Page 118 - Fiber Bragg Gratings

3.1 Methods for fiber Bragg grating fabrication 97

demonstrated [100]. Using the same method, different structures have
been fabricated, such as a grating with a 77/2 phase shift in the middle.
A fiber in which the taper in one half has been etched more than the other
was stretched before a grating was written. Relaxing the fiber introduced a
phase shift and therefore a band pass in the center of the transmission
spectrum of the otherwise unchirped grating [991.
A somewhat less flexible method relies on the tapering of the fiber
core [94]. Tapering the core affects the local effective index n eff of the
mode. To the first approximation, the effective index varies linearly with
decreasing diameter for an initial fiber V-value of approximately 2.4, but
varies more slowly, asymptotically approaching the cladding index, as the
core diameter goes to zero. Thus, a uniform-period grating written in
tapered section will be chirped. The maximum chirp AA achievable in a
fiber may be calculated from

where An is the difference between the mode index and the cladding
refractive index, Equation (3.1.27) translates to a maximum chirp on the
order of 30 nm (Arc = 0.03); however, it would be difficult for practical
reasons to achieve more than —10 nm of chirp.
A chirp of 2.7 nm for a 10-mm long grating was reported for a fiber
tapered by 50 /urn over that length [94]. Local heating and stretching may
fabricate a tapered fiber. Note, however, that a fiber with a large taper
will have a lower reflectivity for the shorter wavelengths (with a uniform
period grating), since the mode power spreads to the nonphotosensitive
cladding, reducing the efficiency of the grating.
Another technique, that overcomes the problem associated with the
core-taper method described above is based on expanding the core by
thermal out-diffusion of the photosensitive core dopant [101]. The im-
portant difference between the two methods is that while the tapering of
the core reduces the V-value of the fiber, the out-diffusion of the photosensi-
tive core leaves the V-value unchanged [102]. This may be understood by
remembering that the reduction in the core index as the dopant out-
diffuses is compensated for by the increase in the core radius. The frac-
tional power in the core remains unchanged (due to the fixed V-value),
but since the core index is reduced, so is the mode index.
Heating the fiber locally by an oxyhydrogen flame for 2 minutes
resulted in the mode field diameter expanding from 7.8 to 16.8 /am. Subse-
quent writing of a 10-mm long grating in the tapered core region of a