  The problem of diffraction of a waveguide mode by a thin Neumann screen is
considered. The incident mode is assumed to have frequency close to the
cut-off. The problem is reduced to a propagation problem on a branched surface
and then is considered in the parabolic approximation. Using the embedding
formula approach, the reflection and transmission coefficients are expressed
through the directivities of the edge Green's function of the propagation
problem. The asymptotics of the directivities of the edge Green's functions are
constructed for the case of small gaps between the screen and the walls of the
waveguide. As the result, the reflection and transmission coefficients are
found. The validity of known asymptotics of these coefficients is studied.
