We apply a mode expansion technique to the three-dimensional vectorial diffraction problem of an electromagnetic field that is incident on a perfectly conducting, metallic disc containing a pattern of rectangular pits. The mode expansion technique reduces the three-dimensional diffraction problem to a two-dimensional numerical problem. Furthermore, by choosing a particular numerical discretization, the a priori unknown amplitudes of the propagating and evanescent scattered plane waves in the half space above the metallic plate can be eliminated from the system of equations. The relatively small remaining system of equations for the amplitudes of the propagating and evanescent modes inside the pits, can be solved very rapidly. Some first results are presented. Furthermore, the application of the scanning of an optical beam by a pit structure on a metallic optical disc is discussed.