5.1         Axial strain field distribution measurements

5.1.5        Reconstruction of the complex coupling coefficient

The reconstruction of the complex coupling coefficient has been performed with the layer-peeling algorithm using 5 mm layer thickness and a design period corresponding to l_cm(F).

It is observed in Fig. 5-10 (top) that the applied strain field does not perturb the coupling coefficient amplitude. This is expected as the coupling coefficient amplitude is only related to the refractive index modulation amplitude and effective refractive index and these parameters are not significantly modified (0.22 % of relative variations). The local variations of the refractive index modulation amplitude are well determined and the reproducibility between the different measurements is very good.

Fig. 5-10 Coupling coefficient amplitude (top), phase (middle) and phase polynomial fit at the 6^th order (bottom) retrieved using the layer-peeling method; the design wavelength corresponds to the Bragg wavelength obtained from the frequency mass center; the curves are shifted to enhance the visibility

In the case of axial stress fields, we have seen in equation (5-6) that the stress is proportional to the relative Bragg wavelength change. In non-homogeneous axial strain fields, the effective Bragg wavelength distribution l_eff(z) is used and can be related to the coupling phase distribution f_q (Fig. 5-10 middle) from equation (3-19) (where L_d = l_mc/2n_eff)

where n_eff is the effective refractive index (n_eff = 1.45 in this experiment).

A polynomial fit to the 6^th order is performed on f_q to reduce the local variations effects in the derivative operation needed to obtain l_eff (Fig. 5-10 bottom).

The local Bragg wavelength is presented in Fig. 5-11 (left) and the difference with l_mc(F) in the right part. The polynomial fitting of the coupling coefficient phase shows larger errors at the extremities that are amplified by the derivative process. This explains that the first and last millimeter of the grating has been plotted in gray in the Bragg wavelength difference to indicate not well-defined values. We observe that the position in the fiber of the minimal Bragg wavelength difference (corresponding to the sample center) is displaced by 600 mm from 384 to 116 N. This could indicate a non-symmetric loading.

Fig. 5-11 Effective Bragg wavelength distribution (left) and effective Bragg wavelength difference with the average Bragg wavelength obtained from the frequency mass center (right)

From equation (5-6), the axial strain distribution e_z(z) can be deducted from the effective Bragg wavelength