Analysis of clusters and uniformity of distribution of states of polarization on the Poincaré sphere

Abstract

An analysis of the clusters and the uniformity of distribution of states of polarization on the surface of a Poincaré sphere generated by rotating wave plates is given. The analysis of clusters of the states of polarization is based on a spherical radial distribution function. For uniform analysis of the distribution, two methods are proposed. The first method is based on calculation of the correlation coefficient; the second method is based on calculation of the angles between pairs of the states of polarization on the Poincaré sphere. For polarization scramblers consisting of eight or more rotating wave plates, nonclustered and near-uniform distribution of states of polarization is obtained.

Polarization Effects in Optical Fiber Links

“…Furthermore, it is often necessary that the scrambler output SOPs are distributed uniformly on the entire Poincarè sphere. The spherical radial distribution function is very useful tool for the SOPs distribution analysis on the Poincarè sphere [22]. The spherical radial distribution function is the modified form of the well known plane radial distribution function.…”

“…The spherical radial distribution function is the modified form of the well known plane radial distribution function. The spherical radial distribution function is defined as follows [22]:…”

“…We can distinguish three typical theoretical distributions: uniform (Figure 22a), random ( Figure 23a) and clustered (Figure 24a). In turn, Figures 22b, 23b and 24b show the spherical radial distribution as a function of the distance d for the uniform, random and clustered distribution, respectively [22]. For the uniform distribution ( Figure 22b) the peaks on the g(d) curve provides information about the mean distance of the following neighbouring points (SOPs) on the Poincarè sphere.…”

“…The analysis of the distribution of SOPs generated by polarization scramblers shows that SOPs distribution is clustered for three (and less) rotating retarders and for four (and less) phase shifting elements. For four and more rotating retarders and for five and more phase shifting elements random distribution is obtained [22].…”