5.2        Characterization of a Fiber Bragg Grating under Diametric Loading

5.2.3       Diametric Load of low-birefringent fiber

The model used to simulate the response of a FBG written in a low-birefringence fiber is based on the following hypotheses:

-         The applying region of diametric load is longer than the FBG length, then the state of strain can be said Plane-strain (no deformation in the direction of the fiber axis)

-         No shear stress

-         The fiber is mechanically homogeneous, isotropic and the deformations are elastic (linearity between stresses and strains)

-         The core fiber is dielectric, isotropic, homogeneous and non dispersive

From the Bragg wavelength equation, the variation of Bragg wavelength is

where

The geometrical variation DL/L , which correspond to the deformation along the Z axis, is zero due to the Plane-strain hypothesis. Then

In the reference where the inverse dielectric permeability tensor e^-1 is diagonal :

and then

where

The relative Bragg wavelength sensitivity depends on light polarization and might be different in the x and y direction. Combining the equations above the variation of Bragg wavelength is given by

The relation between s_i and e_i are derived from the general case and the hypothesis of Plain Strain (e_z = 0). In the last equation, n_x and n_y are approximated by n₀.

For the diametric load of an optical fiber, the core is small regarding the fiber diameter, therefore the stress should be uniform in the core and equal to the stress at (x,y)=(0,0) (Fig. 5-19) [5-14]:

Fig. 5-19 : Diametric load of optical fiber (Z-direction along the fiber axis)

where

Fig. 5-20 FBG reflectivity under diametric load from 0 N to 155 N.

Fig. 5-20 shows the experimental results for a low-birefringence fiber under diametric load. Each curve represents two measurements for a given load applied on a length of 26 mm. Each spectrum is the superposition of the two independent polarization measurements. There is no initial birefringence. For small diametric load both modes are degenerated. For higher values the two modes are clearly separated. For 155 N the separation is about 0.45nm.

Fig. 5-21 shows the measured and calculated peak reflectivity as a function of applied load for the two polarization modes. The wavelength changes are strongly different for the two modes. Slow and fast axis have sensitivities of 31.0 10^-4 and -1.36 10^-4 nm/N. A very good agreement between experimental and calculated values is observed.

Fig. 5-21 FBG Bragg wavelength under diametric load; circles or triangles: experimental data; solid line: calculated values.

In Fig. 5-21 the following values have been taken [5-15, 5-16] for the theoretical model: