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2019-10-11
Retrieval Approach for Determining Surface Susceptibilities and Surface Porosities of a Symmetric Metascreen from Reflection and Transmission Coefficients
By
Progress In Electromagnetics Research, Vol. 166, 1-22, 2019
Abstract
Recently we derived generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen (a metasurface with a ``fishnet'' structure, i.e., a periodic array of arbitrary spaced apertures in a relatively impenetrable surface). The parameters in these GSTCs are interpreted as effective surface susceptibilities and surface porosities, which themselves are related to the geometry of the apertures that constitute the metascreen. In this paper, we use these GSTCs to derive the plane-wave reflection (R) and transmission (T) coefficients of a symmetric metascreen, expressed in terms of these surface parameters. From these equations, we develop a retrieval approach for determining the uniquely defined effective surface susceptibilities and surface porosities that characterize the metascreen from measured or simulated data for the R and T coefficients. We present the retrieved surface parameters for metascreens composed of five different types of apertures (circular holes, square holes, crosses, slots, and a square aperture filled with a high-contrast dielectric). The last example exhibits interesting resonances at frequencies where no resonances exist when the aperture is not filled, which opens up the possibility of designing metasurfaces with unique filtering properties. The retrieved surface parameters are validated by comparing them to other approaches.
Citation
Christopher L. Holloway, Edward F. Kuester, and Abdulaziz H. Haddab, "Retrieval Approach for Determining Surface Susceptibilities and Surface Porosities of a Symmetric Metascreen from Reflection and Transmission Coefficients," Progress In Electromagnetics Research, Vol. 166, 1-22, 2019.
doi:10.2528/PIER19022305
References

1. 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, April 2012.
doi:10.1109/MAP.2012.6230714

2. Maradudin, A. A., Structured Surfaces as Optical Metamaterials, Cambridge University Press, Cambridge, UK, 2011.
doi:10.1017/CBO9780511921261

3. Zouhdi, S., A. Sihvola, and M. Arsalane, Advances in Electromagnetics of Complex Media and Metamaterials, Kluwer Academic Pub., Boston, 2002.
doi:10.1007/978-94-007-1067-2

4. Caloz, C. and T. Itoh, "Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications," IEEE Press, Hoboken, NJ, 2005.

5. Eleftheriades, G. V. and K. G. Balmain, Negative Refraction Metamaterials: Fundamental Principles and Applications, IEEE Press, Hoboken, NJ, 2005.
doi:10.1002/0471744751

6. Engheta, N. and R. W. Ziolkowski, Electromagnetic Metamaterials: Physics and Engineering Explorations, IEEE Press, Piscataway, NJ, 2006.

7. Marques, R., F. Martın, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications, Wiley-Interscience, Hoboken, NJ, 2008.

8. Capolino, F., "Metamaterials Handbook: Theory and Phenomena of Metamaterials," CRC Press, Boca Raton, FL, 2009.

9. Cui, T. J., D. R. Smith, and R. Liu, "Metamaterials: Theory, Design, and Applications," Springer, New York, 2010.

10. Kuester, E. F., M. A. Mohamed, M. Piket-May, and C. L. Holloway, "Averaged transition conditions for electromagnetic fields at a metafilm," IEEE Trans. on Antennas and Propagation, Vol. 51, No. 10, 2641-2651, 2003.
doi:10.1109/TAP.2003.817560

11. Holloway, C. L. and E. F. Kuester, "Generalized sheet transition conditions for a metascreen — A fishnet metasurface," IEEE Trans. on Antennas and Propagation, Vol. 66, No. 5, 2414-2427, 2018.
doi:10.1109/TAP.2018.2809620

12. Holloway, C. L., E. F. Kuester, and A. Dienstfrey, "A homogenization technique for obtaining generalized sheet transition conditions for an arbitrarily shaped coated-wire grating," Radio Science, Vol. 49, No. 10, 813-850, 2014.
doi:10.1002/2014RS005556

13. Holloway, C. L., A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, "A discussion on the interpretation and characterization of metafilms-metasurfaces: The twodimensional equivalent of metamaterials," Metamaterials, Vol. 3, No. 2, 100-112, 2009.
doi:10.1016/j.metmat.2009.08.001

14. Holloway, C. L., E. F. Kuester, and A. Dienstfrey, "Characterizing metasurfaces/metafilms: The connection between surface susceptibilities and effective material properties," IEEE Ant. Wireless Prop. Lett., Vol. 10, 1507-1511, 2011.
doi:10.1109/LAWP.2011.2182591

15. Holloway, C. L. and E. F. Kuester, "A homogenization technique for obtaining generalized sheet transition conditions (GSTCs) for a metafilm embedded in a magneto-dielectric interface," IEEE Trans. on Antennas and Propagation, Vol. 64, No. 11, 4671-4686, 2016.
doi:10.1109/TAP.2016.2600764

16. Kuester, E. F. and E. Liu, "Average transition conditions for electromagnetic fields at a metascreen of nonzero thickness,", arXiv:1905.05871, arxiv.org, 2019.

