Skip to main content
SpringerLink
Log in

Permeability Measurement of Metamaterials with Split-Ring-Resonators Using Free-Space Calibration-Independent Methods

  • Published:
Journal of Infrared, Millimeter, and Terahertz Waves Aims and scope Submit manuscript

Abstract

A calibration-independent microwave method is proposed for complex permeability extraction of metamaterial structures composed of periodic split-ring resonators. For the retrieval process, uncalibrated (raw) complex scattering parameter measurements of three measurement configurations in free-space are utilized. Two metric functions are derived for retrieval of complex permeability of homogeneous metamaterial slabs even when their lengths are unknown. The method is validated by retrieving the magnetic properties of some homogeneous SRR metamaterial slabs with a pre-assigned magnetic resonant frequency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. J. J. Barroso, P. J. Castro, and J. P. Leite Neto, Experiments on wave propagation at 6.0 GHz in a left-handed waveguide, Microw. Opt. Technol. Lett. 52(10), 2175 (2010).

    Article  Google Scholar 

  2. V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. USPEKHI 10(4), 509 (1968).

    Article  Google Scholar 

  3. Z. Li, K. Aydin, and E. Ozbay, Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients, Phys. Rev. E 79, 026610 (2009).

    Article  Google Scholar 

  4. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Extremely low frequency plasmons in metallic mesostructures, Phys. Rev. Lett. 76(25), 4773 (1996).

    Article  Google Scholar 

  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, Low frequency plasmons in thin-wire structures, J. Phys.: Condens. Matter 10(22), 4785 (1998).

    Article  Google Scholar 

  6. J. B. Pendry, A. J. Hold, D. J. Robbins, and W. J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microw. Theory Tech. 47(11), 2075 (1999).

    Article  Google Scholar 

  7. S. A. Ramakrishna, Physics of negative refractive index materials, Rep. Prog. Phys. 68, 449 (2005).

    Article  Google Scholar 

  8. 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).

    Article  Google Scholar 

  9. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, Robust method to retrieve the constitutive effective parameters of metamaterials, Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 70, 016608 (2004).

    Article  Google Scholar 

  10. H. Wang, X. Chen, and K. Huang, An improved approach to determine the branch index for retrieving the constitutive effective parameters of metamaterials, Journal of Electromagnetic Waves and Applications 25, 85 (2011).

    Article  Google Scholar 

  11. U. C. Hasar and J. J. Barroso, Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials, Progress In Electromagnetics Research 112, 109 (2011).

    Google Scholar 

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

    Article  Google Scholar 

  13. X. Chen, B.-I. Wu, J. A. Kong, and T. Grzegorczyk, Retrieval of the effective constitutive parameters of bianisotropic metamaterials, Phys. Rev. E 71, 046610 (2005).

    Article  Google Scholar 

  14. D. R. Smith, Analytic expressions for the constitutive parameters of magnetoelectric metamaterials, Phys. Rev. E 81, 036605 (2010).

    Article  Google Scholar 

  15. C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, Retrieving effective parameters for quasiplanar chiral metamaterials, Appl. Phys. Lett. 93, 233106 (2008).

    Article  Google Scholar 

  16. D. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, Material parameter retrieval procedure for general bi-anisotropic metamaterials and its application to optical chiral negative-index metamaterial design, Opt. Express 16, 11822 (2008).

    Article  Google Scholar 

  17. E. Plum. J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Metamaterial with negative index due to chirality, Phy. Rev. B 79, 035407 (2009).

    Article  Google Scholar 

  18. A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, Wave propagation retrieval method for metamaterials: Unambiguous restoration of effective parameters, Phys. Rev. B 80, 193101 (2009).

    Article  Google Scholar 

  19. Bombay, M. S. and O. M. Ramahi, Near-field probes using double and single negative media, Phys. Rev. E. 79, 016602 (2009).

    Article  Google Scholar 

  20. Bombay, M. S. and O. M. Ramahi, Open-ended coaxial line probes with negative permittivity materials, IEEE Trans. Antennas Propagat. 59(5), 1765 (2011).

    Article  Google Scholar 

  21. G. F. Engen and C. A. Hoer, ‘Thru−reflect−line’: An improved technique for calibrating the dual six−port automatic network analyzer, IEEE Microw. Theory and Tech. MTT−27(12), 987 (1979).

