volume | PIER Journals

Abstract

Metasheet structures together with bulk composite dielectric layers can be used for antenna radomes, absorbers, and band gap structures. Transmission (T) and reflection (G) coefficients for a plane wave incident at any angle upon a metasheet embedded in a dielectric layer are considered. These metasheets are either patch-type or an aperture-type, and they can be either single-layered or multi-layered. To calculate T and Γ for a patch-type metasheet, a concise unified matrix approach is derived using the Generalized Sheet Transition Conditions (GSTC). The Babinet duality principle is utilized to get T and G for single-layered aperture-type metasheets (as complementary to the patch-type ones) at an arbitrary angle of incidence. The T-matrix approach is applied to calculate characteristics of multilayered metasheet structures containing a cascade of metasheets and dielectric slabs. In this paper, the minimum distance for neglecting higher-order evanescent mode interactions between the metasheets has been determined. Computed results based on the proposed analytical approach are compared with the fullwave numerical simulations. The analytical results are verified for satisfying the energy balance condition.

1. Pokrovsky, A. L. and A. L. Efros, "Electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett., Vol. 89, 093901, 2002.
doi:10.1103/PhysRevLett.89.093901

2. Rahmat-Samii, Y., "The marvels of electromagnetic band gap (EBG) structures: Novel microwave and optical applications," Proc. Microwave and Optoelectronics Conference, 265-275, Sep. 2003.

3. Foteinopoulou, S., E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refractive index," Phys. Rev. Lett., Vol. 90, 107402, 2003.
doi:10.1103/PhysRevLett.90.107402

4. Shvets, G., "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B, Vol. 67, 035109, 2003.
doi:10.1103/PhysRevB.67.035109

5. Krowne, C. M. and Y. Zhang, Physics of Negative Refraction and Negative Index Materials, Springer Series in Materials Science, Vol. 98, Springer, 2007.

6. Wu, T. K., "Frequency Selective Surface and Grid Array," Wiley, 1995.

7. Munk, B. A., Frequency Selective Surfaces: Theory and Design, Wiley, New York, 2000.
doi:10.1002/0471723770

8. Munk, B. A., Metamaterials, Critique and Alternatives, Wiley, 2007.

9. Knott, E. F., J. F. Shaeffer, and M. T. Tuley, "Radar Cross Section: Its Prediction, Measurement and Reduction," Ch. 9, Artech House, 1986.

10. Narayan, S., K. Prasad, R. U. Nair, and R. M. Jha, "A novel EM analysis of double-layered thick FSS based on MM-GSM technique for radome applications," Progress In Electromagnetics Research Letters, Vol. 28, 53-62, 2012.
doi:10.2528/PIERL11101710

11. Mahdy, M. R. C., M. R. A. Zuboraj, A. A. N. Ovi, and M. A. Matin, "Novel design of triple band rectangular patch antenna loaded with metamaterial," Progress In Electromagnetics Research Letters, Vol. 21, 99-107, 2011.

12. Xu, Z., W. Lin, and L. Kong, "Controllable absorbing structure of metamaterial at microwave," Progress In Electromagnetics Research, Vol. 69, 117-125, 2007.
doi:10.2528/PIER06120801

13. Mittra, R., C. H. Chan, and T. Cwik, "Techniques for analyzing frequency selective surfaces-a review," Proceedings of the IEEE , Vol. 76, No. 12, 1593-1615, Dec. 1988.
doi:10.1109/5.16352

14. Lockyer, D. S., J. C. Vardaxoglou, and R. A. Simpkin, "Complementary frequency selective surfaces," IEE Proceedings --- Microwaves, Antennas and Propagation, Vol. 147, No. 6, 501-507, Dec. 2000.
doi:10.1049/ip-map:20000799

15. Moss, C. D., T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Numerical studies of left-handed metamaterials," Progress In Electromagnetics Research, Vol. 35, 315-334, 2002.
doi:10.2528/PIER02052409

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

17. Levy-Nathanson, R. and D. J. Bergman, "Decoupling and testing of the generalized Ohm's law," Phys. Rev. B, Vol. 55, 5425-5439, 1997.
doi:10.1103/PhysRevB.55.5425

18. Lee, S. W., G. Zarrillo, and C. L. Law, "Simple formulas for transmission through periodic metal grids or plates," IEEE Trans. Antennas Propagat., Vol. 30, No. 5, 904-909, 1982.
doi:10.1109/TAP.1982.1142923

19. Kazantsev, Y. N., V. P. Mal'tsev, and A. D. Shatrov, "Diffraction of a plane wave from a two-dimensional grating of elements with inductive and capacitive coupling," Journal of Communications Technology and Electronics, Vol. 46, No. 12, 1303-1313, Dec. 2001.

20. Yatsenko, V. V., S. I. Maslovski, S. A. Tretyakov, S. L. Prosvirnin, and S. Zouhd, "Plane-wave reflection from double arrays of small magnetoelectric scatterers," IEEE Trans. Antennas Propagat., Vol. 51, No. 1, 2-11, Jan. 2003.
doi:10.1109/TAP.2003.808569

21. Holloway, C. L., M. A. Mohamed, and E. F. Kuester, "Reflection and transmission properties of a metafilm with application to a controllable surface composed of resonant particles," IEEE Trans. Electromag. Compat., Vol. 47, No. 4, 1-13, Oct. 2005.

