volume | PIER Journals

Abstract

We present a generally symmetrical circuit model to describe all kinds of metamaterials with effective permittivity and permeability. The model is composed of periodic structures whose unit cell is a general T-type circuit. Using the effective medium theory, we derive analytical formulations for the effective permittivity and effective permeability of the circuit model, which are quite different from the published formulas [1, 2]. Rigorous study shows that such a generally symmetrical model can represent right-handed materials, left-handed materials, pure electric plasmas, pure magnetic plasmas, electric-type and magnetic-type crystal bandgap materials at different frequency regimes, with corresponding effective medium parameters. Circuit simulations of real periodic structures and theoretical results of effective medium models in this paper and in [1] and [2] are presented. The comparison of such results shows that the proposed medium model is much more accurate than the published medium model [1, 2] in the whole frequency band.

1. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, 68, John Wiley & Sons, New York, 2004.

2. Eleftheriades, G. V. and K. G. Balmain, Negative Refraction Metamaterials: Fundamental Properties and Applications, 15, John Wiley & Sons, New York, 2005.

3. Mao, S. G. and Y. Z. Chueh, "Broadband composite right/left-handed coplanar waveguide power splitters with arbitrary phase responses and balun and antenna applications," IEEE Transactions on Antennas and Propagation, Vol. 54, 243-250, 2006.
doi:10.1109/TAP.2005.861574

4. Cui, T. J., Q. Cheng, Z. Z. Huang, and Y. J. Feng, "Electromagnetic wave localization using a left-handed transmission-line superlens," Phys. Rev. B, Vol. 72, 035112, 2005.
doi:10.1103/PhysRevB.72.035112

5. Alu, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propagat., Vol. 51, 2558-2566, 2003.
doi:10.1109/TAP.2003.817553

6. Eleftheriades, G. V., "A generalized negative-refractive-index transmission-line (NRICTL) metamaterial for dual-band and quad-band applications," IEEE Microwave Wireless Compon. Lett., Vol. 17, 415-417, 2007.
doi:10.1109/LMWC.2007.897786

7. Eleftheriades, G. V., A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory. Tech., Vol. 50, 2702-2710, 2002.
doi:10.1109/TMTT.2002.805197

8. Lin, X. Q., Q. Cheng, R. Liu, D. Bao, and T. J. Cui, "Compact resonator filters and power dividers designed with simplified metastructures," Journal of Electromagnetic Waves and Applications, Vol. 21, 1663-1672, 2007.
doi:10.1163/156939307783239483

9. Li, Z. and T. J. Cui, "Novel waveguide directional couplers using left-handed materials," Journal of Electromagnetic Waves and Applications, Vol. 21, 1053-1062, 2007.

10. Guo, Y. and R. M. Xu, "Planar metamaterials supporting multiple left-hande dmodes," Progress In Electromagnetics Research, Vol. 66, 239-251, 2006.
doi:10.2528/PIER06113001

11. Wu, B.-I., W. Wang, J. Pacheco, X. Chen, T. M. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, Vol. 51, 295-328, 2005.
doi:10.2528/PIER04070701

12. Qin, Y. and T. J. Cui, "A general representation of left-handed materials using LC-loaded transmission lines," Microwave Opt. Tech. Letts., Vol. 48, 2167-2171, 2006.
doi:10.1002/mop.21883

13. Liu, R., B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, "Evanescent-wave amplification studied using a bilayer periodic circuit structure and its effective medium model," Phys. Rev. B, Vol. 75, 125118, 2007.
doi:10.1103/PhysRevB.75.125118

14. Liu, R., T. J. Cui, B. Zhao, X. Q. Lin, H. F. Ma, D. Huang, and D. R. Smith, "Resonant crystal bandgap metamaterials in microwave regime and their exotic amplification of evanescent waves," Appl. Phys. Lett., Vol. 90, 091912, 2007.
doi:10.1063/1.2709897

15. 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, 026606, 2007.
doi:10.1103/PhysRevE.76.026606

16. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, New York, 1986.

17. Yu, G. X. and T. J. Cui, "Imaging and localization properties of LHM superlens excited by 3D horizontal electric dipoles," Journal of Electromagnetic Waves and Applications, Vol. 21, 35-46, 2007.
doi:10.1163/156939307779391795

18. Li, Z. and T. J. Cui, "Sandwich-structure waveguides for very-high power generation and transmission using left-handed materials," Progress In Electromagnetics Research, Vol. 69, 101-116, 2007.
doi:10.2528/PIER06121001

19. Li, Z., T. J. Cui, and J. F. Zhang, "TM wave coupling for high power generation and transmission in parallel-plate waveguide," Journal of Electromagnetic Waves and Applications, Vol. 21, 947-961, 2007.
doi:10.1163/156939307780749039

20. Brovenko, A., P. N. Melezhik, A. Y. Poyedinchuk, and N. P. Yashina, "Surface resonances of metal stripe grating on the plane boundary of metamaterial," Progress In Electromagnetics Research, Vol. 63, 209-222, 2006.
doi:10.2528/PIER06052401

21. Chew, W. C., "Some reflections on double negative materials," Progress In Electromagnetics Research, Vol. 51, 1-26, 2005.
doi:10.2528/PIER04032602

22. Ishimaru, A., S. Jaruwatanadilok, and Y. Kuga, "Generalized surface plasmon resonance sensors using metamaterials and negative index materials," Progress In Electromagnetics Research, Vol. 51, 139-152, 2005.
doi:10.2528/PIER04020603

23. Yao, H.-Y., L.-W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress In Electromagnetics Research, Vol. 51, 197-217, 2005.
doi:10.2528/PIER04020301

Professor Tie-Jun Cui

Dr. Hui-Feng Ma

Dr. Ruo Liu

Dr. Bo Zhao

Dr. Qiang Cheng

Dr. Jessie Chin