Explicit Analytical Results for One-Mode Normal Reflection and Transmission by a Periodic Array of Screens

An analytical approach to scattering of a plane scalar wave through a periodic array of screens is studied. The one-mode problem with normal incidence is considered and reduced to an integral equation holding over each opening. Explicit results are given for a uniform approximation of the relevant coefficients. Numerical comparison with previous results and a proof of the energy balance for the two-mode problem are included.