2018-12-19
Diffraction at Thick Curved Layers with a Nonuniform Dielectric Permittivity
By
Progress In Electromagnetics Research B, Vol. 83, 1-24, 2019
Abstract
In this paper, we obtain an asymptotic solution for the problem of electromagnetic diffraction at a thick curved dielectric layer with a nonuniform dielectric permittivity. We show that, in the case of thick layers, the main asymptotic approximation already comprises the curvature correction, verify the results by comparison with a solution obtained with the integral equation method, and offer to approximate the piecewise constant dielectric permittivity of a stratified layer with a continuous function.
Citation
Ilya O. Sukharevsky, "Diffraction at Thick Curved Layers with a Nonuniform Dielectric Permittivity," Progress In Electromagnetics Research B, Vol. 83, 1-24, 2019.
doi:10.2528/PIERB18092512
References

1. Fiscus, T. E. and G. P. Tricoles, "Multi-octave thick dielectric radome wall,", U.S. Patent No. 4,725,475, U.S. Patent and Trademark Office, Washington, DC, 1988.        Google Scholar

2. Hower, R. V. and S. V. Hoang, "Polyimide foam-containing radomes,", U.S. Patent No. 5.662.293, Sep. 2, 1997.
doi:10.1109/8.309998        Google Scholar

3. Glabe, J. R., "Radomes, aircraft and spacecraft including such radomes, and methods of forming radomes,", U.S. Patent No. 8.130.167, Mar. 6, 2012.
doi:10.1049/el:20010945        Google Scholar

4. Raring, J. W., D. F. Feezell, and N. Pfister, "Self-aligned multi-dielectric-layer lift off process for laser diode stripes,", U.S. Patent No. 8.143.148, Mar. 27, 2012.        Google Scholar

5. Day, T. and D. F. Arnone, "Lenses, optical sources, and their couplings,", U.S. Patent No. 7,796,341, Sep. 14, 2010.
doi:10.2528/PIER10012005        Google Scholar

6. Du Castel, F., "Tropospheric radiowave propagation beyond the horizon: International series of monographs in electromagnetic waves," Elsevier, Vol. 8, 2013.
doi:10.1134/S1064226912080128        Google Scholar

7. Kaklamani, D. I. and N. K. Uzunoglu, "Scattering from a conductive rectangular plate covered by a thick dielectric layer and excited from a dipole source or a plane wave," IEEE Trans. on Antennas and Propagation, Vol. 42, No. 8, 1065-1076, 1994.
doi:10.1109/LPT.2013.2247392        Google Scholar

8. Verma, A. K., et al., "Resonance frequency of rectangular microstrip antenna on thick substrate," Electronics Letters, Vol. 37, No. 23, 1373-1374, 2001.
doi:10.1016/0031-8914(49)90116-0        Google Scholar

9. Carpenter, M. P., M. M. Osward, and D. A. Gibbs, "Lens of gradient dielectric constant and methods of production,", U.S. Patent No. 6,433,936, U.S. Patent and Trademark Office, Washington, DC, 2002.
doi:10.1002/cpa.3160040111        Google Scholar

10. Chen, F., Q. Shen, and L. Zhang, "Electromagnetic optimal design and preparation of broadband ceramic radome material with graded porous structure," Progress In Electromagnetics Research, Vol. 105, 445-461, 2010.
doi:10.1121/1.1916627        Google Scholar

11. Balkhanov, V. K., L. K. Angarkhaeva, Y. B. Bashkuev, and A. G. Gantimurov, "The transmission and reflection coefficients of an electromagnetic wave for a gradient dielectric layer," Journal of Communications Technology and Electronics, Vol. 57, No. 11, 1160-1165, 2012.
doi:10.1063/1.1699779        Google Scholar

12. Park, Y. S., S. Seo, P. Gruenberg, and J. H. Lee, "Self-centering effect of a thickness-gradient dielectric of an electrowetting liquid lens," IEEE Photonics Technology Letters, Vol. 25, No. 6, 623-625, 2013.        Google Scholar

