2.3        FBG properties

2.3.3       Temperature and strain sensitivity

Temperature changes induce two effects on the FBG parameters. The thermal elongation of the fiber dilatation modifies the grating period L and the thermo-optic effects modify the refractive index functions (Dn_ac, Dn_dc). In the same manner, an applied stress on the fiber will lead to a geometric effect on the grating period and a refractive index change due to the photoelastic effect. Both effects can coexist and the Bragg wavelength shift Dl_b can be expressed as

where L represent the grating length and T the temperature. We have assumed that the temperature and the strain fields are constant over the grating length. More details on the strains effects are presented in Chapter 5 and 6, while thermal effects are presented in Chapter 7.

The strain field is described with a tensor that derives from the stress tensor. The stress tensor can be approximated in many cases by a vector (s_x, s_y, s_z) representing the stresses in the three orthogonal directions as indicated in Fig. 2-10

Fig. 2-10 Stress components

The high sensitivity of FBGs to temperature and axial stress has been widely used for sensing applications. Transversal stress measurements are more difficult as the sensitivity is much lower than the axial stress sensitivity and the directions x and y are not defined a priori except for gratings written in PM fibers. This aspect is presented in Chapter 5.