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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 10 — Oct. 1, 2004
  • pp: 1907–1916

Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space

Tomohiro Shirai and Emil Wolf  »View Author Affiliations

JOSA A, Vol. 21, Issue 10, pp. 1907-1916 (2004)

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The spectral degree of coherence and of polarization of some model electromagnetic beams modulated by a polarization-dependent phase-modulating device, such as a liquid-crystal spatial light modulator, acting as a random phase screen are examined on the basis of the recent theory formulated in terms of the 2×2 cross-spectral density matrix of the beam. The phase-modulating device is assumed to have strong polarization dependence that modulates only one of the orthogonal components of the electric vector, and the phase of the phase-modulating device is assumed to be a random function of position imitating a random phase screen and is assumed to obey Gaussian statistics with zero mean. The propagation of the modulated beam is also examined to show how the spectral degrees of coherence and of polarization of the beam change on propagation, even in free space. The results are illustrated by numerical examples.

© 2004 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(260.5430) Physical optics : Polarization

Original Manuscript: December 5, 2003
Revised Manuscript: May 12, 2004
Manuscript Accepted: May 12, 2004
Published: October 1, 2004

Tomohiro Shirai and Emil Wolf, "Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space," J. Opt. Soc. Am. A 21, 1907-1916 (2004)

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  21. This expression, which is a generalization of the transformation law for the coherence matrix, is readily derived using the analysis given in Sec. 6.4 of Ref. 20.
  22. See, for example, B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Sec. 6.1.
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  24. When the phase-modulating device is a reflection type, rather than a transmission type, as employed in Ref. 23, the transmission matrix must be replaced by the reflection matrix.
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  26. In order for the paraxial propagation equation given by Eq. (6) to be valid for analyzing the propagation of the modu-lated field produced just behind the LC SLM, the condition 1/(4σS2)+1/ση2≪2π2/λ2 must be satisfied. This condition is basically the same as the “beam condition” for scalar Gaussian Schell-model (GSM) beams (Sec. 5.6.4 of Ref. 20). For more general discussion on the beam conditions for electromagnetic GSM beams, see O. Korotkova, M. Salem, E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004). [CrossRef] [PubMed]

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