We compare two algorithms to determine the radial profile of the photoelastic coefficient C in glass optical fibers. We first measure the retardance profile of a transversally illuminated fiber as a function of tensile load. The radial profile C(r) is obtained from the inverse Abel transform of this retardance profile. Our first algorithm expands the measured retardance in its Fourier coefficients before computing the inverse Abel transform. With the second algorithm the expected result of the inverse Abel transform is expanded and the forward Abel transform of that expansion is compared to the measured retardance. We apply both approaches on the retardance measurement of commercially available single mode and multi-mode fibers.
We determine the radial profile of the photoelastic constant C(r) in two single mode and one multimode polymer optical fibers (POFs), all fabricated from polymethylmethacrylate (PMMA). To determine C(r) we first determine the retardance of the laterally illuminated fiber submitted to a known tensile stress uniformly distributed over the fiber cross-section. Then we determine the inverse Abel transform of the measured retardance to finally obtain C(r). We compare two algorithms based on the Fourier theory to perform the inverse transform. We obtain disparate distributions of C(r) in the three fibers. The mean value of C(r) varies from -7.6×10-14 to 5.4×10-12 Pa-1. This indicates that, in contrast to glass fibers, the radial profile of the photoelastic constant can considerable vary depending on the type and treatment of POFs, even when made from similar materials, and hence the photoelastic constant should be measured for each type of POF.
We describe a measurement method to determine the radial distribution of the photoelastic coefficient C in a step-index optical glass fiber. This method is based on the measurement of the retardance profile of a transversally illuminated fiber for increasing tensile load. The radial profile C(r) is obtained from the inverse Abel transform of this retardance profile. We measured three step-index glass fibers with three different core radii. The results suggest that C may be constant across the fiber section and that the mean absolute value of C is slightly larger for glass fibers than for fused silica. Additionally, the shape of the actual refractive index profile can be derived from the retardance measurements.