## Definitions of the degree of polarization of a light beam

Optics Letters, Vol. 32, Issue 9, pp. 1015-1016 (2007)

http://dx.doi.org/10.1364/OL.32.001015

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### Abstract

A necessary and sufficient condition is derived for certain *ad hoc* expressions that are frequently used in the literature to represent correctly the degree of polarization of a light beam.

© 2007 Optical Society of America

**OCIS Codes**

(030.6600) Coherence and statistical optics : Statistical optics

(260.0260) Physical optics : Physical optics

(260.5430) Physical optics : Polarization

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: November 29, 2006

Revised Manuscript: January 29, 2007

Manuscript Accepted: January 29, 2007

Published: April 3, 2007

**Citation**

Asma Al-Qasimi, Olga Korotkova, Daniel James, and Emil Wolf, "Definitions of the degree of polarization of a light beam," Opt. Lett. **32**, 1015-1016 (2007)

http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-9-1015

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### References

- G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 339 (1952), Sec. 19. Reprinted in Polarized Light, W.Swindell, ed. (Dowden, Hutchinson and Ross, 1975), pp. 124-141.
- E. Wolf, Nuovo Cimento 13, 1165 (1959). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- S. Chandrasekhar, Radiative Transfer (Dover, 1960), p. 247, Eq. (100).
- W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge University Press, 2000), p. 82, Eq. (3.71).
- F. W. Byron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Addison-Wesley, 1969, reprinted by Dover, 1992), p. 165, Theorem 4.20.
- In his classic paper on generalized harmonic analysis N. Wiener, Acta Math. 55, 117 (1930) defined 'percentage of polarization' in term of the coherency matrix (Eq. (9.5.1), p. 191). It is not difficult to show that his definition can be expressed in the form of Eq. . Wiener obtained the formula by use of a real unitary transformation. However, in general, the unitary transformation which diagonalizes the coherency matrix is a complex matrix. To perform the diagonalization physically one has, in general, to make use not only of a rotator (real transformer) but also of a phase plate (complex transformer). [CrossRef]

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