volume | PIER Journals

Abstract

igh-frequency asymptotic expansions of electric and magnetic fields are obtained at a perfectly conducting smooth 2-D surface illuminated by a plane incident wave in two cases of TE and TM linear polarization. Diffraction corrections up to the second order of the inverse large parameter p = ak (where a is a curvature radius at the specularly reflected point, and k is a field wavenumber) to the geometrical optics fields, and specifically to their phases, backscattering cross-sections (HH and VV for TE and TM polarizations, correspondingly), as well as the polarization ratio HH/VV, are derived for the specular points of a general form. These general results are applied to backscattering from cylinders with conical section directrixes (circle, parabola, ellipse and hyperbola), and a number of new compact explicit equations are derived, especially for elliptic and hyperbolic cylinders illuminated at an arbitrary incidence angle relative to their axes of symmetry.

1. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, Part I, 1953.

2. Watson, G. N., "The diffraction of electrical waves by the earth," Proc. Roy. Soc. (London), Vol. A95, 83-99, 1918.

3. Wait, J. R., Electromagnetic Radiation from Cylindrical Structures, Pergamon, 1959.

4. Kouyoumjian, R. G., "Asymptotic high-frequency methods," Proc. IEEE, Vol. 53, No. 8, 864-876, 1965.

5. Bowman, J. J., T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, Hemisphere Publishing Corp., 1987.

6. Keller, J. B., R. M. Lewis, and B. D. Seckler, "Asymptotic solution of some diffraction problems," Comm. Pure Appl. Mathem., Vol. 9, 207-265, 1956.

7. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Sci. Am., Vol. 52, 116-130, 1962.

8. Babic, V. M. and V. S. Buldyrev, Short-wavelength Diffraction Theory, Springer-Verlag, 1991.

9. Borovikov, V. A. and B. Ye. Kinber, Geometrical Theory of Diffraction, The Institution of Electrical Engineers, 1994.

10. Kravtsov, Yu. A. and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag, 1990.

11. Fuks, I. M., "Reflection and refraction of a wave of arbitrary shape on a curvilinear surface (in Russian)," Izv. VUZ., Vol. 8, No. 6, 772-779.

12. Gel'chinskii, B. Ya., "Reflection and refraction of an elastic wave of arbitrary form in the case of a curved interface," Soviet Phys. -Doklady, Vol. 3, No. 1, 186-188, 1958.

13. Fok, V. A., "Generalization of reflecting formulas to the case of reflection of an arbitrary wave from a surface of arbitrary shape," Soviet Phys.-JTF, Vol. 20, No. 11, 961-978, 1950.

14. Keller, J. B. and H. B. Keller, "Determination of reflected and transmitted fields by geometrical optics," J. Opt. Soc. Am., Vol. 40, No. 1, 48-52, 1950.

15. Bass F. G. and I. M. Fuks, Wave Scattering from Statistical ly Rough Surfaces (in Russian), Wave Scattering from Statistical ly Rough Surfaces (in Russian), Vol. 93, Nauka.

16. Schensted, C. E., "Electromagnetic and acoustical scattering by a semi-infinite body of revolution," J. Appl. Phys., Vol. 26, 306-308, 1955.
doi:10.1063/1.1721982

17. Lee, S.-W., "Electromagnetic reflection from a conducting surface: geometrical optics solution," IEEE Trans. Antennas Propagat., Vol. AP-23, No. 2, 184-191, 1975.
doi:10.1109/TAP.1975.1141040

18. Fuks, I. M., "High-frequency asymptotic expansions of a backscattered cross-section and HH/VV polarization ratio for smooth two-dimensional surfaces," Waves Random Media, Vol. 14, 143-156, 2004.
doi:10.1088/0959-7174/14/2/005

19. West, J. C., "Low-grazing-angle (LGA) sea-spike backscattering from plunging breaker crests," IEEE Trans. Geosci. Remote Sensing, Vol. 40, 523-526, 2002.
doi:10.1109/36.992830

20. Brekhovskikh, L. M., "Wave diffraction by a rough surface," Parts 1 and 2, Vol. 23, No. 3(9), 289-304, 1952.

21. Isakovich, M. A., "Wave scattering from a statistically rough surface," Sov. Phys. JETF, Vol. 23, No. 3(9), 305-314, 1952.

22. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, 1972.

Professor Iosif Fuks