Page 111 - Fiber Bragg Gratings

90 Chapter 3 Fabrication of Bragg Gratings

this is merely the change in the refractive index of the fiber core as a
function of temperature. Equation (3.1.16) maybe simplified by expanding
and rearranging to

The thermal expansion coefficient of silica a is approximately +5.2
7 5 1
X 1(T , whereas dn/dT ~ +1.1 X 10~ "(T ; the contribution of the
thermal expansion coefficient term is approximately 10% in comparison.
Equation (3.1.17) is further simplified to

where the combined effect of the thermal expansion and the refractive
index change is included in ri, so that the change shift in the Bragg
wavelength is simply

2 1
Typically, dn'/dT ~ 0.5 to 1.0 X 10' °C~ . At a wavelength of 1500 nm
2
the change in the Bragg wavelength with temperature is ~1 to 2 X 10~
1
nm °C- [82,71.
With long uniform gratings, a thin heating wire suitably placed below
a point in the grating can result in a distributed feedback (DFB) structure,
with a double-peaked reflection spectrum. The transfer characteristics of
each half of the grating are identical; however, a A/4 phase difference
induced by the heating wire causes a hole to appear within the band stop
[83]. Such a grating in rare-earth-doped fiber can be used in DFB lasers,
which require the suppression of one of the two lasing modes to force the
laser into single-frequency operation, and in narrow band-pass filters. A
number of methods have been reported for fabricating DFB structures in
fibers, including postprocessing a uniform grating to locally induce a "gap"
in the center of the grating [84]. Alternatively, two gratings may be written
on top of each other, each with a slightly shifted wavelength to form a
Moire phase-shifted grating, opening a bandgap once again [77].