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Chapter 10:
Intrinsic Degrees of Coherence for Electromagnetic Fields
Editor(s): Ari T. Friberg; René Dändliker
Author(s): Réfrégier, Philippe; Roueff, Antoine
Published: 2008
DOI: 10.1117/3.793309.ch10
These last few years, the analysis of partial coherence of partially polarized light has been the subject of intensive research. In classical optics, the standard approach consists of considering the light as a realization of a random function and in analyzing its second-order statistical properties. In the case of partially polarized light, the physical situation is characterized by the knowledge of the polarization matrix of each field and of the mutual coherence matrix. Each polarization matrix is described by four real parameters while the mutual coherence matrix is described by eight real parameters. The second-order statistical properties of a couple of two electric fields of the light is thus characterized by 16 real parameters. In order to get a physically meaningful interpretation of the correlation properties, it can be interesting to define parameters that allow one to check if some properties are satisfied. In classical optics, the concept of interference plays a central role. It is thus interesting to characterize the coherence properties in relation to the visibility of the interference fringes that can be obtained with the couple of electric fields of the light beams. It is worth noting that in this chapter only interference fringes relative to the intensity are considered. In particular, the modulation of the different Stokes parameters that appear as discussed in Refs. 11 and 12 in the interference plane are not analyzed. The intrinsic degrees of coherence allow one to get two parameters that can be easily determined from the 16 parameters mentioned above and that can be useful in order to analyze some practical properties of the light. We propose to discuss in the following some theoretical motivations, some basic properties, and some physical interpretations of this approach. After a presentation of some background concepts, the discussion first points out the invariance properties of the theory of intrinsic degrees of coherence. In particular, this notion is related to the invariance properties of the factorization condition at order one introduced in the quantum theory of coherence. Then, it is shown that the intrinsic degrees of coherence are useful to predict the ability of light to interfere when the polarization states of both interfering fields are optimized or when only the polarization state of one field is optimized. Afterward, an experimental situation of mixing two uncorrelated perfectly polarized lights with different temporal coherence properties is presented. Finally, a general statistical interpretation will be discussed.
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Analytical research

Geometrical optics

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