Mutual information-based degrees of coherence of partially polarized light with Gaussian fluctuations

Spatial propagation of coherency matrix in polarization optics

In this work, the question of the coherency matrix propagation of a light beam is addressed by means of the analysis of interpolation processes between two physical situations. These physical situations are defined according to the second order statistical properties of the underlying process. Two states of a light beam or the path in a medium to go from a physical situation at distance z(1) to another one at distance z(2) is related to the correlation between both these physical situations. Equivalence classes are derived from the definition of a group action on the set of coherency matrices. The geodesic curves on each equivalence class define the process of interpolation. The general solution is derived as a symbolic equation, and the solution is explicitly developed for the situation of uncorrelated statistical processes. Interpolating coherency matrix in this particular case describes the propagation of a light beam into a uniform nondepolarizing medium characterized by a differential Jones matrix determined by the far points of the interpolation curve up to a unitary matrix.

Irreversible effects of random unitary transformations on coherence properties of partially polarized electromagnetic fields

We demonstrate monotonic, irreversible effects on the entropy, the degree of polarization, and different degrees of coherence when random, energy-preserving unitary transformations are applied to vectorial electromagnetic fields.

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.

Linear relations of partially polarized and coherent electromagnetic fields

We show that having a Wolf degree of coherence of unit modulus or having intrinsic degrees of coherence of unit modulus imply different relations between the electric fields of the light. The mean square meaning of such relations is discussed. On the one hand, we demonstrate that if the intrinsic degrees of coherence are equal to 1, then there is a linear relation between the electrical fields. On the other hand, we show that a Wolf degree of coherence of unit modulus corresponds to a stronger property that implies that the fields have to be proportional.

Coherence polarization filtering and relation with intrinsic degrees of coherence

It is demonstrated for stationary fields that when the polarization state of the electric field can be modified arbitrarily the maximal value of the modulus of the degree of coherence proposed by Wolf [Phys. Lett. A312, 263 (2003)] is equal to the largest intrinsic degree of coherence. In addition, when the light is a mixing of a coherent light that satisfies the factorization condition in the two spatial variables with a statistically uncorrelated, partially coherent, perfectly polarized light, but with a nonparallel polarization state, we show that the polarization modifications that maximize the modulus of the Wolf degree of coherence lead to a light that also satisfies the factorization condition.

Effects of coherence on the degree of polarization in a young interference pattern

Recent predictions concerning the relationship between the degree of polarization at a typical point of a Young interference pattern and the degree of coherence of the electromagnetic field at the pinholes are tested by a simple experiment. In particular, it is shown that light that is completely unpolarized at the pinholes can become partially polarized across the fringe pattern.