22. De Meulenaere, F. and J. Van Bladel, "Polarizability of some small apertures," IEEE Trans. Antennas Propagat., Vol. 25, No. 2, 198-205, Mar. 1977.
doi:10.1109/TAP.1977.1141568

23. Fabrikant, V. I., "Magnetic polarizability of small apertures: Analytical approach," J. Phys. A: Math. Gen., Vol. 20, 328-338, 1987.
doi:10.1088/0305-4470/20/2/018

24. McDonald, N. A., "Polynomial approximations for the electric polarizabilities of some small apertures," IEEE Trans. Microw. Theory Techn., Vol. 33, No. 11, 1146-1149, Nov. 1985.
doi:10.1109/TMTT.1985.1133186

25. McDonald, N. A., "Polynomial approximations for the transverse magnetic polarizabilities of some small apertures," IEEE Trans. Microw. Theory Techn., Vol. 35, No. 1, 20-23, Jan. 1987.
doi:10.1109/TMTT.1987.1133589

26. Podosenov, S. A., A. A. Sokolov, and S. V. Al'betkov, "Method for determining the electric and magnetic polarizability of arbitrarily shaped conducting bodies," IEEE Trans. Electromag. Compat., Vol. 39, No. 1, 1-10, Feb. 1997.
doi:10.1109/15.554689

27. 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 Propagat., Vol. 51, No. 10, 2572-2581, Oct. 2003.
doi:10.1109/TAP.2003.817562

28. Simovski, C. R. and P. A. Belov, "Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators," IEEE Trans. Antennas Propagat., Vol. 51, No. 10, 2582-2591, Oct. 2003.
doi:10.1109/TAP.2003.817554

29. Sauviac, B., "Double split-ring resonators: Analytical modeling and numerical simulations," Electromagnetics, Vol. 24, No. 5, 317-338, 2004.
doi:10.1080/02726340490457890

30. Simovski, C. R., M. S. Kondratjev, P. A. Belov, and S. A. Tretyakov, "Interaction effects in two-dimensional bian-isotropic arrays," IEEE Trans. Antennas Propagat., Vol. 47, No. 9, 1429-1439, Sept. 1999.
doi:10.1109/8.793323

31. Collin, R. E., Field Theory of Guided Waves, 2nd Ed., 1991.

32. Maslovski , S. I. and S. A. Tretyakov, "Full-wave interaction field in two-dimensional arrays of dipole scatterers," Int. J. Electron. Commun., Vol. 53, 135-139, Arch. Elek. Ubertragungstechn.(AEU), 1999.

33. Idemen, M., "Straightforward derivation of boundary conditions on sheet simulating an anisotropic thin layer," Electron. Lett., Vol. 24, 663-665, 1988.
doi:10.1049/el:19880449

34. Idemen, M., "Universal boundary relations of the electromagnetic field," J. Phys. Soc. Japan., Vol. 59, 71-80, 1990.

35. Kong, J. A., "Electromagnetic Wave Theory," Wiley, 1990.

36. Jackson, J. D., "Classical Electrodynamics," Wiley, 1999.

37. Inan, U. and A. Inan, Electromagnetic Waves, Ch. 3.5, Prentice Hall, New Jersey, 2000.

38. Weber, R. J., Introduction to Microwave Circuits: Radio Frequency and Design Application, Ch. 2, 25{27, IEEE, New York, 2001.

39. Eggimann, W. H. and R. E. Collin, "Dynamic interaction fields in a two-dimensional lattice," IEEE Trans. Microw. Theory Techn., Vol. 9, No. 2, 110-115, Mar. 1961.
doi:10.1109/TMTT.1961.1125284

40. Eggimann, W. H., "Higher-order evaluation of electromagnetic diffraction by circular disks," IEEE Trans. Microw. Theory Techn., Vol. 9, No. 5, 408-418, Sep. 1961.
doi:10.1109/TMTT.1961.1125362

41. Huang, J. Y., P. C. Ravva, M. Y. Koledintseva, R. E. DuBroff, J. L. Drewniak, B. Archambeault,K. N. Rozanov "Design of a meta¯lm-composite dielectric shielding structure using a genetic algorithm," Progress In Electromagnetics Research Symposium, 297-301, Cambridge, MA, USA, Mar. 26-29, 2006.

42. Koledintseva, M. Y., J. L. Drewniak, R. E. DuBroff, K. N. Rozanov, B. Archambeault, "Modeling of shielding omposite materials and structures for microwave frequencies," Progress In Electromagnetic Research B, Vol. 15, 197-215, 2009.
doi:10.2528/PIERB09050410

Professor Marina Koledintseva

Dr. Jingyu Huang

Professor James Drewniak

Dr. Richard E. DuBroff

Dr. Bruce Archambeault