Diffraction of scalar waves at plane apertures: A different approach

We present a different approach of dealing with integral equations develope d to tackle diffraction of scalar harmonic waves by a hole in a perfectly r eflecting screen with a thickness assumed to be negligibly small. This appr oach uses a cartesian representation of the Green's functions which satisfy on the screen the same Dirichlet or Neumann boundary conditions as the tot al field incident, reflected and diffracted while the continuity of the tot al held is imposed through the aperture. The solution of the corresponding integral equations is given harmonic plane waves with an application to the diffraction at slits and rectangular apertures.