1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 46 Number 8, August 1998

Time-Domain Three-Dimensional Diffraction by the Isorefractive Wedge

Page 1148.

Abstract:

The extension of the Biot-Tolstoy exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described. The TM field generated by a Hertzian electric dipole can be represented by a vector potential parallel to the apex of the wedge and a scalar potential necessitated by the three dimensionality of the magnetic field. The derivation of the former is exactly that of the pressure in the corresponding acoustic situation [1], and a more efficient version of the lengthy details is presented herein. A Lorentz gauge determines the scalar potential from the vector potential, and the diffracted field contains impulsive and "switch-on" terms that cannot be evaluated in closed form. The ratio of arrival times, at a given point, of the geometrical optics and diffracted fields provides a convenient parameter, in addition to the usual metric-related variable, for graphically displaying this scalar potential.

References

1. A. M. J. Davis and R. W. Scharstein, "The complete extension of the Biot-Tolstoy solution to the density contrast wedge with sample calculations," J. Acoust. Soc. Amer., vol. 101, no. 4, pp. 1821-1835, Apr. 1997.
2. M. A. Biot and I. Tolstoy, "Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction," J. Acoust. Soc. Amer., vol. 29, no. 3, pp. 381-391, Mar. 1957.
3. R. S. Keiffer and J. C. Novarini, "A wedge assemblage method for 3-D acoustic scattering from sea surfaces: Comparison with a Helmholtz-Kirchhoff method," in Computational Acoustics--Volume 1, D. Lee, A. Cakmak, and R. Vichnevetsky, Eds.Amsterdam: Elsevier, 1990, pp. 67-81.
4. L. B. Felsen, "Diffraction of the pulsed field from an arbitrarily oriented electric or magnetic dipole by a perfectly conducting wedge," SIAM J. Appl. Math., vol. 26, no. 2, pp. 306-312, Mar. 1974.
5. V. A. Borovikov and B. Y. Kinber, Geometrical Theory of Diffraction.London, U.K.: IEE, 1994, pp. 352-355.
6. T. W. Veruttipong, "Time domain version of the uniform GTD," IEEE Trans. Antennas Propagat., vol. 38, pp. 1757-1764, Nov. 1990.
7. P. R. Rousseau and P. H. Pathak, "Time-domain uniform geometrical theory of diffraction for a curved wedge," IEEE Trans. Antennas Propagat., vol. 43, pp. 1375-1382, Dec. 1995.
8. L. Knockaert, F. Olyslager, and D. De Zutter, "The diaphanous wedge," IEEE Trans. Antennas Propagat., vol. 45, pp. 1374-1381, Sept. 1997.
9. P. L. E. Uslenghi, "Exact scattering by isorefractive bodies," IEEE Trans. Antennas Propagat., vol. 45, pp. 1382-1385, Sept. 1997.
10. E. Marx, "Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation," IEEE Trans. Antennas Propagat., vol. 41, pp. 1001-1008, Aug. 1993.
11. A. M. J. Davis, "Two-dimensional acoustical diffraction by a penetrable wedge," J. Acoust. Soc. Amer., vol. 100, pp. 1316-1324, Sept. 1996.
12. A. D. Rawlins, "Diffraction by a dielectric wedge," J. Inst. Math Appl., vol. 19, pp. 261-279, 1977.
13. D. S. Jones, Acoustic and Electromagnetic Waves.Oxford, U.K.: Clarendon, 1986, p. 462.
14. IMSL, Inc. User's Manual: FORTRAN Subroutines for Mathematical Applications, Houston, TX, 1991, p. 686.
15. R. W. Scharstein, "Mellin transform solution for the static line-source excitation of a dielectric wedge," IEEE Trans. Antennas Propagat., vol. 41, pp. 1675-1679, Dec. 1993; corrections vol. 42, p. 445, Mar. 1994).
16. K. I. Nikoskinen and I. V. Lindell, "Image solution for Poisson's equation in wedge geometry," IEEE Trans. Antennas Propagat., vol. 43, pp. 179-187, Feb. 1995.