Scattering of plane waves by corrugated surfaces

30 SUMMARY Corrugated surfaces are widely used in microwave applications. Discontinuity formed by two corrugated surfaces with different corrugation widths may be very interesting for waveguides. Weinstein [8] has shown that higher, order impedance boundary conditions can be employed to simulate corrugated surfaces. In this study, scattering mechanism of plane electromagnetic wave at the junc tion of two corrugated half-planes is investigated. First, standard impedance boundary conditions are used to simulate anisotropic corugated half-planes. So the problem is reduced to the discontinuity formed by two anisotropic impedance half planes. The problem is formulated by Fourier Transform technique and all tangential field components are derived from Hertz vector fields. Using Leontovich impedance boundary conditions, four functional equations are obtained and this system of equation is written in Matrix Wiener-Hopf system. The system is also solved in a manner given by [9] and this is carried in Appendix-I. The solution of a Matrix Wiener-Hopf system is identical to the solution pro cedure of a scalar Wiener-Hopf equation. The classical Wiener-Hopf procedure requires the factorization of a kernel matrix which can be faetorized into regular two matrices in lower and upper complex half planes. When the kernel matrix is a scalar, the factorization can easily be carried out by means of Cauchy's theorem. Since a matrix do not form a commutative algebra, standard procedure cannot be operated generally. This is the main source of difficulty in solving matrix Wiener- Hopf equations. Another difficulty comes from the exponential growth of the kernel matrix and this is achieved by introducing a polynomial matrix to ensure the reg ularity condition. Daniele-Khrapkov method is applicable for this kind of problem and here, this method is used. After the necessary spectral coefficients are determined, the resultant integral form of diffracted field is evaluated by the method of steepest descent path (SDP) for large k. This method is very powerful for the integrals to be evaluated in high- frequency electromagnetic techniques. Diffraction coefficients and diffracted fields are determined and the results are given. The residue contribution of the expression inside the resultant integral gives the surface waves. The effect of the geometrical parameters of the structure on the velocity of the surface waves is very important and this is considered. It is shown31 that there is good agreement between the results in literature and those which we obtained. This kind of structure can be used as slow-wave structure in microwave applications.