PIER M
 
Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 29 > pp. 79-93

DETERMINING THE EFFECTIVE ELECTROMAGNETIC PARAMETERS OF BIANISOTROPIC METAMATERIALS WITH PERIODIC STRUCTURES

By L. Chen, Z.-Y. Lei, R. Yang, X.-W. Shi, and J. Zhang

Full Article PDF (375 KB)

Abstract:
A straightforward approach is proposed to retrieve the effective electromagnetic parameters of a slab of bianisotropic material from the scattering parameters. We first obtain the values of the impedance and refractive index of a slab of metamaterial, followed by the deduction of the expressions for determining these electromagnetic parameters including permittivity, permeability and magnetoelectric coupling coefficient. Then, comparisons between the results coming respectively from retrieval technique and analytical method are made. Finally, we demonstrate the properties of split-ring resonator materials in other two orientations with respect to the incident plane wave and apply the proposed method to anisotropic materials to reveal its generality.

Citation:
L. Chen, Z.-Y. Lei, R. Yang, X.-W. Shi, and J. Zhang, "Determining the Effective Electromagnetic Parameters of Bianisotropic Metamaterials with Periodic Structures," Progress In Electromagnetics Research M, Vol. 29, 79-93, 2013.
doi:10.2528/PIERM13010204

References:
1. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, No. 18, 4184-4187, 2000.

2. Smith, D. R. and J. B. Pendry, "Homogenization of metamaterials by field averaging," JOSA B, Vol. 23, No. 3, 391-403, 2006.

3. Chen, , H., L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys., Vol. 100, No. 2, 24915, 2006.

4. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Transactions on Instrumentation and Measurement, Vol. 19, No. 4, 377-382, 1970.

5. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from re┬░ection and transmission coefficients," Phys. Rev. B, Vol. 65, No. 19, 195104, 2002.

6. Smith, D. R. , D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E, Vol. 71, No. 3, 36617, 2005.

7. Chen, X., 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, Vol. 70, No. 1, 16608, 2004.

8. Hasar, U. C., J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, "Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs," Opt. Express, Vol. 20, No. 27, 29002-29022, 2012.

9. Hasar, U. C., J. J. Barroso, C. Sabah, I. Y. Ozbek, Y. Kaya, D. Dal, and T. Aydin, "Retrieval of effective electromagnetic parameters of isotropic metamaterials using reference-plane invariant expressions," Progress In Electromagnetics Research, Vol. 132, 425-441, 2012.

10. Barroso, J. J. and U. C. Hasar, "Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method," Journal of Infrared, Millimeter and Terahertz Waves, Vol. 33, No. 2, 237-244, 2012.

11. Kim, S., E. F. Kuester, C. L. Holloway, A. D. Scher, and J. R. Baker-Jarvis, "Effective material property extraction of a metamaterial by taking boundary effects into account at TE/TM polarized incidence," Progress In Electromagnetics Research B, Vol. 36, 1-33, 2012.

12. Chen, H., J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong, "Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express, Vol. 14, No. 26, 12944-12949, 2006.

13. Tretyakov, S. A., C. R. Simovski, and M. Hudlicka, "Bianisotropic route to the realization and matching of backward-wave metamaterial slabs," Phys. Rev. B, Vol. 75, No. 15, 153104, 2007.

14. Marques, R., F. Medina, and R. Rafii-El-Idrissi, "Role of bian-isotropy in negative permeability and left-handed metamaterials," Phys. Rev. B, Vol. 65, No. 14, 144440, 2002.

15. Chen, X., T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab," Progress In Electromagnetics Research, Vol. 60, 1-18, 2006.

16. Chen, X., B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E, Vol. 71, No. 4, 4661, 2005.

17. Li, , Z., , K. Aydin, and E. Ozbay, "Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients," Phys. Rev. E, Vol. 79, No. 2, 26610, 2009.

18. Kriegler, C. E., M. S. Rill, S. Linden, and M. Wegener, "Bianisotropic photonic metamaterials," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 16, No. 2, 367-375, 2010.

19. Smith, , D. R., J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, "Calculation and measurement of bianisotropy in a split ring resonator metamaterial," J. Appl. Phys., Vol. 100, No. 2, 024507, 2006.

20. Hasar, U. C. and J. J. Barroso, "Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials," Progress In Electromagnetics Research, Vol. 112, 109-124, 2011.

21. Yang, R., Y. J. Xie, X. F. Li, Y. Y. Wang, R. Wang, and J. Jiang, "Causality in the resonance behavior of metamaterials," EPL (Europhysics Letters), Vol. 84, No. 3, 34001, 2008.

22. Kong, J. A., Electromagnetic Wave Theory, Wiley, 1990.

23. Marques, R., F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications, Wiley, 2008.

24. Sydoruk, O. , E. Tatartschuk, E. Shamonina, and L. Solymar, "Analytical formulation for the resonant frequency of split rings," J. Appl. Phys., Vol. 105, No. 1, 14903, 2009.

25. Liu, R., T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E,, Vol. 76, No. 2, 26606, 2007.

26. Smith, D. R., "Analytic expressions for the constitutive parameters of magnetoelectric metamaterials," Phys. Rev. E, Vol. 81, No. 3, 36605, 2010.

27. Marques, R., "Novel small resonant electromagnetic particles for metamaterial and filter design," Proc. ICEAA' 03, 439-442, Torino, Italy, 2003.

28. Marques, R., F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design --- Theory and experiments," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 2572-2581, 2003.


© Copyright 2010 EMW Publishing. All Rights Reserved