Finite element model for embedded fiber Bragg grating sensor

This paper presents an integrated formulation for the calculation of the spectral response of a fiber Bragg grating sensor embedded in a host material system, as a function of the loading applied to the host structure. In particular, the calculation of the transverse strain sensitivity of a fiber Bragg grating sensor through the calculation of the change in effective index (or indices) of refraction of the fiber cross-section due to the applied load is presented in detail. For the calculation of the fiber propagation constants, a two-step finite element formulation is used incorporating the optical, geometric and material properties of the cross-section. Once the propagation constants and principal optical axes are known along the fiber, a modified transfer matrix method is applied to calculate the spectral response of the FBG. It is shown that the FE formulation yields close agreement with previous methods for benchmark diametrical compression cases. However, the current method provides the potential to evaluate the effects of high strain gradients across the optical fiber core present in some loading applications.