Formulation of the Diffraction Problem of Almost Grazing Incident Plane Wave by an Anisotropic Impedance Wedge
محورهای موضوعی : Majlesi Journal of Telecommunication DevicesEmine Avsar Aydin 1 , Turgut İkiz 2
1 - Department of Electrical and Electronics Engineering, Çukurova University, Adana, Turkey
2 - Department of Electrical and Electronics Engineering, Çukurova University, Adana, Turkey
کلید واژه: en,
چکیده مقاله :
In this paper, formulation of the problem of plane wave diffraction by a wedge with anisotropic impedances is given for the case of almost grazing incidence. All steps of problem are given in detailed. Wedge is a canonic structure and diffraction from wedge may be used in modelling scattering from a variety of complex structures. In this study, by using the Maxwell’s equations the field components can be expressed in terms of z-components. By applying appropriate boundary conditions, a coupled system of equations is obtained in terms of field component and derivatives of field components with respect to and r. By using similarity transform to the coupled system of equations, the coupling is reduced to the simplest form in which Malyuzhinets theorem can be applied. The solution of field components is sought in the form of Sommerfeld integrals. The Malyuzhinets theorem is applied to the Sommerfeld integrals. By using Sommerfeld integrals the problem is reduced to a system of coupled functional equations. Solution of homogeneous functional equations is given in terms of χф functions. For a small parameter of the problem (sinθ0<<1 where θ0 is the angle between z-axis and incident wave) the perturbation procedure is used to reduce the coupled functional equations to a system of linear equations with this small parameter being at the integral terms of equations. As a result the closed form solution is given for functional equations. The obtained analytic expression for the spectral functions is substituted to the Sommerfeld integrals, which are evaluated by means of steepest descent technique.Then, the analytical expressions for the diffraction coefficient for both magnetic and electric field components are derived. Considering these different geometries and small skewness angle, it is concluded that this approach enlarge the class of solvable diffraction problem in a small range. Additionally, the results are valuable for the comparison purposes for the other approximate methods.
[1] BUCCI O. M. , G. FRANCESCHETTI. “Electromagnetic Scattering by a Half-Plane with Two Impedances.” Radio Sci., Vol.11, 49-59, 1976.
[2] İKİZ, T. , F. KARAÖMERLİOĞLU, “Diffraction of Plane Waves by a Two-Impedance Wedge in Cold Plasma”, Journal of Electromagnetic Waves and Applications, Vol. 18, No.10, 1361-1372,2004..
[3] KIM S.-Y., RA J.-W. and S.-Y. SHIN,. “Edge Diffraction by Dielectric Wedge of Arbitrary Angle,” Electronic Letters, 19(20), 851-853, 1983.
[4] LIU Y. , R. CIRIC. “Improved Formulas for the Diffraction by a Wedge,” Radio Science, 28(5), pp. 859-863, 1993.
[5] LYALINOV M. A. , N. Y. ZHU. “Diffraction of Skewly Incident Plane Wave by an Anisotropic Impedance Wedge- A Class of Exactly Solvable Cases,” Wave Motion, 30, pp. 275-288, 1999.
[6] MALYUZHINETS G. D.. “Generalisation of the Reflection Method in the Theory of Diffraction of Sinusoidal Waves”. Doctoral dissertation , P.N. Lebedev Phys. Inst. Acad. Sci. USSR, 1950.
[7] ______, “The radiation of sound by the vibrating boundaries of an arbitrary wedge. Part I”, Sov. Phys. Acoust., I, pp.152-174,1955..
[8] ______, 1955. “Radiation of sound from the vibrating faces of an arbitrary wedge”. Part II, Sov. Phys. Acoust., I, pp.40-248, 1955.
[9] MOHSEN A. “On the Diffraction of an Arbitrary Wave by a Wedge,” Can. J. Phys., 60, pp.1686-1690., 1982.
[10] NORRIS A. N. , A. V. OSIPOV. “Far-Field Analysis of the Malyuzhinets Solution for Plane and Surface Waves Diffraction by an Impedance Wedge,” Wave Motion, 30,pp. 69-89, 1999.
[11] OSIPOV A. V., A.N. NORRIS. “The Malyuzhinets Theory for Scattering from Wedge Boundaries: a review,” Wave Motion, 29, pp.313-340. , 1999
[12] RAWLINS A. D. “Diffraction of an E-or H-polarized Plane Wave by a Right-Angle Wedge with Imperfectly Conducting Faces,” Q.JI Mech. Appl. Math., 43, pt. 2, pp.161-172. , 1990.
[13] SAKHAROVA M. P, A. F. FILIPPOV. “The Solution of a Nonstationary Problem of Diffraction by an Impedance Wedge in Tabulated Functions,” Zh. Vych. Matem. i Mat. Fiziki 7, pp.568-579, 1967.
[14] SENIOR T. B. A. “Diffraction by an Imperfectly Conducting Wedge,” Comm. Pure Appl. Math., 12, pp.337-372., 1959.
[15] SENIOR, T. B. A. , J. L. VOLAKIS “Scattering by an Imperfect Right-Angled Wedge,” IEEE Trans. Antennas and Propagation, Vol. AP-34,pp. 681-689, 1986..
[16] TIBERIO R., 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. on Antennas and Propagation, 37(2),pp. 212-218, 1989.
[17] VACCARO, V. G. “Electromagnetic Diffraction from a Right-Angled Wedge with Soft Conditions on One Face.”, Opt. Acta, Vol. 28, pp.293-311., 1981.
[18] VOLAKIS, J. L. “A Uniform Geometrical Theory of Diffraction for an Imperfectly Conducting Half-Plane,” IEEE Trans. Antennas and Propagation, Vol. AP-34, pp.172-180., 1986.
[19] WILLIAMS W. E. “Diffraction of an E-polarized Plane Wave by an Imperfectly Conducting Wedge,” Proc. R. Soc. London A 252. pp. 376-393., 1959.