    Article  Google Scholar 

  22. R. B. Marks, A multiline method for network analyzer calibration, IEEE Trans. Microw. Theory Tech. 39(7), 1205 (1991).

    Article  Google Scholar 

  23. C. Wan, B. Nauwelaers, W. De Raedt, and M. Van Rossum, Complex permittivity measurement method based on asymmetry of reciprocal two-ports, Electron. Lett. 32, 1497 (1996).

    Article  Google Scholar 

  24. C. Wan, B. Nauwelaers, and W. De Raedt, A simple error correction method for two-port transmission parameter measurement, IEEE Microwave Guided Wave Lett. 8, 58 (1998).

    Article  Google Scholar 

  25. C. Wan, Simple, accurate method for characterizing two-port devices with small reflections, Electron. Lett. 34, 1761 (1998).

    Article  Google Scholar 

  26. C. Wan, B. Nauwelaers, W. De Raedt, and M. Van Rossum, Two new measurement methods for explicit determination of complex permittivity, IEEE Trans. Microw. Theory Tech. 46(11), 1614 (1998).

    Article  Google Scholar 

  27. A. Enders, An accurate measurement technique for line properties, junction effects, and dielectric and magnetic material properties, IEEE Trans. Microw. Theory Tech. MTT-37(3), 598 (1989).

    Article  Google Scholar 

  28. K.-H. Baek, H.-Y. Sung, W. S. and Park, A 3-position Transmission/Reflection method for measuring the permittivity of low loss materials, IEEE Microwave Guided Wave Lett. 5(1), 3 (1995).

    Article  Google Scholar 

  29. M.-Q. Lee and S. Nam, An accurate broadband measurement of substrate dielectric constant, IEEE Microwave Guided Wave Lett. 6(4), 168 (1996).

    Article  Google Scholar 

  30. M. D. Janezic and J. A. Jargon, Complex permittivity determination from propagation constant measurements, IEEE Microwave Guided Wave Lett. 9(2), 76 (1999).

    Article  Google Scholar 

  31. J. A. Reynoso-Hernandez, C. F. Estrada-Maldonado, T. Parra, K. Grenier, and J. Graffeuil, An improved method for the wave propagation constant γ estimation in broadband uniform millimeter-wave transmission line, Microwave Opt. Technol. Lett. 22(4), 268 (1999).

    Article  Google Scholar 

  32. I. Huygen, C. Steukers, and F. Duhamel, A wideband line-line dielectrometric method for liquids, solids, and planar substrates, IEEE Trans. Instrum. Meas. 50(5), 1343 (2001).

    Article  Google Scholar 

  33. L. Lanzi, M. Carla, C. M. C. Gambi, and L. Lanzi, Differential and double-differential dielectric spectroscopy to measure complex permittivity in transmission lines, Rev. Sci. Instrum. 73, 3085 (2002).

    Article  Google Scholar 

  34. J. A. Reynoso-Hernandez, Unified method for determining the complex propagation constant of reflecting and nonreflecting transmission lines, IEEE Microw. Wireless Compon. Lett. 13(8), 351 (2003).

    Article  Google Scholar 

  35. N. J. Farcich, J. Salonen and P. M. Asbeck, Single-length method used to determine the dielectric constant of polydimethylsiloxane, IEEE Trans. Microw. Theory Tech. 56(12), 2963 (2008).

    Article  Google Scholar 

  36. U. C. Hasar, Calibration-independent method for complex permittivity determination of liquid and granular materials, Electron. Lett. 44, 585 (2008).

    Article  Google Scholar 

  37. U. C. Hasar, A calibration-independent method for accurate complex permittivity determination of liquid materials, Rev. Sci. Instrum. 79, 086114 (2008).

    Article  Google Scholar 

  38. U. C. Hasar, A new calibration-independent method for complex permittivity extraction of solid dielectric materials, IEEE Microw. Wireless Compon. Lett. 18(12), 788 (2008).

    Article  Google Scholar 

  39. U. C. Hasar and O. E. Inan, A position-invariant calibration-independent method for permittivity measurements, Microwave Opt. Technol. Lett. 51(6), 1406 (2009).

