2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85204In this Letter, it is claimed that, in addition to the Chiao-Wu geometric phase and optical Aharonov-Carmi geometric phase, there exists a new interesting geometric phase caused by the helicity inversion of photons in the optical fiber composed periodically of left- and right- handed (LRH) media. By making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, we calculate this geometric phase. It is emphasized that this geometric phase should not been neglected when considering the anomalous refraction on the interfaces between left- and right- handed media.5 pages, LatexOpticsGeneral Physicstext