Investigation of Planar and Helical Bend Losses in Single- and Few-Mode Optical Fibers

Abstract

In this paper, we describe experimental, simulation, and analytical approaches to study bend losses in single and few-mode optical fibers bent into a circle (in-plane bend) and helix. For the in-plane bend case, we compute loss through simulations and experiments, over the bend diameter range of $9.5\text{--}19.5$ mm at 1550 nm wavelength. For in-plane bend simulations, we obtain the refractive index profile of an equivalent straight fiber by applying the geometrically exact beam theory (GEBT) and conformal mapping, against the conventional approach to use an elasto-optic factor to account for stresses experienced by the fiber. We apply GEBT to compute the strain tensor of a bent fiber. The strain tensor, in turn, is used in the stress-optic law to obtain the refractive index due to bending stress. To account for the geometric effect, we apply the conformal mapping technique. The refractive index profile obtained by applying GEBT followed by conformal mapping is used in full-vectorial FEM simulations carried out in COMSOL to compute bend loss at different diameters. The simulation and experimental results are in close agreement. We extend our approach to few-mode fibers by calculating the planar bend losses for higher order modes. The close agreement of the simulation results, generated without making any ad hoc assumptions about the elasto-optic factor to account for the stress effects, with literature validates our approach. Next, we describe the results of experiments to measure the bending losses of fibers wound helically around the mandrel for bend diameter range $9.5\text{--}19.5$ mm and different helix pitch values. We derive an analytical formula to compute helical bend losses based on the method outlined by Marcuse. Although the results from the formula are in close agreement with the experimental results and predict the exponential decrease of loss with increasing pitch, the formula does not account for the non-monotonous dependence of bend loss on helix pitch, observed experimentally. We present a simple empirical formula to account for the non-monotonic dependence. Finally, we study the influence of micro-bend loss, due to the surface roughness of the mandrels used in the experiments on the bending losses. While the effect of surface roughness can be neglected for the mandrels used in our experiments, its effect may become important in mandrels with higher surface roughness, especially at larger bend diameters.