One of the major challenges faced by externally occulted solar coronagraphs is the suppression of the light diffracted by the occulter edge. It is a contribution to the stray light that overwhelms the coronal signal on the focal plane and must be reduced by modifying the geometrical shape of the occulter. There is a rich literature, mostly experimental, on the appropriate choice of the most suitable shape. The problem arises when huge coronagraphs, such as those in formation flight, shall be tested in a laboratory. A recent contribution [Opt. Lett.41, 757 (2016)OPLEDP0146-959210.1364/OL.41.000757] provides the guidelines for scaling the geometry and replicate in the laboratory the flight diffraction pattern as produced by the whole solar disk and a flight occulter but leaves the conclusion on the occulter scale law somehow unjustified. This paper provides the numerical support for validating that conclusion and presents the first-ever simulation of the diffraction behind an occulter with an optimized shape along the optical axis with the solar disk as a source. This paper, together with Opt. Lett.41, 757 (2016)OPLEDP0146-959210.1364/OL.41.000757, aims at constituting a complete guide for scaling the coronagraphs' geometry.