Making use of mode matching method, a theoretical analysis of a metamaterial layer is presented. The unit cell of the structure is modeled by a TEM waveguide, and the metamaterial element is supposed as a discontinuity in the waveguide. Analyzing the structure using this model, mathematical relations between s-parameters of a metasurface are extracted. It is evident that the variation of each s-parameter is limited to an arc of circle on Smith chart. The key factors determining the location of each circle on plane are specified. Moreover, a discussion on the role of metasurface element in the determination of s-parameters of the structure is given. The variations of scattering transfer parameters on the plane are determined, too. The steps needed to derive these relations are described. Using these relations, simple and straightforward formulas are devised which can be used to predict the response of the metasurface. Finally, some metasurfaces will be analyzed by full-wave method. The new relations are well-agreed with simulation results.
2. Holloway, C. L., E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, "An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials," IEEE Antennas and Propagation Magazine, Vol. 54, No. 2, 10-35, 2012.
doi:10.1109/MAP.2012.6230714
3. Watts, C. M., X. Liu, and W. J. Padilla, "Metamaterial electromagnetic wave absorbers," Adv. Mater., Vol. 24, No. 1, OP98-OP120, 2012.
4. Withayachumnankul, W. and D. Abbott, "Metamaterials in the terahertz regime," IEEE Photonics Journal, Vol. 1, No. 2, 99-118, 2009.
doi:10.1109/JPHOT.2009.2026288
5. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, 2011.
6. Campione, S., M. Albani, and F. Capolino, "Complex modes and near-zero permittivity in 3D arrays of plasmonic nanoshells: Loss compensation using gain," Optical Materials Express, Vol. 1, No. 6, 1077-1089, 2011.
doi:10.1364/OME.1.001077
7. Engheta, N., "Pursuing near-zero response," Science, Vol. 340, No. 6130, 286-287, 2013.
doi:10.1126/science.1235589
8. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.
doi:10.1126/science.1125907
9. Itoh, T., "Invited paper: Prospects for metamaterials," Electronics Letters, Vol. 40, No. 16, 972-973, 2004.
doi:10.1049/el:20046267
10. Caloz, C. and T. Itoh, "Metamaterials for high-frequency electronics," Proceedings of the IEEE, Vol. 93, No. 10, 1744-1752, 2005.
doi:10.1109/JPROC.2005.853540
11. Shestopalov, V. P., "Spectral theory and excitation of open structures," IET, No. 42, 1996.
12. Kuester, E. F., M. A. Mohamed, M. Piket-May, and C. L. Holloway, "Averaged transition conditions for electromagnetic fields at a metafilm," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 10, 2641-2651, 2003.
doi:10.1109/TAP.2003.817560
13. Holloway, C. L., M. A. Mohamed, E. F. Kuester, and A. Dienstfrey, "Reflection and transmission properties of a metafilm: With an application to a controllable surface composed of resonant particles," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 853-865, 2005.
doi:10.1109/TEMC.2005.853719
14. Marcuvitz, N., Waveguide Handbook, Peregrinus, Institution of Electrical Engineers, London, 1951.
15. Ulrich, R., "Far-infrared properties of metallic mesh and its complementary structure," Infrared Physics, Vol. 7, No. 1, 37-55, 1967.
doi:10.1016/0020-0891(67)90028-0
16. Marques, R., F. Mesa, L. Jelinek, and F. Medina, "Analytical theory of extraordinary transmission through metallic diffraction screens perforated by small holes," Opt. Express, Vol. 17, 5571-5579, 2009.
doi:10.1364/OE.17.005571
17. Bilotti, F. and L. Sevgi, "Metamaterials: Definitions, properties, applications, and FDTD based modeling and simulation," International Journal of RF and Microwave Computer Aided Engineering, Vol. 22, No. 4, 422-438, 2012.
doi:10.1002/mmce.20634
18. Huang, R., Z.-W. Li, L. B. Kong, L. Liu, and S. Matitsine, "Analysis and design of an ultra-thin metamaterial absorber," Progress In Electromagnetics Research B, Vol. 14, 407-429, 2009.
doi:10.2528/PIERB09040902
19. Ziolkowski, R. W., "Design, fabrication, and testing of double negative metamaterials," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 7, 1516-1529, 2003.
doi:10.1109/TAP.2003.813622
20. Hsu, C. C., K. H. Lin, and H. L. Su, "Implementation of broadband isolator using metamaterialinspired resonators and a T-shaped branch for MIMO antennas," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 10, 3936-3939, 2011.
doi:10.1109/TAP.2011.2163741
21. Beruete, M., I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, "Molding left- or righthanded metamaterials by stacked cutoff metallic hole arrays," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 6, 1514-1521, 2007.
doi:10.1109/TAP.2007.897324
22. Itoh, T., "Numerical Techniques for Microwave and Millimeter-wave Passive Structures," Wiley, Science, 1980.
23. Pozar, D. M., Microwave Engineering, Wiely, 2012.
24. Collin, R. E., Field Theory of Guided Waves, Wiely, 1990.
doi:10.1109/9780470544648
25. Guglielmi, M., G. Gheri, M. Calamia, and G. Pelosi, "Rigorous multimode network numerical representation of inductive step," IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 2, 317-326, 1994.
doi:10.1109/22.275263
26. Widarta, A., S. Kuwano, and K. Kokubun, "Simple and accurate solutions of the scattering coefficients of E-plane junctions in rectangular waveguides," IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 12, 2716-2718, 1995.
doi:10.1109/22.477852
27. Wexler, A., "Solution of waveguide discontinuities by modal analysis," Journal Title Abbreviation, Vol. 15, No. 9, 508-517, 1967.
28. Mesa, F., R. Rodriguez-Berral, M. Garcia-Vigueras, F. Medina, and J. R. Mosig, "Simplified modal expansion to analyze frequency-selective surfaces: An equivalent circuit approach," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 3, 1106-1111, 2016.
doi:10.1109/TAP.2015.2513423
29. Campione, S., F. Mesa, and F. Capolino, "Magnetoinductive waves and complex modes in two-dimensional periodic arrays of split ring resonators," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 7, 3554-3563, 2013.
doi:10.1109/TAP.2013.2258395
30. Gonzalez, G., , Microwave Transistor Ampli ers: Analysis and Design, Prentice Hall, 1997.
31. Conciauro, G., M. Guglielmi, and R. Sorrentino, "Advanced Modal Analysis: CAD Techniques for Waveguide Components and Filters," John Wiley & Sons Inc., 2000.
32. Stamatopoulos, I. D. and I. D. Robertson, "Rigorous network representation of microwave components by the use of indirect mode matching," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 3, 935-944, 2004.
doi:10.1109/TMTT.2004.823597
33. Ade, P. A., G. Pisano, C. Tucker, and S. Weaver, "A review of metal mesh filters," Proceedings of SPIE, Vol. 6275, 62750U-62750U, 2006.
doi:10.1117/12.673162
Submit
