Intrinsic Angular Momentum Contribution to the Sagnac Response of a Rotating Helical Optical Fiber

We investigate rotation-induced phase accumulation of structured light in a mechanically rotating uniform helical optical fiber using a four-component optical Dirac-like equation. In the paraxial and weak-geometry regime, the intrinsic dynamics contain a torsion-induced geometric coupling and a mechanical rotation–angular-momentum coupling. We show that, in a common-path mirror-reflection geometry, both the torsion-induced geometric phase and the conventional area-dependent Sagnac contribution cancel over a complete round trip, whereas the intrinsic rotation–angular-momentum phase survives. The surviving phase depends on the intrinsic total angular momentum of the structured optical mode and provides a common-path interferometric route for probing intrinsic angular momentum effects in rotational sensing.