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 bo...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2008-05, Vol.31 (7), p.793-820
Main Authors: Kunik, Matthias, Skrzypacz, Piotr
Format: Article
Language:English
Subjects:
energy conditions
Exact sciences and technology
Fourier analysis
Functional analysis
Hankel functions
Integral equations
Mathematical analysis
Mathematics
Maxwell-Helmholtz equations
Partial differential equations
Sciences and techniques of general use
singular boundary fields
Sobolev spaces
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Summary: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. Copyright © 2007 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.945