Principal analysis of embedded fibre Bragg grating sensors

3 Principal analysis of embedded fibre Bragg grating sensors 

Cartesian coordinate system is used, with 1, 2, 3 representing the three principal directions respectively. Eq. (10.1) can be rewritten as  

For strain, subscript (j = 1,2,3,4,5,6) is used. The first three represent the normal strains in the first (fibre axis), second, third directions, respectively, the latter three being the three shear strains, respectively. The strain s of an optic fibre may be contributed by either thermal expansion or stress, hence the symbol s is used for the optic fibre strain induced by stress only. The refraction index n is related to both temperature T and strain g, therefore  

For a homogeneous isotropic medium, it can be assumed that the index of refraction n has a linear relation with temperature T  

Because lights are transverse waves, only the transverse (2, 3 directions) deviations of the reflective index can cause the shift of the Bragg wavelength. Substituting Eqs. (10.4), (10.5) and (10.6) into Eq. (10.3), the peak wavelength shifts for the light linearly polarized in the second and third directions are given below  

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