The internal birefringence η of an optical medium develops the dynamical phase through natural rotation of incident polarized light. The uniform twist of the medium induces an external birefringence in the system represented by k, the angular twist per unit thickness of the medium. This can be visualized through the geometric phase (GP) in association with internal birefringence. The representation of polarized photon, polarization matrix, and birefringent matrix are expressed in the l = 1 orbital angular momentum (OAM) sphere where the corresponding GP is OAM dependent.
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