Diffraction of a normally incident plane wave by three parallel half-planes with different face impedances

The diffraction problem of plane waves by a set of three parallel half-planes one of which is placed in the opposite direction and having characterized with different surface impedances on upper and lower faces is solved by mode-matching method where available and Fourier transform technique elsewhere. The solution includes two independent Wiener-Hopf equations each involving infinite number of expansion coefficients which satisfy an infinite system of linear algebraic equations. After the determination of these coefficients numerically, some graphical results are presented showing the influence of the surface impedances and the distances between the half-planes on the diffracted and transmitted waves.