Generalized Sagnac-Wang-Fizeau formula

We present a special-relativistic analysis of deformable interferometers where counterpropagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that the phase shift has two contributions: One contribution is independent of the refractive index n and has the form of a line integral. This term gives the Wang empirical formula for deformable Sagnac interferometers. The second term is quadratic in n and has the form of a double integral. The analysis provides a unifying framework incorporating the Sagnac, Wang, and Fizeau effects in a single scheme, gives a rigorous proof of Wang empirical formula, and can be used to study various perturbations of Sagnac interferometers.