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

Abstract

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.

Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers

“…Assuming that there are Rayleigh scatterers in the SMF under investigation, as illustrated in Figure 1 , the Jones matrix , which governs the polarization properties of the coherent RB, has been derived as [ 24 ] …”

“…The matrix elements in Equation (1) are [ 24 ] where . The notations in Equation (2) are defined as [ 24 ] where the subscript stands for the k -th Rayleigh scatterer in the SMF; , is the fiber attenuation, and is the RB reflection coefficient; is the optical phase.…”

“…The matrix elements in Equation (1) are [ 24 ] where . The notations in Equation (2) are defined as [ 24 ] where the subscript stands for the k -th Rayleigh scatterer in the SMF; , is the fiber attenuation, and is the RB reflection coefficient; is the optical phase. The items are the matrix elements of the forward Mueller matrix at the fourth row and the second, third and fourth column, respectively [ 24 ].…”

“…Since the detailed result is not presented, the polarization effects are not considered in the reported physical models of φ-OTDR [ 22 , 23 ]. To understand the polarization properties of the coherent RB when the incident light is perfectly coherent, we recently derived the Jones matrix and the Mueller matrix that govern the polarization properties of the coherent RB [ 24 ]. With these matrices, we theoretically predicted and then experimentally verified the properties of the SOP and the degree of polarization (DOP) of the coherently superposed RB light [ 24 ].…”

“…To understand the polarization properties of the coherent RB when the incident light is perfectly coherent, we recently derived the Jones matrix and the Mueller matrix that govern the polarization properties of the coherent RB [ 24 ]. With these matrices, we theoretically predicted and then experimentally verified the properties of the SOP and the degree of polarization (DOP) of the coherently superposed RB light [ 24 ]. However, the polarization properties of the optical signals detected in φ-OTDR have not yet been investigated in detail, especially the relationship between the distributions of optical phase and fiber birefringence, and the common optical phase and optical power (intensity), which are two optical signals usually detected in φ-OTDR.…”