Diffraction of a δ-function pulse at a half plane: the boundary pulse

Abstract

The diffraction of a plane δ-function pulse by a black half plane is treated by Stokes’ diffraction formula. The solution is a superposition of the incident pulse terminated at the geometric shadow boundary and a separate cylindrical boundary pulse exhibiting diffusion. The boundary pulse satisfies Lamb’s theorem, and its Fourier transform yields the monochromatic boundary wave. The mathematical reason for the π/4 phase shift is seen in the Fourier transform of the pulse tail. The character of the solution is sufficient to show that the boundary pulse originates at the edge of the diffracting aperture, and to illustrate clearly the kinematical aspects of diffraction at a black screen.