Humidity response analysis of optical fibers with hygroscopic coatings based on Lamé’s equations

Optical fibers with hygroscopic coatings are widely used for humidity sensing, where the coating expands upon absorbing water, inducing strain in the fiber. This strain is then used to determine humidity. However, previous studies have oversimplified the strain generation process. A comprehensive three-dimensional model of the mechanical interaction between the coating and the fiber is built based on Lamé’s equations. An analytical expression for the induced strain is derived. The proposed model predicts larger humidity-induced strain compared to the reported ones, given the same Young’s modulus or coefficient of humidity expansion for the coating. Interestingly, the effect of coating thickness on strain response are quite similar for both methods. Experimental validation using fibers with a polyimide coating shows strong agreement with the theoretical predictions.