Diffraction of Gaussian beams by plane apertures: a different approach

We first develop an integral equation formalism to solve the boundary value problems of the paraxial scalar wave equation when data, of the Dirichlet or Neumann type, are given on a closed surface S, in particular when S is a plane. Then, we show how this formalism can be used to analyse the scatter ing by perfectly conducting planes of paraxial waves, specially of Gaussian beams, and how it may be applied to paraxial wave diffraction by plane ape rtures. Finally, the diffraction of Gaussian beams by slits, rectangular an d circular apertures is investigated.