Wiener-Hopf solution for impenetrable wedges at skew incidence

IEEE Transactions on Antennas and Propagation

Volumn 54, Issue 9, 2006, Pages 2472-2485

  Daniele, Vito G ^b,c   Lombardi, Guido ^a,b  

^a IEEE   (Italy)

^b POLITECNICO DI TORINO   (Italy)

^c ISTITUTO SUPERIORE MARIO BOELLA   (Italy)

Author keywords

Diffraction; Electromagnetic diffraction; Electromagnetic surface waves; Fredholm integral equations; Geometrical theory of diffraction (GTD); Uniform theory of diffraction (UTD); Wedges; Wiener Hopf method

Indexed keywords

ELECTROMAGNETIC SURFACE WAVES; GEOMETRICAL THEORY OF DIFFRACTION (GTD); SKEW INCIDENCE; UNIFORM THEORY OF DIFFRACTION (UTD); WIENER HOPF METHOD;

BOUNDARY VALUE PROBLEMS; ELECTROMAGNETIC WAVE DIFFRACTION; PROBLEM SOLVING; SURFACE WAVES;

INTEGRAL EQUATIONS;

EID: 33947170356     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2006.880723     Document Type: Article

References (55)

1. G. D. Malyuzhinets, "Excitation, reflection and emission of surface waves from a wedge with given face impedances," Sov. Phys. Dokl., vol. 3, pp. 752-755, 1958.
2. A. V. Osipov and A. N. Norris, "The Malyuzhinets theory for scattering from wedge boundaries: A review," Wave Motion, vol. 29, pp. 313-340, 1999.
3. T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics. London, U.K.: Institution of Electrical Engineers, 1995.
4. B. Budaev, Diffraction by Wedges. London, UK: Longman Scientific, 1995.
5. V. S. Buldyrev and M. A. Lyalinov, Mathematical Methods in Modern Diffraction Theory. Tokyo, Japan: Science House, 2001.
6. G. Pelosi and J. L. Volakis, Eds., "The centennial of Sommerfield's diffraction problem" Electromagnetics (Special Issue), vol. 18, no. 3, May-Jun. 1998.
7. J. M. L. Bernard, "Diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory; A new class of canonical cases," J. Phys. A: Math. Gen., vol. 31, no. 2, pp. 595-613, Jan. 1998.
8. G. Pelosi, G. Manara, and P. Nepa, "Electromagnetic scattering by a wedge with anisotropic impedance faces," IEEE Antennas Propag. Ma., vol. 40, pp. 29-35, Dec. 1998.
9. M. A. Lyalinov and N. Y. Zhu, "Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: Oblique incidence of a plane electromagnetic wave," IEEE Trans. Antennas Propag., vol. 51, pp. 1216-12201 Jun. 2003.
10. G. Manara and P. Nepa, "Electromagnetic diffraction of an obliquely incident plane wave by a right-angled anisotropic impedance wedge with a perfectly conducting face," IEEE Trans. Antennas Propag., vol. 48, pp. 547-565, Apr. 2000.
11. G. Manara, P. Nepa, and G. Pelosi, "Skew incidence diffraction by an anisotropic impedance half plane with a PEC face and arbitrarily oriented anisotropy axes," IEEE Trans. Antennas Propag., vol. 52, pp. 487-496, Feb. 2004.
12. _, "High-frequency EM scattering by edges in artificially hard and soft surfaces illuminated at oblique incidence," IEEE Trans. Antennas Propag., vol. 48, pp. 790-800, May 2000.
13. P. Nepa, G. Manara, and A. Armogida, "Electromagnetic scattering by anisotropic impedance half and full planes illuminated at oblique incidence," IEEE Trans. Antennas Propag., vol. 49, pp. 106-108, Jan. 2001.
14. Y. A. Antipov and V. V. Silvestrov, "Vector functional-difference equation in electromagnetic scattering," IMA J. Appl. Math., no. 69, pp. 27-69, 2004.
15. _, "Second-order functional-difference equations - I: Method of the Riemann-Hilbert problem on Riemann surfaces," Q. J. Mech. Appl. Math., vol. 57, no. 2, pp. 245-265. 2004.
