By applying an external stress to an optical fiber its refractive index can change due
to the photoelastic effect. When the optical fiber contains a Bragg grating inscribed
in its core besides of the refractive index their spacial period changes too, allowing
its application as high sensitive optical sensors for measurements of temperature
and stress. From the theoretical point of view, up to date the operation of sensors
using optical fiber with Bragg gratings (FBG) is explained by the photoelastic effect
through appropriate components of the photoelastic tensor but for germanosilicated
optical fibers only, which may to represent limitations to understand the responses
of other classes of FGB used as optical sensors. In this work we show an alternative
theoretical formulation for the studies of the operation properties of an optical sensor
of longitudinal stress based on optical fiber with FBG, which do not depends from
previous knowledge of the components of the photoelastic tensor, but just depends
on the refractive index of the core, Poisson’s ratio, and relative deformation. The
results shown good agreement with the literature and experimental data, allowing to
estimate other features related with the reflectivity of the FGB.
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