Condition of keeping polarization property unchanged in the circle polarization shift keying system

To improve the performance of the free-space optical (FSO) system, we recently proposed circle polarization shift keying (CPolSK). In the CPolSK system, it is important to study the condition of keeping the polarization properties unchanged in the turbulent atmosphere. Based on the unified theory of coherence and polarization, three formulas are derived to describe the condition of keeping the polarization degree invariant for the GaussianSchell model (GSM) beam. The third formula includes all the polarization states. Consequently, it is defined as the condition of polarization invariance in CPolSK systems. If this condition is satisfied, the two parameters of the polarization ellipse will remain the values of the source during the propagation. Several GSM beams with different parameters are numerically calculated to verify the conditions. This result is helpful in designing the transmitter of the polarization modulation system.