Diffraction of light revisited

The diffraction of monochromatic light is considered for a plane screen with an open infinite slit by solving the vectorial Maxwell-Helmholtz system in the upper half-space with the Fourier method. With this approach we can represent each solution satisfying an appropriate energy condition by its boundary fields in the Sobolev spaces H^±1/2. We show that Sommerfeld's theory using a boundary integral equation with Hankel kernels for the so-called B-polarization is covered by our approach, but in general it violates a necessary energy condition. Our representation includes also solutions which are not covered by Sommerfeld's theory.