Nonholonomic relation between the electromagnetic field state and the torsion angle in a single-mode lightguide with linear birefringence

The relation between the electromagnetic field state and the torsion angle in a twisted single-mode fiber lightguide (SFL) with linear birefringence is considered for the case where the lightguide is stretched into a straight line. It is shown that this relation is nonholonomic, because of the noncommutativity of two infinitesimal but different changes in the length and torsion of the lightguide. This indicates that the relation between the radiation polarization and the torsion angle in a twisted lightguide is also nonholonomic, and so is the relation between the Pancharatnam geometric-optics phase increment due to the evolution of the light polarization state in an anisotropic optical medium and the SFL torsion angle.