16. _, "Second-order functional-difference equations - II: Scattering from a right-angled conductive wedge for E-polarization," Q. J. Mech. Appl. Math., vol. 57, no. 2, pp. 267-313, 2004.
17. C. Demetrescu, "A general solution of the second-order difference equation occurring in diffraction theory," Radio Sci., no. 31, pp. 461-467, 1996.
18. T. B. A. Senior and S. R. Legault, "Second-order difference equations in diffraction theory," Radio Sci., no. 35, pp. 683-690, 2000.
19. C. Demetrescu, C. C. Constantinou, and M. J. Mehler, "Diffraction by a right-angled resistive wedge," Radio Sci., no. 33, pp. 39-53, 1998.
20. S. R. Legault and T. B. A. Senior, "Solution of a second-order difference equation using the bilinear relations of Riemann," J. Math. Phys., no. 43, pp. 1598-1621, 2002.
21. C. Demetrescu, C. C. Constantinou, M. J. Mehler, and B. V. Budaev, "Diffraction by a resistive sheet attached to a two-sided impedance plane," Electromagnetics, no. 18, pp. 315-332, 1998.
22. H. J. Bilow, "Scattering by an infinite wedge with tensor impedance boundary conditions - A moment method/physical optics solution for the currents," IEEE Trans. Antennas Propag., vol. 39, pp. 767-773, Jun. 1991.
23. G. Pelosi, G. Manara, and P. Nepa, "A UTD solution for the scattering by a wedge with anisotropic impedance faces: Skew incidence case," IEEE Trans. Antennas Propag., vol. 46, no. 4, pp. 579-588, Apr. 1998.
24. G. Pelosi, S. Selleri, and R. D. Graglia, "The parabolic equation model for the numerical analysis of the diffraction at an anisotropic impedance wedge," IEEE Trans. Antennas Propag., vol. 45, no. 5, pp. 767-771, 1997.
25. N. Y. Zhu and F. M. Landstofer, "Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves," IEEE Trans. Antennas Propag., vol. 45, pp. 822-828, 1997.
26. A. V. Osipov, "A hybrid technique for the analysis of scattering by impedance wedges," in Proc. VRSI Int. Symp. Electromagn. Theory, Pisa, Italy, 2004, vol. 2, pp. 1140-1142.
27. B. V. Budaev and D. B. Bogy, 'Two-dimensional diffraction by a wedge with impedance boundary conditions," IEEE Trans. Antennas Propag., vol. 53, pp. 2073-2080, Jun. 2005.
28. M. A. Lyalinov and N. Y. Zhu, "A solution procedure for second-order difference equations and its application to electromagnetic-wave diffraction in a wedae-shaped region," Proc. Roy. Soc. Lond. A, no. 459, pp. 3159-3180, 2003.
29. N. Y. Zhu and M. A. Lyalinov, "Diffraction of a normally incident plane wave by an impedance wedge with its exterior bisected by a semiinfinite impedance sheet," IEEE Trans. Antennas Propag., vol. 52, pp. 2753-2758, Oct. 2004.
30. T. B. A. Senior and S. R. Legault, "Diffraction by an anisotropic impedance half plane at skew incidence," Electromagnetics, no. 18, pp. 207-225, 1998.
31. T. B. A. Senior, S. R. Legault, and J. L. Volakis, "A novel technique for the solution of second-order difference equations," IEEE Trans. Antennas Propag., vol. 49, pp. 1612-1617, Dec. 2001.
32. B. Noble, Methods Based on the Wiener-Hopf Technique: For the Solution of Partial Differential Equations. London, U.K.: Pergamon, 1958.
33. L. A. Weinstein, The Theory of Diffraction and the Factorization Method: Generalized Wiener-Hopf Technique Transi.: P. Beckmann. Boulder, CO: Golem, 1969.
34. R. Mittra and S. W. Lee, Analytical Techniques in the Theory of Guided Waves. New York: MacMillan, 1971.
