Advertisement

Pramana

, Volume 25, Issue 4, pp 497–503 | Cite as

Group theoretical methods in optics

  • N Mukunda
Optics
  • 39 Downloads

Abstract

Scalar Fourier optics is concerned with the passage of paraxial light beams through ideal optical systems. It is well known that the action of the latter on the former can be given in the framework of the two- and four-dimensional real symplectic groups. It is shown here that, based on an analysis of the Poincaré symmetry of the complete Maxwell equations in the front form, a natural representation for paraxial Maxwell beams emerges, which moreover shows the way to a generalization of scalar to vector Fourier optics preserving the group structure of ideal optical systems. Properties of generalized rays, and the usefulness of some pseudo-orthogonal groups in the treatment of Gaussian Schell-model beams, are also brought out.

Keywords

Vector Fourier optics first order optical systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bacry H 1984 Group theory and paraxial optics. Invited talk at 13th Int. Colloq. on group theoretical methods, University of MarylandGoogle Scholar
  2. Bacry H and Cadilhac M 1981Phys. Rev. A23 2533ADSMathSciNetGoogle Scholar
  3. Dirac P A M 1949Rev. Mod. Phys. 21 392MATHCrossRefADSMathSciNetGoogle Scholar
  4. Mukunda N, Simon R and Sudarshan E C G 1985aJ. Opt. Soc. Am. A2 416ADSMathSciNetCrossRefGoogle Scholar
  5. Mukunda N, Simon R and Sudarshan E C G 1985bJ. Opt. Soc. Am. A (in press)Google Scholar
  6. Simon R 1983Pramana 20 105ADSGoogle Scholar
  7. Simon R, Sudarshan E C G and Mukunda N 1984Phys. Rev. A29 3273ADSMathSciNetGoogle Scholar
  8. Simon R, Sudarshan E C G and Mukunda N 1985Phys. Rev. A (in press)Google Scholar
  9. Sudarshan E C G 1979aPhys. Lett. A73 269ADSMathSciNetGoogle Scholar
  10. Sudarshan E C G 1979bPhysica A96 315ADSGoogle Scholar
  11. Sudarshan E C G 1981Phys. Rev. A23 2802ADSMathSciNetGoogle Scholar
  12. Sudarshan E C G and Mukunda N 1974Classical dynamics: A modern perspective (New York: John Wiley) ch. 9MATHGoogle Scholar
  13. Sudarshan E C G, Mukunda N and Simon R 1985Opt. Acta (in press)Google Scholar
  14. Sudarshan E C G, Simon R and Mukunda N 1983Phys. Rev. A28 2921ADSGoogle Scholar

Copyright information

© the Indian Academy of Sciences 1985

Authors and Affiliations

  • N Mukunda
    • 1
  1. 1.Centre for Theoretical StudiesIndian Institute of ScienceBangaloreIndia

Personalised recommendations