4.5        Reconstructed FBG

4.5.2       Non-homogenous grating

The grating has been inscribed in a photosentive fiber (Spectran Photosil) with a 193 nm ArF excimer laser. The writing process consists of two irradiation steps :

-         five localalized homogeneous irradiations through a 780 mm-pitch amplitude mask (2000 pulses)

-         an homogeneous FBG exposure through a 902.9 nm-pitch phase mask over a length of 5 mm (500 pulses)

The FBG reflection intensity and time delay are presented in Fig. 4-18.

Fig. 4-18 Reflection intensity and time delay of the non-homogeneous FBG and amplitude / phase masks parameters

The first illumination added a constant index change Dn_dc to the exposed regions. The second exposure through a phase mask produces two different index modulation amplitudes Dn_ac1,2 due to the modified sensitivity in pre-exposed regions (Fig. 4-19a). Fig. 4-19b presents schematically n(z) where the pre-exposed region exhibits higher Dn_dc(z) and lower Dn_ac,2.

Fig. 4-19 Fiber photosentivity curve (a) and FBG refractive index function (b)

The OLCR measurement of our test FBG has been performed from both sides. Fig. 4-20 shows the results for one side where A is the OLCR amplitude and Df the difference between the OLCR phase and the laser phase. A sampling interval of 20 mm in air and a scan speed 3 mm/min have been used. The amplitude S/N is -120 dB. The matching of the laser wavelength with the Bragg wavelength limits Df to a 10 radians range. The grating entrance and output are marked with vertical dotted lines. The grating length is 5.13 mm (half the measured OPLD divided by the fiber group refractive index n_g = 1.45). The FBG regions that have been pre-exposed exhibit lower A and a lower Df slope. This is fully explained by the fabrication process. In the pre-exposed region the modulation amplitude Dn_ac,2 is lower than Dn_ac,1, (lower photosensitivity) and this results in lower local reflectivity. On the other hand, the added index offset Dn_dc leads to a locally higher n_g, resulting in a lower slope for Df. The positive and negative slopes are given by the particular choice of the laser wavelength, that resides between the two local Bragg wavelengths. The amplitude drop at 7.3 mm in A and Df is probably due the fabrication process (small remaining coating part or local laser beam inhomogeneity). Small variations of A and Df in the grating can also be explained by UV-laser beam inhomogeneity. At the end of the grating the amplitude drops by 10 dB and then slowly decreases. The pre-exposure process suppresses the typical oscillations due to the global FBG Fabry-Perot effect observed in homogeneous FBG.

The reconstruction process uses the same parameters we have seen for the homogeneous grating reconstruction, except for the design wavelength (l_d = 1309.25) and the maximal reflection intensity (52 ± 1 %) obtained from an independent measurement. Fig. 4-21 presents the reconstructed coupling coefficient amplitude (a) and phase (b) from one side. The grating limits (circles) have been defined by the phase response where the slope strongly increases. The reconstructed grating is 5.13 mm long as expected. The amplitude in the pre-exposed region is between 140 and 160 m^-1. Based on equation (2), we evaluate for Dn_ac,2 values ranging from 0.70 to 0.8×10^-4. The local amplitude variations are probably due to inhomogeneities in illumination during FBG fabrication. The amplitude level in the other regions is between 210 and 240 m^-1 (Dn_ac,1 between 1.05 and 1.21×10^-4). The phase slope gives information about Dn_dc and the grating period deviation from the design period. Considering a 100 % fringe visibility, a 451.37 nm grating period is obtained from regions only exposed to the phase mask. This value is 0.08 nm smaller than half the phase mask period. This effect is expected as the fiber is stretched during inscription. The grating period is constant along the grating and then, the Dn_dc is found from pre-exposed region. A value of 5.5 to 6.0×10^-4 is calculated and Dn_dc is around five-time Dn_ac, compatible with the number of pulses used in both exposures, 2000 and 400 respectively.

Fig. 4-20 OLCR amplitude (a) and phase difference between OLCR phase and reference laser phase at l_B (b)

Fig. 4-21c is a close-up of the amplitude between the dotted vertical lines. The strong defect observed in the grating enables us to estimate the axial resolution to a value below 20 mm. Fig. 4-21d shows the amplitude and phase differences between reconstructions from both sides. The amplitude difference D|q| and phase difference DArg(q) from independent reconstruction of both sides are below 5 % of the average coupling coefficient amplitude and phase signal respectively. This indicates small OLCR measurement and reconstruction errors. A small slope in the angle difference can be explained by a temperature difference between the measurements.

Fig. 4-21 Coupling coefficient amplitude (a); phase (b); expanded view of coupling coefficient amplitude (c); differences between reconstructions from both sides (d)