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
Externally publishedYes

Fingerprint

Diffraction
Sobolev spaces
Fourier Method
Hankel
Boundary integral equations
Hermann Von Helmholtz
Boundary Integral Equations
Violate
Energy
Half-space
Sobolev Spaces
Polarization
kernel
Necessary

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Diffraction of light revisited. / Kunik, Matthias; Skrzypacz, Piotr.

In: Mathematical Methods in the Applied Sciences, Vol. 31, No. 7, 10.05.2008, p. 793-820.

Research output: Contribution to journalArticle

Kunik, Matthias ; Skrzypacz, Piotr. / Diffraction of light revisited. In: Mathematical Methods in the Applied Sciences. 2008 ; Vol. 31, No. 7. pp. 793-820.
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