5.1         Axial strain field distribution measurements

5.1.3        OLCR measurements

When the FBG is subjected to a non-homogeneous axial strain field, the Bragg condition depends on the position, and an effective Bragg wavelength l_eff(z) can be defined that takes into account the local chirp. An average Bragg wavelength l_mc can be calculated from the reflectivity intensity as the mass center of the spectrum (equation 2-17), which depends on the applied force value F.

The complex OLCR measurement is performed with an arbitrary laser wavelength reference l_L chosen in the stop-band wavelength range of the grating. Nevertheless, the OLCR phase difference Df in this case depends on the laser choice. For this reason, a new phase difference Df_mc is calculated for a reference wavelength corresponding to the average Bragg wavelength l_mc(F)

In this experiment, the spectral response has been calculated by Fourier transform from the complex OLCR measurements. We present in Fig. 5-5 the calculated average Bragg wavelengths l_mc(F).

The time interval between the three measurements at 384, 299, 207 and 116 N was the same. This explains the good linearity observed between these four points. The measurement at 0 N after the experiment has been performed after 8 hours of relaxation. The Bragg wavelength for this case is much lower than the expected value from the linear fit performed from the four previous points. It is also observed that the grating embedding process increase the Bragg wavelength. This wavelength increase is explained by the sample fabrication process, where an important charging force is applied to the fiber to guaranty the grating alignment and positioning. The fact that the Bragg wavelengths before and after the experiment are not coincident indicates that the applied loads are high enough to induce plastic deformations.

Fig. 5-5 Bragg wavelength obtained from the mass center of the frequency response calculated from the OLCR measurements; the solid line represents the linear fit for the loading cases between 116 and 384 N

The complex OLCR responses using the average Bragg wavelength at the mass center l_cm(F), where F is the force (Fig. 5-6).

Fig. 5-6 OLCR measurements at different axial loads; amplitude (top) and phase difference (bottom), calculated from the Bragg wavelength at the mass center; the curves are shifted in order to improve the visibility

The OLCR amplitude is closely related to the refractive index modulation amplitude Dn_ac, but also takes into account the attenuation of the light beam propagating in the grating. The OLCR amplitude similarity is then explained by the fact that Dn_ac is not significantly modified by the applied stress, and except from the 0 N loading case, the induced chirp is important and then limits the light attenuation. Several inhomogeneities in the FBG are well observed, at the same place and with the same strength in all amplitude curves. The phase difference between the OLCR phase and the Bragg wavelength at the spectral mass center is obtained from equation (5-7). We observe that the phase difference variations increase with the loading amplitude. Locally, the phase difference shows important ripples, much bigger than those observed for the phase difference of the grating before the embedding in the sample (Fig. 5-7). This can be due to local inhomogeneous strain fields produced by the epoxy relaxation.

Fig. 5-7 Phase difference calculated from the Bragg wavelength at frequency mass center for the grating before embedding in the sample (thin line) and after the experiment at 0 N (thick line)

When the sample is charged, the grating length is increased (insert part of the figure Fig. 5-8 for the 384 N loading case) and the induced chirp reduces significantly the Fabry-Perot effect. This can be observed in Fig. 5-8 for the 384 N loading case, where the amplitude drop at the grating output is 20 dB deeper than for the 0 N case.

Fig. 5-8 OLCR amplitude response at 384 N (thin line) and 0 N (thick line)