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In order to understand the various phenomenon in fiber gyroscopes, we have developed a unified theory of polarization and vector coherence theory for fiber optics, using propagator techniques, which is valid for arbitrarily large relative polarization phase delays, arbitrary source polarization properties, in combination with birefringent phase modulation. The propagator representation makes clear the multi-path nature of the polarization effects, similar to the multiple scattering of waves, and an example illustrating this point is given. A "master" equation has been obtained for fiber gyroscopes which i s sufficiently general to permit modeling of the many parasitic effects and their interactions, as well as allow realistic assessment of methods for their reduction. As a result of the development of the propagator approach, several interesting results have been found. One important issue is the performance and characterization of the polarizer used in the fiber gyro. A theorem has been shown that "not all polarizers are created equal", even though they have equal extinction ratios. We have found that the fiber gyroscope probes properties of polarizers that cannot be probed without an interferometer that is equivalent to a ring interferometer. It has been found that there is a considerable difference in performance between two polarizers having the same extinction ratio, but one short, the other long, depending on the birefringence and mode coupling. This leads to an extended classification of polarizer properties beyond an ordinary Jones matrix. A new bound on polarizer performance using the propagator approach is given. Another important issue with fiber optic gyroscopes is drift as a function of temperature. Those familiar with testing of fiber gyroscopes are well aware of the often bizarre (highly non monotonic) drift behaviour as a function of temperature. It is shown how temperature drift can be related to the location of various types of birefringence in the gyro coil using a realistic coil model. The propagator for this coil model is also obtained.
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