Diffraction of light revisited

Matthias Kunik, Piotr Skrzypacz

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)793-820
Number of pages28
JournalMathematical Methods in the Applied Sciences
Volume31
Issue number7
DOIs
Publication statusPublished - May 10 2008

Keywords

  • Energy conditions
  • Fourier analysis
  • Hankel functions
  • Maxwell-Helmholtz equations
  • Singular boundary fields
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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