Page 178 - Fiber Bragg Gratings

4.6 Properties of uniform Bragg gratings 155

first zeroes is twice the bandwidth between the peak and the first zero,
leads to

2
2
From Eq. (4.6.14) it follows that if (K acL) < 7J , then the bandwidth is
an inverse function of the grating length as

2
2
while if the reverse is true, (K acL) > 7T , then the bandwidth is indepen-
dent of the length of the grating and is proportional to the ac coupling
constant,

so that increasing K ac increases the bandwidth.
Zeroes in the reflection spectrum of the grating can be evaluated by
using a similar analysis, to occur at

from which the corresponding detuning follows,

It is also useful to note the approximate position of the side-lobe
peaks at

which leads to

4.6.1 Phase and group delay of uniform period gratings
Figure 4.12 shows the phase response of the two gratings in Fig. 4.11, as
a function of detuning, in units of radians per meter of grating. In the