Fig. 1. Schematic representation of the DPS statistics: (a) sampling a certain part of the Poincaré sphere for DPS statistics, $k$, the distance between two center points of the sampling part and its cross section; (b) scrambling simulation results of 10,000 polarization states; (c) complete DPS distribution of the results in (b).

Fig. 2. Experimental setup for polarization scrambling. PC: manual polarization controller, PZT: piezoelectric ceramics, PA: polarization analyzer.

Fig. 3. (a) Experiment scrambling results of 10,000 polarization states; (b) normalized DPS statistics for $k=0.1$; (c1)–(c3) histograms obtained by the Stokes components analysis method.

Fig. 4. (a) SOP distribution on the Poincaré sphere for a defective polarization scrambling system $(S_1<0$, ${\mathit{S}}_2<0$, ${\mathit{S}}_3<0$; ${\mathit{S}}_1>0$, ${\mathit{S}}_2>0$, ${\mathit{S}}_3>0)$; (b) complete normalized DPS statistics for $k=0.06$; (c1)–(c3) accompanying histograms obtained by the Stokes components analysis method.

Fig. 5. (a) 10,000 SOPs distribution on the Poincaré sphere for a commercial scrambler; (b) complete normalized DPS statistics for $k=0.1$; (c1)–(c3) corresponding histograms of DPS statistics at different values of $k$.