volume | PIER Journals

Abstract

In a previous study [1] it was shown that the generalized soft-and-hard/DB (GSHDB) boundary has the unique property that the two eigen plane waves are reflected as from the PEC or PMC boundary, i.e., with reflection coefficients -1 or +1, for any angle of incidence. The present paper discusses a more general class of boundaries by requiring that the reflection coefficients R₊ and R_-, corresponding to the two eigen plane waves, have opposite values, R_±=±R with R independent of the angle of incidence. It turns out that there are two possibilities, R=1 for the class of GSHDB boundaries, and R=j, defining an extension of the class of perfect electromagnetic conductor (PEMC) boundaries. Matched waves at, and plane-waves reflected from, boundaries of the latter class are studied in the paper.

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, "Boundary Conditions in Electromagnetics," Wiley and IEEE Press, 2020.

3. Hoppe, D. J. and Y. Rahmat-Samii, Impedance Boundary Conditions in Electromagnetics, Taylor & Francis, 1995.

4. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, IEE, 1995.
doi:10.1049/PBEW041E

5. Sievenpiper, D., L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yablonovitch, "High-impedance electromagnetic surfaces with a forbidden frequency band," IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 11, 2059-2074, Nov. 1999.
doi:10.1109/22.798001

6. Fong, B. H., J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, "Scalar and tensor holographic artificial impedance surfaces," IEEE Trans. Antennas Propag., Vol. 58, No. 10, 3212-3221, Oct. 2010.
doi:10.1109/TAP.2010.2055812

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

8. 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 Propag. Mag., Vol. 54, No. 2, 10-35, Apr. 2012.
doi:10.1109/MAP.2012.6230714

9. Munk, B., Frequency Selective Surfaces: Theory and Design, Wiley, 2000.
doi:10.1002/0471723770

10. Maci, S. and A. Cucini, "FSS-based EBG metasurfaces," Metamaterials: Physics and Engineering Explorations, ed., N. Engheta and R. Ziolkowski, IEEE, Piscataway, NJ, 2006.

11. Gok, G. and A. Grbic, "Tailoring the phase and power flow of electromagnetic fields," Phys. Rev. Lett., Vol. 111, 233904, 2013.
doi:10.1103/PhysRevLett.111.233904

12. Lavigne, G. and C. Caloz, "Magnetless reflective gyrotropic spatial isolator metasurface," New Journal of Physics, Vol. 23, No. 7, 1-11, Jul. 2021.

13. Monticone, F., C. A. Valagiannopoulos, and A. Alu, "Aberration-free imaging based on parity-time symmetric nonlocal metasurfaces," Phys. Rev. X, Vol. 6, 041018, 2016.

14. Kildishev, A. V., A. Boltasseva, and V. M. Shalaev, "Planar photonics with metasurfaces," Science, Vol. 339, 1232009, 2013.
doi:10.1126/science.1232009

15. Yu, N. and F. Capasso, "Flat optics with designer metasurfaces," Nature Mater., Vol. 13, 13950, 2014.

16. 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

17. Shahvarpour, A., T. Kodera, A. Parsa, and C. Caloz, "Arbitrary electromagnetic conductor boundaries using Faraday rotation in a grounded ferrite slab," IEEE Trans. Microwave Theory Tech., Vol. 58, No. 11, 2781-2793, 2010.
doi:10.1109/TMTT.2010.2078010

18. Lindell, I. V. and A. Sihvola, "Electromagnetic wave re ection from boundaries defined by general linear and local conditions," IEEE Trans. Antennas Propag., Vol. 65, No. 9, 4656-4663, 2017.
doi:10.1109/TAP.2017.2723913

19. Lindell, I. V. and A. Sihvola, "Transformation method for problems involving Perfect Electromagnetic Conductor (PEMC) structures," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 3012-3018, 2005.
doi:10.1109/TAP.2005.854524

20. Lindell, I. V. and A. Sihvola, "Generalization of perfect electromagnetic conductor boundary," IEEE Trans. Antennas Propag., Vol. 68, No. 11, 7406-7413, 2020.
doi:10.1109/TAP.2020.2996780

21. Lindell, I. V. and A. Sihvola, "Electromagnetic boundary condition and its realization with anisotropic metamaterial," Phys. Rev. E, Vol. 79, No. 2, 026604 (, 2009.
doi:10.1103/PhysRevE.79.026604

22. Kildal, P.-S., "Definition of artificially soft and hard surfaces for electromagnetic waves," Electron. Lett., Vol. 24, 168-170, 1988.
doi:10.1049/el:19880112

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

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

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

26. Lindell, I. V., Methods in Electromagnetic Field Analysis, 2nd Ed., Wiley, 1995.

Prof. Ismo Veikko Lindell

Dr. Ari Sihvola