Investigating the Refractive Index Sensitivity of U-Bent Fiber Optic Sensors Using Ray Optics

Geometrically modified fiber optic sensors (FOS), particularly U-bent FOS, have gained significant attention due to their remarkably high refractive index (RI) and evanescent wave absorbance (EWA) sensitivity, as well as their ergonomic design and ease in handling. In this article, we present a theoretical model for the U-bent FOS probes to predict the sensor behavior by numerically simulating the light propagation in an equivalent 2D semi-circular ring using ray tracing approach. In addition to the effects due to the modification of geometry, this article presents a thorough investigation of the influence of the bend-induced material deformation on the nature of light propagation and refractive losses. We introduce "bend ratio" (ratio of bend radius to fiber core radius) to explain the influence of geometry modification and the bend-induced inhomogeneity in RI (BIRI) of the fiber core on RI sensitivity. The bend ratio of bent plastic optical fiber sensors falls under one of the four bending regimes, namely, gentle, geometric, saturation, and plastic, for which the bend ratios are less than ~35, ~25, 17, and 7, respectively. The results also show that for bend ratios less than 7, BIRI inhomogeneity is responsible for the high RI sensitivity observed with U-bent probes as opposed to the simple geometric modification. This article also indicates the existence of an optimum bend ratio (for a given value of RI of the surrounding medium) where RI sensitivity is maximum. These findings were validated with previously reported experimental results.