Asymptotic behaviour of multiple scattering on infinite number of parallel demi-planes

The exact solution for the scattering of electromagnetic waves on an infinite number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins in 1947 using the Wiener-Hopf method. We analyze their solution in the semiclassical limit of small wavelength and find the asymptotic behaviour of the reflection and transmission coefficients. The results are compared with the ones obtained within the Kirchhoff approximation.