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.Comment: 8 pages, Latex. accepted by Phys. Lett.