Abstract
AbstractThe 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. Copyright © 2007 John Wiley & Sons, Ltd.
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