Geometric Phase and Helicity Inversion of Photons Propagating inside a Noncoplanarly Curved Optical Fiber

The Letter presents an exact expression for the non-adiabatic non-cyclic geometric phase of photons propagating inside a noncoplanarly curved optical fiber by using the Lewis-Riesenfeld invariant theory. It is shown that the helicity inversion of photons arises in the curved fiber. Since we have exactly solved the time-dependent Schr\"{o}dinger equation that governs the propagation of photons in a curved fiber and, moreover, the chronological product is not involved in this exact solution, our formulation therefore has several advantages over other treatments based on the classical Maxwell's theory and the Berry's adiabatic quantum theory. The potential application of helicity inversion of photons to information science is briefly suggested.