Fringe polarimetry enabled by the geometric phase: preliminary theory

In a typical interferometric experiment, the overlap between the reference and probe beams produces an intensity pattern composed of fringes. This fringe pattern contains information regarding the interaction of the probe beam with the sample. If the probe beam passes through a polarizing system, it acquires both a dynamic and geometric phase. The former related to the optical pathlength, whereas the latter related to changes in the state of polarization. As a consequence, the fringe pattern suffers a lateral spatial shift and, mainly due to the geometric phase, change its visibility. In this work, we derive simple expressions relating the fringe visibility with the geometric phase and retardance introduced by the polarizing optical system, in terms of the input polarization state. By doing so, we extract the eigenvectors and eigenvalues of the Jones matrix that characterizes the sample. Therefore, our results enable the implementation of a fringe polarimetry technique, i.e., we can infer the polarization properties of the test sample through visibility measurements.