The present paper analyzes the propagation behavior of light beams along parabolic index optical fibers for the cases where the center axes of the fibers are deformed along helical bends, which are caused when several optical fibers are twisted into a bundle for the purpose of cabling. The analysis is based on geometrical optics and is limited to the case where the center axes of the fibers are bent along a double helix, which arises when two fibers are twisted into a bundle, and the two bundles thus obtained are entwisted once more into a cable. It is also assumed that the center axis of the cable thus established is curved in a circular bend with a constant curvature. Ray equations for this case are derived, and their solutions are studied in detail theoretically and numerically. As a result, conditions are obtained for the occurrence of the divergence phenomenon of the beam trajectory as well as for the matched incidence of light beams to minimize the undulation amplitude of beam trajectories. Moreover, it is clarified that whether the two helices composing the double helix are twisted in the same or opposite directions has somewhat different effects upon the conditions for the divergence phenomenon and the matched incidence as well as the propagation behavior of light beams. Some problems with the application of the present cabling technique to parabolic index optical fibers are also discussed.
Shinnosuke Sawa, "Light beam propagation along helical bands of parabolic index optical fibers," Appl. Opt. 15, 2792-2799 (1976)