## Generalized Stokes parameters of random electromagnetic beams

Optics Letters, Vol. 30, Issue 2, pp. 198-200 (2005)

http://dx.doi.org/10.1364/OL.30.000198

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### Abstract

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.

© 2005 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(260.0260) Physical optics : Physical optics

(260.5430) Physical optics : Polarization

(350.5500) Other areas of optics : Propagation

**Citation**

Olga Korotkova and Emil Wolf, "Generalized Stokes parameters of random electromagnetic
beams," Opt. Lett. **30**, 198-200 (2005)

http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-2-198

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### References

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- H. Roychowdhury and E. Wolf, Opt. Commun. 266, 57 (2003) The sentence after Eq.(12) in that reference is misleading and should be replaced by "The other off-diagonal element can be determined in an analogous manner." .
- H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, "Change of polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere," J. Mod. Opt. (to be published) ().
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- The spectral Stokes parameters are a refinement of the usual Stokes parameters, which are independent of both frequency and time (see Ref.2, Sec.10.9.3). The usual ones are essentially the integrals of the spectral Stokes parameters that we use taken over the bandwidth of the light, which is usually assumed to be quasi-monochromatic. .
- Two-point Stokes parameters in the space-time domain rather than in the space-frequency domain were recently introduced somewhat formally in J. Ellis and A. Dogariu, Opt. Lett. 29 536 (2004) Although it was not shown in that Letter, these generalized Stokes parameters obey, in free space, two wave equations; however, for propagation in inhomogeneous media they are governed by rather complicated laws. On the other hand, the generalized spectral Stokes parameters introduced in this Letter propagate according to relatively simple laws.

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