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We review the kinematic explanation of the Sagnac effect in fiber gyroscopes and recall that the index of the dielectric medium does not have any influence. Furthermore, we present a novel electrodynamic approach that confirms in more detail that the Sagnac phase shift of a ring-waveguide interferometer is the same as for the original Sagnac experiment with plane waves in a vacuum.
Arditty et al. (1981) studied this question.