13. Bremmer, H., "The propagation of electromagnetic waves through a stratified medium and its WKB approximation for oblique incidence," Physica, Vol. 15, No. 7, 593-608, 1949.        Google Scholar

14. Bremmer, H., "The WKB approximation as the first term of a geometric-optical series," Comm. Pure Appl. Math., Vol. 4, No. 1, 105-115, 1951.        Google Scholar

15. Primakoff, H. and J. B. Keller, "Reflection and transmition of sound by thin curved shells," J. of the Acoustical Society of America, Vol. 19, No. 2, 820-832, 1947.        Google Scholar

16. Keller, J. B., "Reflection and transmission of electromagnetic waves by thin curved shells," J. of Appl. Physics, Vol. 21, 896-901, Sept. 1950.        Google Scholar

17. Sukharevskii, I. V., "Passage of electromagnetic waves through a radio-transparent layer," Radio Eng. Electron. Phys., Vol. 12, 191-197, 19671967; (transl. Radiotekhn. i Elektronika, Vol. 12, No. 2, 208-215).        Google Scholar

18. Sukharevsky, I. O., "Beyond geometrical optics: higher-order diffraction at thin curved dielectric layers," IEEE Trans. Antennas and Propagation, 2018 (accepted for publication).
doi:10.1109/TAP.2014.2331991        Google Scholar

19. Gukasov, Yu. G. and I. V. Sukharevskii, "Asymptotic treatment of short-wave radiation of dielectric-coated reflector antenna," Radio Eng. Electron. Phys., No. 5, 784-790, 1963.        Google Scholar

20. Kravchenko, A. G. and I. V. Sukharevsky, "Asymptotic solution of one class of short-wave diffraction problems for bodies with big (finite) conductivity," Proc. of V All-Union Symp. on Diffraction and Propagation of Waves, 118-124, 118–124, Leningrad, Publishing House ``Nauka", Jul. 13–17, 1970 (in Russian).        Google Scholar

21. Kravchenko, A. G., "On the high-frequency diffraction by good conductors," Radiotekh. Electron., Vol. 18, No. 1, 49-57, 1973 (in Russian).
doi:10.1016/0041-5553(73)90107-9        Google Scholar

22. Sommerfeld, A., "Theoretisches uber die Beugung der Rontgenstrahlen," Z. Math. Phys., Vol. 46, 11-96, 1901.        Google Scholar

23. Sukharevsky, I. O. and A. Altintas, "Validation of higher-order approximations and boundary conditions for lossy conducting bodies," IEEE Trans. Antennas and Propagation, Vol. 62, No. 9, 4656-4663, 2014.        Google Scholar

24. Semenyaka, E. N. and I. V. Sukharevsky, "Diffraction by slightly curved layered structures of big thickness," Proc. of V All-Union Symp. on Diffraction and Propagation of Waves, 118–124, Leningrad, Publishing House ``Nauka", Jul. 13–17, 1970 (in Russian).        Google Scholar

25. Semeniaka, Ye. N., "Asymptotic solution of the problem of diffraction of electromagnetic waves from a slightly bent dielectric layer of much greater thickness than the wavelength," Radio Eng. Electron. Phys., Vol. 18, No. 1, 41-49, (transl. from Radiotekh. Electron., 1973..        Google Scholar

26. Grinberg, S. I., E. N. Semenyaka, and I. V. Sukharevskii, "Short-wave asymptotic behaviour of Green's function in the problem of diffraction at a plane layer," USSR Comp. Math. and Math. Physics, Vol. 13, No. 3, 170-186, 1973, doi:10.1016/0041-5553(73)90107-9 (transl. from Zh. Vych. Mat. i Mat. Fiz., Vol. 13, No. 3, 670-682, 1973).        Google Scholar