volume | PIER Journals

Abstract

Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is studied. Expressing the boundary conditions in terms of a generalized impedance dyadic, the self-dual boundaries fall in two sets depending on symmetry or antisymmetry of the impedance dyadic. Previously known cases are found to appear as special cases of the general theory. Plane-wave reflection from boundaries defined by each of the two cases of self-dual conditions are analyzed and waves matched to the corresponding boundaries are determined. As a numerical example, reflection from a special case, the self-dual EH boundary, is computed for two planes of incidence.

1. Lindell, I. V. and A. Sihvola, "Electromagnetic boundaries with PEC/PMC equivalence," Progress In Electromagnetics Research Letters, Vol. 61, 119-123, 2016.
doi:10.2528/PIERL16061805

2. Lindell, I. V. and A. Sihvola, "Electromagnetic wave reflection from boundaries defined by general linear and local conditions," IEEE Trans. Antennas Propag., Vol. 5, No. 9, 4656-4663, September 2017.
doi:10.1109/TAP.2017.2723913

3. Lindell, I. V. and A. Sihvola, Boundary Conditions in Electromagnetics, Wiley and IEEE Press, Hoboken, NJ, 2020.

4. Lindell, I. V. and A. Sihvola, "Perfect electromagnetic conductor," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 7, 861-869, 2005.
doi:10.1163/156939305775468741

5. Sihvola, A. and I. V. Lindell, "Perfect electromagnetic conductor medium," Ann. Phys., Vol. 17, 787-802, Berlin, September/October 2008.

6. Lindell, I. V., Methods for Electromagnetic Field Analysis, 2nd Ed., Wiley and IEEE Press, Piscataway, N.J., 1995.

7. Kildal, P.-S., "Definition of artificially soft and hard surfaces in electromagnetics," Electron. Lett., Vol. 24, 168-170, 1988.
doi:10.1049/el:19880112

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

9. Lindell, I. V., "Generalized soft-and-hard surface," IEEE Trans. Antennas Propag., Vol. 50, No. 7, 926-929, 2002.
doi:10.1109/TAP.2002.800698

10. Rumsey, V. H., "Some new forms of Huygens' principle," IRE Trans. Antennas Propag., Vol. 7, S103-S116, December 1959.
doi:10.1109/TAP.1959.1144766

11. Lindell, I. V. and A. Sihvola, "DB boundary as isotropic soft surface," Proc. Asian Pacific Microwave Conf., 4 pages, Hong Kong, December 2008.

12. Lindell, I. V. and A. Sihvola, "Electromagnetic boundary conditions defined in terms of normal field components," IEEE Trans. Antennas Propag., Vol. 58, No. 4, 1128-1135, April 2010.
doi:10.1109/TAP.2010.2041149

13. Lindell, I. V. and A. Sihvola, "Soft-and-hard/DB boundary conditions realized by a skewon-axion medium," IEEE Trans. Antennas Propag., Vol. 61, No. 2, 768-774, February 2013.
doi:10.1109/TAP.2012.2223445

14. Lindell, I. V. and A. Sihvola, "Generalized soft-and-hard/DB boundary," IEEE Trans. Antennas Propag., Vol. 65, No. 1, 226-233, January 2017.
doi:10.1109/TAP.2016.2628360

15. Heaviside, O., Electrical Papers, New York, Chelsea, 1970; reprint of the first edition, Vol. 1, 447; Vol. 2, 172–175, London, 1892; The original articles were respectively published in The Electrician, 306, 1885, and Phil. Mag., 118, August 1886.

16. Lindell, I. V. and A. H. Sihvola, "Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 3005-3011, September 2005.
doi:10.1109/TAP.2005.854519

17. Fushchich, W. I. and A. G. Nikitin, "On the new symmetries of Maxwell equations," Czech. J. Phys., Vol. B32, 476-480, 1982.
doi:10.1007/BF01596203

18. Mignaco, J. A., "Electromagnetic duality, charges, monopoles, topology, ...," Braz. J. Phys., Vol. 31, No. 2, 2001.
doi:10.1590/S0103-97332001000200014

19. Lindell, I. V., A. Sihvola, P. Yl¨a-Oijala, and H. Wallen, "Zero backscattering from self-dual objects of finite size," IEEE Trans. Antennas Propag., Vol. 57, No. 9, 2725-2731, September 2009.
doi:10.1109/TAP.2009.2027180

20. Lindell, I. V. and A. Sihvola, "Generalization of perfect electromagnetic conductor (PEMC) boundary,", arXiv:1912.00436v1 [physics.class-ph], December 1, 2019.
doi:10.1109/TAP.2009.2027180

21. Liu, F., S. Xiao, A. Sihvola, and J. Li, "Perfect co-circular polarization reflector: A class of reciprocal perfect conductors with total co-circular polarization reflection," IEEE Trans. Antennas Propag., Vol. 62, No. 12, 6274-6281, 2014.
doi:10.1109/TAP.2014.2364298

22. Tedeschi, N., F. Frezza, and A. Sihvola, "Reflection and transmission at the interface with an electric-eagnetic uniaxial medium with application to boundary conditions," IEEE Trans. Antennas Propag., Vol. 61, No. 11, 5666-5675, November 2013.
doi:10.1109/TAP.2013.2275749

Prof. Ismo Veikko Lindell

Dr. Ari Sihvola