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 9, September 1998

Ray-Optical Prediction of Radio-Wave Propagation Characteristics in Tunnel Environments-- Part 1: Theory

Page 1328.

Abstract:

A tunnel is modeled as congregates of walls, with the wall being approximated by uniform impedance surface. The aim is to get a solution for a canonical problem of a wedge with uniform impedance surface. The diffraction by a right-angle wedge with different impedance boundary conditions at its two surfaces is first considered. A functional transformation is used to simplify the boundary conditions. The eigenfunction solutions for the transformed functions are replaced by integral representations, which are then evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. The asymptotic solution is interpreted ray optically to obtain the diffraction coefficient for the uniform geometrical theory of diffraction (UTD). The obtained diffraction coefficients are related directly to Keller diffraction coefficients in uniform version. The total field is continuous across the shadow of the geometrical optics fields.

References

1. R. G. Kouyouijian and P. H. Pathak, "A uniform geometric theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, vol. 62, pp. 1448-1461, Nov. 1974.
2. G. D. Malyughinets, Dokl. Akad. Nauk, vol. 121, no. 3, p. 436, 1958.
3. --, Annal. Phys., vol. 6, nos. 1/2, pp. 107-112, 1960.
4. A. S. Peters, "Water waves over sloping beaches and the solution of a mixed boundary value problem for (\nabla^2-k^2)\phi =0 in a sector," Commun. Pure Appl. Math., vol. 5, pp. 87-108, 1952.
5. T. B. A. Senior, "Diffraction by an imperfectly conducting wedge," Commun. Pure Appl. Math., vol. 12, pp. 337-372, 1959.
6. L. B. Felson, "Field solution for a class of corrugated wedge and cone surface," Polytechnic Inst. Brooklyn, NY, Microwave Res. Inst., Memo 32, July 1957.
7. A. Mohsen and M. A. K. Hamid, "Diffraction by a dielectric-loaded wedge," Radio Sci., vol. 8, no. 1, pp. 71-80, Jan. 1973.
8. W. D. Burnside and K. W. Bergener, "High-frequency scattering by thin lossless dielectric slab," IEEE Trans. Antennas Propagat., vol. 31, no. 1, pp. 104-110, Jan. 1983.
9. R. G. Rojas, "Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces," IEEE Trans. Antennas Propagat., vol. 36, pp. 956-970, July 1988.
10. G. Pelosi, S. Maci, R. Tiberio, and A. Michaeli, "Incremental length diffraction coefficients for an impedance wedge," IEEE Trans. Antennas Propagat., vol. 40, pp. 1201-1210, Oct. 1992.
11. Y. Hwang, "The diffraction at the edge of a uniform impedance surface," Ph.D. dissertation, Dept. Elect. Eng., The Ohio State University, Columbus, OH, 1973.
12. H. Lewy, "Waves on sloping beaches," Bull. Amer. Math. Soc., vol. 52, pp. 737-773, 1946.
13. J. J. Stoker, "Surface waves in water of variable depth," Quart. Appl. Math., vol. 5, pp. 1-54, 1947.
14. S. N. Karp and F. C. Karal, "Vertex excited surface waves on one face of a right-angle wedge," New York Univ., Inst. Math. Sci., Div. Electromagn. Res., Rep. EM-124, 1959.
15. --, "Generalized impedance boundary conditions with applications to surface wave structures," in Proc. Symp. Electromagn. Wave Theory, Delft, The Netherlands, Sept. 1965.
16. T. S. Chu, "Surface wave diffraction and its relationship to surface wave antennas," Ph.D. dissertation, Dept. Elect. Eng., The Ohio State Univ., Columbus, OH, 1960.
17. F. C. Karal, S. N. Karp, T. S. Chu, and R. G. Kouyoumjian, "Scattering of a surface wave by a discontinuity in the surface reactance on a right-angle wedge," Commun. Pure Appl. Math., vol. 14, pp. 35-48, Feb. 1961.
18. T. S. Chu, R. G. Kouyoumjian, F. C. Karal, and S. N. Karp, "The diffraction of surface waves by a terminated structure in the form of right-angled bend," IEEE. Trans. Antennas Propagat., vol. 10, pp. 679-686, Nov. 1962.
19. S. N. Karp, "Two-dimensional Green's function for a right-angled wedge under an impedance boundary condition," Commun. Pure Appl. Math., vol. 13, pp. 203-216, 1960.
20. H. M. MacDonald, Electric Waves.Cambridge, MA: Cambridge Univ. Press, 1902, pp. 186-198.
21. P. H. Pathak and R. G. Kouyoumjian, "The dyadic diffraction coefficient for a perfectly conducting wedge," Electrosci. Lab., Dept. Elect. Eng., The Ohio State Univ., Rep. 2183-2184, June, 1970.
22. R. Tiberio, G. Pelosi, and G. Manara, "A uniform GTD formulation for the diffraction by a wedge with impedance wedge," IEEE Trans. Antennas Propagat., vol. AP-33, pp. 867-872, Aug. 1985.