Diffraction by a Transversal Screen in a Planar Waveguide

The problem of scattering by a transversal Neumann screen with narrow slits in a planar waveguide is studied. The frequency is close to the cut-off frequency of the incident mode, so the Brilluoin partial waves propagate almost normally to the axis of the waveguide. It follows from recent results by S. A. Nazarov that in this case one should observe an anomalous transmission of the incident mode, i.e., the transmission coefficient should be close to 1, while the reflection coefficients and the coefficients of scattering into other modes should be negligibly small. This fact may seem surprising, since there is a wall in the waveguide with narrow slits only. In this paper the authors try to reveal the details of the scattering process in order to demonstrate that the anomalous transmission indeed takes place regardless the structure of the field near the slit.