We investigate the use of a spatially distributed beam of entangled photons for applications of wavefront division interferometry. Using a fiber-based spontaneous parametric down conversion process, which redirect the signal and idler into a common single-mode fiber, we generate a Gaussian beam of colinear entangled photons randomly distributed in space. Coincidence measurements carried by wavefront division demonstrate quantum interference patterns, including classical single photon fringes, two-photon interferences and the Hong-Ou-Mandel effect. Our results are relevant for detecting transverse variations in the statistical properties of weak turbulence.
Measuring the state of polarization of light is critical because it contains information about its source, including radiation, reflection, and any other interactions with matter. However, the traditional method to operate polarimetry relies on knowing the direction of wave propagation. Otherwise, one measures only the projection of the three-dimensional optical field onto the two-dimensional detector. This limitation, however, can be circumvented by using a reference vector field with a non-homogeneous spatial distribution of the state of polarization. Here we demonstrate that a “radially polarized” reference beam offers a simple and robust solution for a single-shot, omnidirectional polarimeter. The technique relies on intensity contrasts measured simultaneously in different orthogonal bases followed by an appropriate Fourier analysis to extract both direction and state of polarization of an incoming beam of light.
Although polarization is historically defined as a local property, one can also regard it as a nonlocal feature of correlated fields for which the correlation between the field components at any locations and fluctuating along any orthogonal directions does not factorize. For such fields, the local states of polarization are randomly distributed on the surface of the Poincare sphere while their average lie somewhere inside of it, but not necessarily at its center. An average degree of polarization can then be defined as distance between this point and the origin of the sphere. Of course, because of nonlocality, there will be different types of randomly polarized fields which, on average, will have the same average degree of polarization. Because these fields could have different physical origins or can be the result of different field transformations, finding a proper way to discriminate among them is an important issue. We introduce the scalar average similarity of an ensemble of randomly polarized states. This global measure is based on the complex degree of mutual polarization between any pair of vector fields in the ensemble. We show that, in the case of fully-correlated and globally unpolarized fields, the variation of this parameter is bounded and its value can effectively discriminate between different configurations of pure states.
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