Diffraction of a Gaussian beam at a perfectly conducting half-screen

We transpose to Gaussian beams which are solutions of the paraxial wave equation a technique applied by Bateman to the diffraction of plane waves by a perfectly conducting screen. Essentially each solution of the paraxial equation generates a secondary solution called the diffracted component. Then, with the incident and reflected waves and their diffracted components we build a solution continuous outside the screen and satisfying some boundary condition on the screen so that this solution represents the total diffracted field. We limit the discussion to the optical domain where the beam keeps its Gaussian structure during propagation. There the angle of reflection is constant so that the reflected beam is also Gaussian.