Thermooptically induced bias drift in fiber optical sagnac interferometers

In a fiber optical Sagnac interferometer bias drift arises if the coil experiences varying environmental conditions. We develop a formalism that describes error generation through dynamically changing inhomogeneities in the fiber, taking into account specific winding geometries. As possible sources we assume thermal waves propagating radially through the coil, We verify the basic relations by comparing to results from a heating experiment on a conventional, so-called cylinder coil. We theoretically explore the performance obtained from coiling schemes with improved characteristics. The quadrupolar scheme constitutes the best solution considering rate and angular error, however, it exhibits a pronounced unsymmetry with respect to the propagation direction of the disturbance. We show that, for a given coiling scheme, the asymptotic angular error depends only on the steady state temperature profile, being independent of the preceding transitional behavior. For the quadrupole arrangement with given fiber length and coil diameter it is uniquely determined by the amount of power traversing the coil cross-sectional area, and is independent of the number of layers. Our theory has been developed to characterize coiling schemes in their dynamical-rather than only asymptotic-behavior. It can thus be extended to cover other dynamical sources of error, e.g., vibrational or acoustical.