Spectral Changes in Focused Partially Coherent Wave Fields

  • T. D. Visser
  • E. Wolf
Conference paper


When light is focused, there are several mechanisms which may cause spectral changes. Among them are diffraction, the state of coherence of the light [1], and propagation through a linear time-invariant system [2]. The focusing configuration is depicted in Fig. 1, it being assumed that fa ≫ λ. The cross-spectral density function of a field U (0) of arbitrary state of coherence on a reference sphere [3] is given by the expression [4, Sec.4.3.2]
$$ {{W}^{{\left( 0 \right)}}}\left( {{{Q}_{1}},{{Q}_{2}},v} \right) = {{W}^{{\left( 0 \right)}}}\left( {{{\rho }_{1}},{{\rho }_{2}},v} \right) = \left\langle {{{U}^{{\left( 0 \right)*}}}\left( {{{\rho }_{1}},v} \right){{U}^{{\left( 0 \right)}}}\left( {{{\rho }_{2}},v} \right)} \right\rangle . $$


Propa Coherence Eter Mandel 

References and links

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    E. Wolf and D.F.V. James, Rep. Prog. Phys. 59, pp. 771–818 (1996).Google Scholar
  2. 2.
    E. Wolf and J.R. Fienup, Opt. Commun. 82, pp. 209–212 (1991).Google Scholar
  3. 3.
    M. Born and E. Wolf, Principles of Opics, 7th (expanded) ed. (Camhridge University Press, Cambridge, 1999). See Sec. 5.1.Google Scholar
  4. 4.
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • T. D. Visser
    • 1
  • E. Wolf
    • 2
  1. 1.Dept. of Physics and AstronomyFree UniversityAmsterdamThe Netherlands
  2. 2.Dept. of Physics and AstronomyUniversity of RochesterRochesterUSA

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