Formulas describing error induced by fiber linear-birefringence in fiber-optic current sensors

In this paper, we derive formulas which generally describe the mechanism of the error induced by the birefringence of the sensing fiber coil, both for Polarimetric OFCS and Sagnac-loop OFCS. The formulas are applied to analyses of the error induced by the current outside the sensing fiber coil. The results are good accordance with numerical simulations.