8.1         Conclusions

The main parameter that describes a fiber Bragg grating is the refractive index distribution that can be expressed with three independent functions, the refractive index modulation amplitude, the average effective refractive index change and the grating period. A FBG is also spatially described by its complex coupling coefficient, which mixes the period chirp and the average refractive index chirp in a single phase function. The variations of these distributions can lead to various spectral and impulse responses.

A FBG can be described in three domains :

-         space (z) domain with the refractive index distribution or the complex coupling coefficient function

-         frequency (n) domain with the reflection and transmission responses (complex)

-         time (t) domain with the complex impulse response (in reflection or transmission)

The T-matrix method has been used to calculate the complex spectral response r(n) when the complex coupling coefficient distribution q(z) is known. Inversely, q(z) has been retrieved from r(n) by the layer-peeling method. A modified T-matrix and the layer-peeling methods has been presented that take into account homogeneous distributed loss inside the grating.

For a wavelength bandwidth where the fiber dispersion is negligible, the complex OLCR response of a FBG corresponds to the convolution of the complex impulse response of the grating with the degree of coherence of the light source. A new OLCR set-up was developed that simultaneously measure the amplitude and the phase response of FBGs. The main results concerns the time-multiplexing OLCR set-up that exhibits a noise level of -120 dB for optical fiber devices (limited by the Rayleigh back-scattering) and a large range of allowed OPLD resolution due to the phase difference measurement principle. The high dynamic range of the OLCR opens the possibility to measure very weak gratings. The time-multiplexing OLCR set-up also offers the possibility to directly measure the complex spectral response of FBGs.

The complex coupling coefficient is obtained by application of the layer-peeling method. In order to distinguish the period chirp from the DC refractive index chirp, at least two reconstructions at different temperatures or axial strains are required.

The reconstruction process by layer-peeling has been simulated, while systematically varying the reconstruction parameters. It was shown that the required dynamic range of the starting spectral or impulse response is not fundamental and that the number of spectral points has to exceed 10 times the number of layers. Observation of the reconstruction of noisy data has shown that the influence of noise is less important for the reconstruction starting from the impulse response. Finally, the reconstruction process by layer-peeling is less accurate when applied to gratings that exhibit a spectral bandwidth saturation in reflection. Measurements from both sides and inducing a temperature or an axial strain ramp can improve the reconstruction of these gratings.

This reconstruction procedure was applied on homogeneous and non-homogeneous FBGs. The main results are an axial resolution of 20 mm and a maximal error of 5 % calculated by comparison between the reconstructions conducted from both side of the FBG. The reconstruction of a FBG that exhibits loss has also been performed using the modified layer-peeling method. The preliminary results show that a good matching between the reconstructions from both sides can be obtained with minimal remaining coupling coefficient amplitude behind the grating.

A fiber Bragg grating has been embedded in an epoxy sample and a non-homogeneous strain field has been induced in the sample by application of an axial stress. The results of the experiment are fairly good as the strain distribution is obtained along the grating (except for a little part less than 1 mm at each grating sides) and the global behavior is more or less corroborated by a finite element analysis. Nevertheless, this experiment needs to be performed a second time, as the applied loads were very high, inducing not-wanted plastic deformations of the epoxy sample.

An analytical model has been developed that simulates the diametric loading of fiber Bragg gratings. The behavior of FBG's written in low-birefringent fibers is completely described with this model. For gratings written in polarization maintaining fibers, the model completely explain the observed non-linear behavior (rotation of the fiber principal axis) but failed to explain the observed anisotropy between the transverse strain sensitivity of the fast and slow axis.

It has been shown that FBGs coated with polyimide show sensitivities to temperature and relative humidity change. A new fiber optic relative humidity sensor using polyimide coated fiber Bragg gratings has been presented. Tests in a controlled climatic chamber have shown a linear, reversible and accurate sensor response for temperature and relative humidity ranges from 13 to 60 °C, and 10 to 90 %RH, respectively. The dependence of this sensor to the coating thickness has been experimentally and mathematically studied.

A new low coherent system has been implemented in force detection schemes for scanning near-field optical microscopy applications. It allows characterizing the SNOM-tip oscillation modes and amplitudes on the one hand, and, on the other hand, performing topographical measurements with a high precision both in dry and aqueous environments using the shear-force technique.