17. Kuester, E. F., E. Liu, and N. J. Krull, "Average transition conditions for electromagnetic fields at a metascreen of vanishing thickness,", arXiv:1905.05869, arxiv.org, 2019.

18. Nicolson, A. M. and G. Ross, "Measurement of the intrinsic properties of materials by time domain techniques," IEEE Trans. Instrum. Meas., Vol. 19, No. 4, 377-382, 1970.
doi:10.1109/TIM.1970.4313932

19. Weir, W. B., "Automatic measurements of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, No. 1, 33-36, 1974.
doi:10.1109/PROC.1974.9382

20. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Review B, Vol. 65, 195104, 2002.
doi:10.1103/PhysRevB.65.195104

21. Ziolkowski, R. W., "Designs, fabrication, and testing of double negative metamaterials," IEEE Trans. on Antennas and Propagation, Vol. 51, No. 7, 1516-1529, 2003.
doi:10.1109/TAP.2003.813622

22. Kim, S., E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, "Boundary effects on the determination of the effective parameters of a metamaterials from normal incidence reflection and transmissions," IEEE Trans. on Antennas and Propagation, Vol. 59, No. 6, 2226-2240, 2011.
doi:10.1109/TAP.2011.2143679

23. 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.

24. Chen, X., T. M. Grezegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Review E, Vol. 70, 016608, 2004.
doi:10.1103/PhysRevE.70.016608

25. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, The Golm Press, Boulder, CO, 1969.

26. Weinstein, L. A., "On the electrodynamic theory of grids," Elektronika Bol’shikh Moshchnostei, P. L. Kapitza and L. A. Weinstein, editors, Vol. 2, 26–74, Moscow, Nauka, 1963 [in Russian; Engl. transl. in High-Power Electronics, Vol. 2, Chapter II, 14–48, Pergamon Press, Oxford, 1966].

27. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, 163, Institution of Electrical Engineers, London, 1995.
doi:10.1049/PBEW041E

28. Sakurai, T., "Theory of electromagnetic wave on metallic mesh and grating," J. Inst. Elec. Eng. Japan, Vol. 68, 144-145, 1948 [in Japanese].

29. Kontorovich, M. I., "Averaged boundary conditions at the surface of a grating with a square mesh," Radiotekh. Elektron, Vol. 8, 1506-1515, 1963 [in Russian; Engl. transl. in Radio Eng. Electron. Phys., Vol. 8, 1446–1454, 1963].

30. Ricoy, M. A. and J. L. Volakis, "Derivation of generalized transition/boundary conditions for planar multiple-layer structures," Radio Science, Vol. 25, No. 4, 391-405, 1990.
doi:10.1029/RS025i004p00391

31. Topsakal, E. and J. L. Volakis, "Surface integral equations for material layers modeled with tensor boundary conditions," Radio Science, Vol. 37, No. 4, 1053, 2002.
doi:10.1029/2000RS002377

32. Holloway, C. L., E. F. Kuester, and A. H. Haddab, "Using reflection and transmission coefficients to retrieve surface parameters for an anisotropic metascreen: With a discussion on conversion between TE and TM polarizations," Journal of Applied Phys., Vol. 125, 095102, 2019.
doi:10.1063/1.5050987

33. Holloway, C. L., M. A. Mohamed, and E. F. Kuester, "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

34. Holloway, C. L. and E. F. Kuester, "Equivalent boundary conditions for a perfectly conducting periodic surface with a cover layer," Radio Science, Vol. 35, No. 3, 661-681, 2000.
doi:10.1029/1999RS002162

35. Auriault, J. L., "Effective macroscopic description for heat conduction in periodic composites," Int. J. Heat Mass Transfer, Vol. 26, 861-869, 1983.
doi:10.1016/S0017-9310(83)80110-0

36. Artola, M. and M. Cessenat, "Un probleme raide avec homogeneisation en electromagnetisme," Comptes Rendus Acad. Sci. Paris, ser. I, Vol. 310, 9-14, 1990.

37. Holloway, C. L. and E. F. Kuester, "Impedance-type boundary conditions for a periodic interface between a dielectric and a highly conducting medium," IEEE Trans. on Antennas and Propagation, Vol. 48, No. 10, 1660-1672, 2000.
doi:10.1109/8.899683

38. Chen, Y. and R. Lipton, "Resonance and double negative behavior in metamaterials," Arch. Rat. Mech. Anal., Vol. 209, 835-868, 2013.
doi:10.1007/s00205-013-0634-8

39. Bouchitte, G., C. Bourel, and D. Felbacq, "Homogenization near resonances and artificial magnetism in three dimensional dielectric metamaterials," Arch. Rat. Mech. Anal., Vol. 225, 1233-1277, 2017.
doi:10.1007/s00205-017-1132-1