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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 1 — Jan. 1, 2005
  • pp: 103–108

Electromagnetic coherence theory of laser resonator modes

Toni Saastamoinen, Jari Turunen, Jani Tervo, Tero Setälä, and Ari T. Friberg  »View Author Affiliations

JOSA A, Vol. 22, Issue 1, pp. 103-108 (2005)

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A theory of open laser resonators is formulated within the framework of the electromagnetic coherence theory. It is shown that if only one Fox–Li mode contributes to the field at a given frequency, then the field at that frequency is necessarily completely coherent in view of the space–frequency counterpart of the recently introduced degree of coherence of electromagnetic fields [Opt. Express 11, 1137 (2003)]. It is also shown that the relation between the number of Fox–Li modes and the new degree of coherence is analogous to the relation established in the scalar theory of laser resonator modes. Difficulties that arise with the formerly introduced visibility-based definition of the electromagnetic degree of coherence are briefly discussed.

© 2005 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(140.4780) Lasers and laser optics : Optical resonators
(260.2110) Physical optics : Electromagnetic optics
(260.5430) Physical optics : Polarization

Original Manuscript: July 2, 2004
Published: January 1, 2005

Toni Saastamoinen, Jani Tervo, Tero Setälä, Ari T. Friberg, and Jari Turunen, "Electromagnetic coherence theory of laser resonator modes," J. Opt. Soc. Am. A 22, 103-108 (2005)

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  27. The exact conditions for the existence and validity of the biothogonal expansion in Eq. (22) do not appear to be known. However, it is readily shown that if the Fox–Li modes are complete in the sense that the field Fj+1(ρ, ω)on the left-hand side of Eq. (15) is expressible as their linear combination, then the resonator kernel admits the biorthogonal series representation as given in Eq. (22). A similar assumption (though stated slightly differently) was also invoked in Footnote 15 of Ref. 2.
  28. The steps are essentially identical to those made in Ref. 2 but with the scalar functions replaced by appropriate vector- or tensor-valued functions. The vectorial formulation is given in detail in Ref. 29.
  29. J. Tervo, T. Saastamoinen, J. Turunen, T. Setälä, A. T. Friberg, “Degree of coherence and electromagnetic resonators,” in Photon Management, F. Wyrowski, ed., Proc. SPIE5456, 28–35 (2004). [CrossRef]
  30. The same result holds also within the scalar theory, although it is not explicitly mentioned in Refs. 2 and 19.

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