A tutorial on the classical theories of electromagnetic scattering and diffraction

Research output: Chapter in Book/Report/Conference proceedingChapter


Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium's optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Original languageEnglish (US)
Title of host publicationFrontiers in Optics and Photonics
Publisherde Gruyter
Number of pages28
ISBN (Electronic)9783110710687
ISBN (Print)9783110709735
StatePublished - Jun 8 2021

ASJC Scopus subject areas

  • General Engineering
  • General Materials Science
  • General Physics and Astronomy


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