Page 175 - Fiber Bragg Gratings

152 Chapter 4 Theory of Fiber Bragg Gratings

the intrinsic birefringence of the fiber. If however, the "duty cycle" of the
UV-exposed region is varied so that less than half of a beat length is
exposed per beat length, then the effective rocking angle per beat length
will be reduced, as with the change in 6.

4.6 Properties of uniform Bragg gratings

Quantities of interest are the bandwidth, AA, reflectivity, transmissivity,
the variation in the phase 0, and the grating dispersion D as a function
of detuning.
For the purpose of illustration, Fig. 4.11 shows the reflection spectrum
of two Bragg gratings with different coupling constants K acL of 2 and 8
calculated from Eq. (4.3.16). Note that the central peak is bounded on
either side by a number of subpeaks. This feature is characteristic of a
uniform-period grating of finite length, with a constant fringe visibility.
The abrupt start and end to the grating is responsible for the side struc-
ture. In the weak grating limit (R < 0.2), the Fourier transform of the
variation in the index modulation results in the reflection spectrum [5].

Figure 4.11: Reflectivity of two gratings with coupling constants K a^L of 2
and 8, as a function of normalized detuning. Note that for the weaker reflection
grating (K a^L = 2, dashed curve), the bandwidth to the first zeroes (between the
main reflection peak and the next subpeaks) is much narrower than for the
stronger grating (x a;(L = 8, continuous curve). The side-mode structure increases
rapidly for stronger gratings.