-ring resonators. Appl. Phys. Lett. 91, 144107 (2007)ADSCrossRefGoogle Scholar

Copyright information

© The Optical Society of India 2018

Authors and Affiliations

  1. 1.Physics DepartmentSouth China University of TechnologyGuangzhouChina
  2. 2.College of Compute Science and Electronic EngineeringHunan UniversityChangshaChina

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