Polarization Properties of Coherently Superposed Rayleigh Backscattered Light in Single-Mode Fibers

The properties of the state of polarization (SOP) and the degree of polarization (DOP) of Rayleigh backscattered light (RBL) in single-mode fibers (SMF) are investigated theoretically and experimentally when the incident probe is a perfectly coherent continuous-wave (CW) light. It is concluded that the instantaneous DOP of the coherently superposed RBL is always 100%, and the instantaneous SOP is determined by the distributions of the birefringence and the optical phase along the SMF. Therefore, the instantaneous SOP of the coherently superposed RBL does not have a constant relationship with the SOP of the incident CW probe. Furthermore, the instantaneous SOP varies randomly with time because the optical phase is very sensitive to ambient temperature and vibration even in the lab environment. Further theoretical derivation and experimental verification demonstrate, for the first time, that the temporally averaged SOP of the coherently superposed RBL has a simple constant relationship with the SOP of the incident CW probe, and the temporally averaged DOP is 1/3 in an SMF with low and randomly distributed birefringence. The derived formulas and obtained findings can be used to enhance the modelling and improve the performances of phase-sensitive optical time-domain reflectometry and other Rayleigh backscattering based fiber-optic sensors.