Page 457 - Fiber Bragg Gratings

434 Chapter 9 Measurement and Characterization of Gratings

refractive index of the fiber is n 0 without stress, and the stress-optic
2
5
coefficients B± and B 2 are both positive, with B 1 = 4.12 X 10~ mm kg" 1
1
5
2
and B 2 = 0.64 X 10~ mm kg" [48]. The radial component of the stress
may be calculated from the axial component as [49]

The sign of the axial stress is found by measurements on silica fibers
with and without strain, and through symmetry properties, cr r(r) = a^r)
= (T 2(r)/2. The axial stress cr^r) indicates positive axial tension for a
positive sign and compressive strain with a negative sign.
By measuring the stress profile, the changes in the refractive index
can be calculated as a function of the UV irradiation. Experiments per-
formed by Fonjallaz et al. [46,50] have found that the axial stress increased
with UV inscription of gratings, contrary to the stress-relief model [42].
The fibers are found to be either under slight axial compression or under
2
tensile stress before UV irradiation (between —5 and +1.6 kg mm"" ).
The stress changes before and after UV irradiation of a fiber with a Ge
concentration of 12% are shown in Fig. 9.26. The maximum stress on the
2
axis of the fiber is found to be 14.2 kg mm"" . An increase in the tension

Figure 9.26: The measured radial stress profile of a fiber before and after
the inscription of the grating (courtesy Hans Limberger [46]). (from: Fonjallaz P
Y, Limberger H G, Salathe, Cochet F and Leuenberger B, "Tension increase corel-
lated to refractive index change in fibers containing UV written Bragg gratings",
Opt. Lett., 20(11), 1346-1348, 1 June 1995.)