Line source diffraction by perfectly conducting successive steps

A rigorous investigation for the high frequency diffraction of the cylindrical waves by the perfectly conducting successive step discontinuities is considered by using the Fourier transform technique in conjunction with the mode-matching method. The corresponding boundary value problem is formulated into a modified scalar Wiener-Hopf equation of the third kind whose approximate solution, which is obtained by iterations of a pair of Fredholm integral equations of the second kind, contains five sets of infinite number of unknown constants satisfying five infinite systems of linear algebraic equations and two types of branch-cut integrals which can be evaluated approximately and numerically due to their types. The effects of the characteristic parameters of the problem such as width and height of the steps on the diffraction phenomenon are shown graphically.