35. T. B. A. Senior, "Some problems involving imperfect half plane," in Electromagnetic Scattering, P. L. E. Uslenghi, Ed. New York: Academic, 1978.
36. R. A. Hurd and E. Luneburg, "Diffraction by an anisotropic impedance half plane," Can. J. Phys., vol. 63, no. 9, pp. 1135-1140, Sep. 1985.
37. V. Daniele, "The Wiener-Hopf technique for impenetrable wedges having arbitrary aperture angle," SIAM J. Appl. Math., vol. 63, no. 4, pp. 1442-1460, 2003.
38. _, The Wiener-Hopf technique for wedge problems Dipartimento di Elettronica, Politecnico di Torino, Internal Rep. ELT-2004-2, Oct. 2004 [Online]. Available: http://www.eln.polito.it/staff/daniele/
39. _, An Introduction to the Wiener-Hopf Technique For The Solution Of Electromagnetic Problems Dipartimento di Elettronica, Politecnico di Torino, Internal Rep. ELT-2004-1, Sep. 2004 [Online]. Available: http://www.eln.polito. it/staff/daniele/
40. V. Daniele and G. Lombardi, "Generalized Wiener-Hopf equations for wedge problems involving arbitrary linear media," in Int. Conf. Electromagn. Adv. Applicat. (ICEAA03), Torino, Italy, Sep. 2003, pp. 761-764.
41. V. G. Daniele and G. Lombardi, "The Wiener-Hopf technique for impenetrable wedge problems," in Days on Diffraction 2005 Int. Conf., Saint Petersburg, Russia, Jun. 2005, pp. 50-61.
42. A. N. Norris and A. V. Osipov, "Far field analysis of the Malyuzhinets solution for plane and surface waves diffraction by an impedance wedge," Wave Motion, vol. 30, pp. 69-89, 1999.
43. V. G. Daniele, "Rotating waves in the Laplace domain for angular regions," Electromagnetics, vol. 23, no. 3, pp. 223-236, 2003.
44. I. D. Abrahams, "On the non commutative factorization of WienerHopf kernels of Khrapkov type," Proc. Roy. Soc. London A, vol. 454, pp. 1719-1743, 1998.
45. N. P. Vekua, Systems of Singular Integral Equations. Groningen, The Netherlands: Noordhoff, 1967.
46. D. Jones, Methods in Electromagnetic Wave Propagation. Oxford, U.K.: Clarendon, 1979.
47. G. Lombardi, "Numerical validation of the Wiener-Hopf approach to wedge problems," in Int. Conf. Electromagn. Adv. Applicat. (ICEAA05), Torino, Italy, Sep. 2005, pp. 693-696.
48. J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Eds., Electromagnetic and Acoustic Scattering by Simple Shapes. New York: Hemisphere, 1969.
49. R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, vol. 62, pp. 1448-1461, Nov. 1974.
50. R. Tiberio, G. Pelosi, G. Manara, and P. H. Pathak, "High-frequency scattering from a wedge with impedance faces illuminated by a line source, Part I: Diffraction," IEEE Trans. Antennas Propag., vol. 37, pp. 212-218, Feb. 1989.
51. R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci., vol. 31, no. 6, pp. 1387-1397, Nov.-Dec. 1996.
52. G. Manara, R. Tiberio, G. Pelosi, and P. H. Pathak, "High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II: Surface waves," IEEE Trans. Antennas Propag., vol. 41, pp. 877-883, Jul. 1993.
53. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves. Englewood Cliffs, NJ: Prentice-Hall, 1973.
54. A. Osipov, K. Hongo, and H. Kobayashi, "High-frequency approximations for electromagnetic field near a face of an impedance wedge," IEEE Trans. Antennas Propag., vol. 50, pp. 930-940, Jul. 2002.
55. Q. A. Naqvi, K. Hongo, and H. Kobayashi, "Surface fields of an impedance wedge at skew incidence," Electromagnetics, vol. 22, no. 3, pp. 209-233, 2002.