A Heaviside unit pulse is applied to a point on the surface of a half‐space. The refractive index of the medium varies in such a manner that the surface casts a shadow. By means of complex contour integral representations of the solution, it is shown how to obtain the pulse shape within the shadow zone at times near the arrival of the diffracted pulse. Two‐dimensional and axisymmetric distributions of refractive index are considered, but it can be shown that the form of the expression for the diffracted pulse shape is valid in more general situati