4.5        Reconstructed FBG

This section presents the reconstruction results obtained on a nearly homogeneous grating, a FBG with local pre-exposure that induce index chirp and finally the case of a blazed grating that exhibits insertion loss and then requires to use the modified layer-peeling method proposed in chapter 3, in section §3.3.2.

4.5.1        Homogeneous FBG

The FBG has been inscribed in an H₂-loaded SMF28 compatible fiber with a 193 nm ArF excimer laser through a 902.9 nm-pitch phase mask over a length of 5 mm. For an ideal homogeneous grating, Dn_ac, Dn_dc and dq/dz are constant. In the reality, Dn_ac and Dn_dc could show some small variations due to laser beam inhomogeneities. Fig. 4-14 presents the spectral response of the grating (intensity) measured with a tunable laser and simulated curve with the best approaching homogeneous grating parameters. We can see an important difference between the curves, probably indicating the presence of non-homogeneities in the grating.

Fig. 4-14 Measured reflection intensity (circles) and spectral fit with the most approaching homogeneous grating

The OLCR measurement of the grating has been performed from both sides. Fig. 4-15 shows the results from one side measurement where A is the OLCR amplitude and Df the difference between the OLCR phase and the laser phase. The OPLD sampling interval is 20 mm, the scan speed is 3 mm/min and the laser wavelength is l_B = 1309.33 nm.

Fig. 4-15 OLCR amplitude (a) and phase difference between OLCR phase and reference laser phase at l_B (b)

The S/N for the amplitude signal is -120 dB. The phase difference Df is nearly linear by parts as expected for a homogeneous grating and the slope is close to zero due to the perfect matching of the laser wavelength to the Bragg condition. It has to be noticed that the range of Df is less than ten radians, as compared to the range of the OLCR phase, which exceeds millions of radians for the same OPLD. The FBG entrance and output positions are located at OPLD₁ = 0.13 and OPLD₂ = 15.6 mm, respectively. Hence a grating length of DOPLD/(2n_g)=5.33 mm is obtained using a group refractive index of n_g =1.45. Inside the grating, the OLCR signal is mainly due to a single reflection. The small variations observed are due to some UV-laser beam inhomogeneities. Behind the output, the FBG acts as a Fabry-Perot and the signal is due to multiple reflections. Each zero in the reflection amplitude (Fig. 2a) corresponds to a p shift in the phase difference (Fig. 2b). A zero is observed in the OLCR amplitude inside the grating region at 14.48 mm. This effect is expected by theory for strong FBGs [4-14]. At this position, the OCLR phase difference has a 2p shift due to noisy data that limits the unwrapping process.

The complex spectral reflectivity r(n) is obtained from the OLCR measurement with the following parameters for the data processing : zero padding to an OPLD of 52 cm and a spectral resolution of 3.6 pm at 1309 nm. The transmission intensity measurement of the grating with the tunable laser gives a maximal reflection intensity of 87.9 ± 1 %. The layer-peeling algorithm has been applied on the r(n) function using the following parameters : 2000 layers of 5mm with l_B as design wavelength, an effective refractive index of 1.45. This corresponds to a spectral range between 1252.8 and 1371.2 nm with 36161 points out of the 2²⁰ from the FFT. The reconstruction length is 10 mm. The maximal reflectivity has been adjusted to minimize the amplitude difference Dq from both sides. A value of 87.5 % was found, consistent with the transmission measurement.

Fig. 4-16 Coupling coefficient amplitude (a); phase (solid line) and fit (dashed line) (b); differences between reconstructions from both sides (c)

Fig. 4-16 presents the reconstructed coupling coefficient amplitude (a) and phase (b) from one side. Fig. 4-16c shows the amplitude and phase differences between reconstructions from both sides. The longitudinal resolution is estimated at 20 mm from the smallest variations observed in both reconstructions. The grating limits (circles in Fig. 4-16) are found in the phase response where the phase variation is nearly asymptotic. The reconstructed grating is 5.33 mm long as expected and has an average coupling amplitude of 3.3 cm^-1 (Dn_AC = 1.25×10^-4) with 25 % variations. The coupling coefficient amplitude behind the grating remains at 0.1 cm^-1 due to small propagating losses in the cladding that are not considered in the reconstruction algorithm. The coupling coefficient phase is limited to ± 0.3 radians, indicating small deviations from design wavelength. The dashed line in Fig. 3b corresponds to average change in Dn_dc. Other variations of Arg(q) are seen in the phase reconstruction but they are not completely understood. It has to be noted that these variations are not artifacts as they disappear in the phase difference DArg(q) from both sides (Fig. 3c). The amplitude difference D|q| from independent reconstruction of both sides is under 3 % of the average coupling coefficient amplitude. This indicates small OLCR measurement and reconstruction errors.

Fig. 4-17 Reflection intensity (a), delay time (b) calculated from the reconstructed coupling coefficient (solid line) and directly measured with a tunable laser (circles)

The T-matrix method is used to compute the reconstructed complex spectral response from the obtained coupling coefficient. A direct measurement of the complex spectral reflectivity of FBG is performed with the same set-up used in an OFDR configuration (optical frequency domain reflectometry, §4.3.7). In this case the laser frequency is scanned while the mirror has a defined position. The phase difference between the laser and the low coherent light source compensates the phase drifts in the same way as in the OLCR configuration. Fig. 4-17 shows both calculated and measured spectral responses. A good agreement is observed, confirming the validity of the entire reconstruction process.