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2005-04-23
Homogenization of Corrugated Interfaces in Electromagnetics
By
Progress In Electromagnetics Research, Vol. 55, 1-31, 2005
Abstract
A surface with periodic corrugations of sufficiently small periodicity is shown to be electromagnetically equivalent to an inhomogeneous transition region (slab). Explicit expressions for the inhomogeneous transition region are found for one-dimensional corrugations and for two-dimensional corrugations a local elliptic problem has to be solved in order to find the equivalent electromagnetic properties. The homogenized surface can be characterized by its surface impedance dyadic or its reflection dyadic. A few numerical examples illustrate the theory.
Citation
Gerhard Kristensson, "Homogenization of Corrugated Interfaces in Electromagnetics," Progress In Electromagnetics Research, Vol. 55, 1-31, 2005.
doi:10.2528/PIER05020302
References

1. Bensoussan, A., J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, Vol. 5, Studies in Mathematics and its Applications, North-Holland, Amsterdam, 1978.

2. Felbacq, D., "Comments on Photonic band gaps: Noncommuting limit and the 'acoustic band' ''," arXiv:cond-mat/0104488 v1, 2001.

3. Holloway, C. L. and E. F. Kuester, "Effective boundary conditions for rough surfaces with a thin cover," Antennas and Propagation Society, Vol. 1, 506-509, 1999.

4. Holloway, C. L. and E. F. Kuester, "A low-frequency model for wedge or pyramid absorber arrays—II: Computed and measured results," IEEE Trans. Electromagn. Compatibility, Vol. 36, No. 4, 307-313, 1994.
doi:10.1109/15.328860

5. Janaswamy, R., "Oblique scattering from lossy periodic surfaces with application to anechoic chamber absorbers," IEEE Trans. Antennas Propagat., Vol. 40, No. 2, 162-169, 1992.
doi:10.1109/8.127400

6. Kildal, P. S., "Artificially soft and hard surfaces in electromagnetics," IEEE Trans. Antennas Propagat., Vol. 38, No. 10, 1537-1544, 1990.
doi:10.1109/8.59765

7. Kristensson, G., "Homogenization of spherical inclusions," Progress In Electromagnetics Research, Vol. 42, 1-25, 2003.

8. Kristensson, G., S. Poulsen, and S. Rikte, "Propagators and scattering of electromagnetic waves in planar bianisotropic slabs — an application to frequency selective structures," Progress In Electromagnetics Research, Vol. 48, 1-25, 2004.
doi:10.2528/PIER04031503

9. Kristensson, G., P. Waller, and A. Derneryd, "Radiation efficiency and surface waves for patch antennas on inhomogeneous substrates," IEE Proc. — Microw. Antennas Propag., Vol. 150, No. 6, 477-483, 2003.
doi:10.1049/ip-map:20030617

10. Kuester, E. F. and C. L. Holloway, "A low-frequency model for wedge or pyramid absorber arrays—I: Theory," IEEE Trans. Electromagn. Compatibility, Vol. 36, No. 4, 300-306, 1994.
doi:10.1109/15.328859

11. McPhedran, R. C., N. A. Nicorovici, and L. C. Botten, "The TEM mode and homogenization of doubly periodic structures," J. Electro. Waves Applic., Vol. 11, No. 7, 981-1012, 1997.

12. Milton, G. W., The Theory of Composites, Cambridge University Press, Cambridge, U.K., 2002.

13. Nevard, J. and J. B. Keller, "Homogenization of rough boundaries and interfaces," SIAM J. Appl. Math., Vol. 57, No. 6, 1660-1686, 1997.
doi:10.1137/S0036139995291088

14. Nicorovici, N. A., R. C. McPhedran, and L. C. Botten, "Photonic band gaps for arrays of perfectly conducting cylinders," Phys. Rev. E, Vol. E52, No. 1, 1135-1145, 1995.
doi:10.1103/PhysRevE.52.1135

15. Nicorovici, N. A., R. C. McPhedran, and L. C. Botten, "Photonic band gaps: Noncommuting limits and the 'acoustic band'," Phys. Rev. Lett., Vol. 75, No. 8, 1507-1510, 1995.
doi:10.1103/PhysRevLett.75.1507

16. Rikte, S., G. Kristensson, and M. Andersson, "Propagation in bianisotropic media—reflection and transmission," TechnicalReportLUTEDX/(TEAT-7067)/1-31/(1998), 1-31, 1998.

17. Rikte, S., G. Kristensson, and M. Andersson, "Propagation in bianisotropic media—reflection and transmission," IEE Proc. Microwaves, Vol. 148, No. 1, 29-36, 2001.
doi:10.1049/ip-map:20010215

18. Sanchez-Palencia, E., Non-Homogeneous media and Vibration Theory, No. 127 in Lecture Notes in Physics, No. 127 in Lecture Notes in Physics, Springer-Verlag, Berlin, 1980.

19. Sihvola, A., Electromagnetic Mixing Formulae and Applications, IEE Electromagnetic Waves Series, 47, Institution of Electrical Engineers, 1999.

20. Sjöberg, D., C. Engström, G. Kristensson, D. J. N. Wall, and N. Wellander, "A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization," TechnicalReportLUTEDX/(TEAT-7119)/1-28/(2003), 1-28, 2003.