    Article  Google Scholar 

  40. U. C. Hasar and O. Simsek, A calibration-independent microwave method for position-insensitive and nonsingular dielectric measurements of solid materials, J. Phys. D: Appl. Phys. 42(7), 075403 (2009).

    Article  Google Scholar 

  41. U. C. Hasar and O. Simsek, On the application of microwave calibration-independent measurements for noninvasive thickness evaluation of medium- and low-loss solid materials, Progress In Electromagnetics Research 91, 377 (2009).

    Article  Google Scholar 

  42. U. C. Hasar, A new microwave method for electrical characterization of low-loss materials, IEEE Microw. Wireless Compon. Lett. 19(12), 801 (2009).

    Article  Google Scholar 

  43. U. C. Hasar, O. Simsek, and M. Gulnahar, A simple procedure to simultaneously evaluate the thickness of and resistive losses in transmission lines from uncalibrated scattering parameter measurements, Journal of Electromagnetic Waves and Applications, 23(8–9), 999 (2009).

    Google Scholar 

  44. U. C. Hasar, O. Simsek, M. K. Zateroglu, and A. E. Ekinci, A microwave method for unique and non-ambiguous permittivity determination of liquid materials from measured uncalibrated scattering parameters, Progress In Electromagnetics Research 95, 73 (2009).

    Article  Google Scholar 

  45. F. Kadiroglu and U. C. Hasar, A highly accurate microwave method for permittivity determination using corrected scattering parameter measurements, Journal of Electromagnetic Waves and Applications, 24(16), 2179 (2010).

    Article  Google Scholar 

  46. R. Melik, E. Unal, N. K. Perkgoz, C. Puttlitz, and H. V. Demir, Metamaterial-based wireless strain sensors, Appl. Phys. Lett., 95(1), 011106 (2009).

    Article  Google Scholar 

  47. R. Melik, E. Unal, N. K. Perkgoz, C. Puttlitz, and H. V. Demir, Flexible metamaterials for wireless strain sensing, Appl. Phys. Lett. 95(18), 181105 (2009).

    Article  Google Scholar 

  48. X. -J. He, Y. Wang, J. M. Wang, and T. L. Gui, Thin-film sensor based tip-shaped split ring resonator metamaterial for microwave application, Microsyst. Technol. 16, 1735 (2010).

    Article  Google Scholar 

  49. X.-J. He, L. Qui, Y. Wang, and Z.-X. Geng, A compact thin-film sensor based on nested split-ring-resonator (SRR) metamaterials for microwave applications, J. Infrared Milli. Terahz Waves, 32(7), 902 (2011).

    Article  Google Scholar 

  50. J. Woodly and M. Mojahedi, On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials, J. Opt. Soc. Am. B. 27(5), 1016 (2010).

    Article  Google Scholar 

Download references

Acknowledgment

U. C. Hasar (Mehmetcik 13) would like to thank The Scientific and Technological Research Council of Turkey (TUBITAK) Münir Birsel National Doctorate Scholarship and Master of Science Scholarship, The Higher Education Council of Turkey (YOK) Doctorate Scholarship, The Outstanding Young Scientist Award in Electromagnetics of Leopold B. Felsen Fund, Binghamton University Distinguished Dissertation Award, Binghamton University Graduate Student Award for Excellence in Research, and Ataturk University Science Encouragement Awards for Publications (1st place) for the year 2009 and 2010, for supporting his studies.

Joaquim J. Barroso also would like to thank CNPq, Brazil, for supporting this study

Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Ataturk University, Erzurum, Turkey

    Ugur C. Hasar

  2. Department of Electrical and Computer Engineering, Binghamton University, New York, NY, 13902, USA

    Ugur C. Hasar

  3. Associated Plasma Laboratory, National Institute for Space Research, 12227-010 São José dos Campos, São Paulo, SP, Brazil

    Joaquim J. Barroso

Authors
  1. Ugur C. Hasar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joaquim J. Barroso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ugur C. Hasar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hasar, U.C., Barroso, J.J. Permeability Measurement of Metamaterials with Split-Ring-Resonators Using Free-Space Calibration-Independent Methods. J Infrared Milli Terahz Waves 33, 218–227 (2012). https://doi.org/10.1007/s10762-011-9859-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10762-011-9859-5

Keywords

Search

Navigation