4.5        Reconstructed FBG

4.5.3       Fiber Bragg grating with excess loss

A preliminary experiment has been performed on a nearly homogeneous FBG that presents non-coincident reconstruction from both sides. The reconstruction problem is assumed to come from losses that occur inside the grating.

The FBG presented in this section has been fabricated with a CW-UV laser at 244 nm in a Spectran Photosil single mode fiber. The peak resonance Bragg wavelength l_b is 1308.75 nm, the grating length is about 12 mm. The grating is assumed to have a small tilt as important transmission cladding losses are observed for wavelength under the Bragg wavelength.

In first approximation, the losses are assumed as a frequency independent excess loss E. Then, the equation that relates the reflection and the transmission amplitudes R and T, respectively, becomes

where l is the wavelength.

A transmission intensity measurement has been conducted and the ratio between the minimal and maximal transmission intensity is calculated. A value of 0.25 is obtained for T_min/T_max. A schematic view of the spectral intensity parameters is presented in Fig. 4-22.

Fig. 4-22 Schematic view of the spectral intensity parameters

An OLCR measurement has been performed from both sides of the grating with an OPLD resolution of 20 mm. The reconstruction of the complex coupling coefficient has been performed for both OLCR measurements, considering two different cases, that is, considering or not the excess loss. The constant parameters between these reconstructions are the design wavelength of l_b and the layer thickness of 5 mm.

If the excess loss is not considered, the maximal grating reflectivity is 75 % (T_max = 1 and R + T = 1). The coupling coefficient amplitudes are presented in Fig. 4-23 (top) and it is observed that the two curves are not identical, even if the local variations seem to be strongly related. The grating length L is 11.9 mm.

If the excess loss is considered, we have to determine the maximal intensity reflection R_max and the loss parameter a. The optimal parameters search has been conducted under two requirements : 1) minimize the difference between the reconstructed amplitudes of the coupling coefficient and 2) minimize the remaining amplitudes after the grating output position.

Fig. 4-23 Coupling coefficient amplitudes from the layer-peeling reconstructions performed from both sides of the grating (thin and thick lines), taking into account (top) or not (bottom) the loss effects

The values of 69 % and 6 m^-1 have been found for R_max and a, respectively. The coupling coefficient amplitudes are presented in Fig. 4-23 and in this case, the two reconstructions are nearly identical for the grating positions and the remaining amplitude after the grating output position is under 3 % of the maximal coupling coefficient amplitude.

The difference between the coupling coefficient amplitudes reconstructed from both sides of the grating is presented in Fig. 4-24 (top) for the two reconstruction cases. It is observed that the differences are well approximated by straight lines and that for the reconstruction with loss, the line is horizontal and close to zero.

Fig. 4-24 Top : coupling coefficient amplitude difference for the case where the losses are not considered (thick line) and in the case with the loss in the reconstruction (thin line); Bottom : effective Bragg wavelength calculated for the reconstruction from both sides (the thin line has been shifted by 1 nm for clarity)

We have not yet presented the coupling coefficient phase information. We have observed that this phase information is not affected by the loss parameter a. For this reason, we limit the representation for the case with a = 6. Instead of representing the coupling coefficient phase, we present in Fig. 4-24 (bottom) the effective Bragg wavelength distributions for the reconstruction from both sides (where one response has been shifted by 1 nm), which is a function of the first derivative of the phase information. The two curves are quite similar but some local differences are observed.

We have two possibilities to calculate the excess loss E from the optimal reconstruction parameters R_max and a used in the reconstruction that takes account of the loss. In the first case, R_max = 0.69 and using the ratio T_min/T_max and equation (4-54) an excess loss of 8 % is obtained. In the second case, the loss factor a of 6 m^-1 gives an excess loss of 6.9 % calculated from the light beam attenuation over the grating distance L = 11.9 mm, where I_out/I_in = exp(-aL). Both value are slightly different and can be due to wavelength dependent excess loss.

The spectral reflection and transmission intensities have been plotted in Fig. 4-25 for the case of constant excess loss of 8 %. We observe that for negative wavelength detuning values, R + T is not constant, indicating wavelength dependent excess loss.

Fig. 4-25 Measured spectral reflection and transmission intensities, considering an wavelength independent excess loss of 8 %; the reference wavelength is the Bragg wavelength

The next step in the reconstruction of such grating would be to consider a wavelength dependent loss coefficient a(l).