Page 361 - Fiber Bragg Gratings

338 Chapter 7 Chirped Fiber Bragg Gratings

in the effective index of a mode. We assume that the central Bragg wave-
length of a chirped grating is

so that the change in the reflection wavelength as a function of the change
in the mode index becomes,

Equating the change in the mode index to the birefringence in the
fiber leads to

For a DCG with a dispersion of D g psec/nm, a change in the Bragg
wavelength as a result of the change in the polarization induces a delay,
T =
PMD ^BraggDg, from which we get the result

where B' is the normalized birefringence, ~B/n eff. Equation (7.4.4) shows
that the PMD is dependent on the dispersion and birefringence but not
on the length of the grating. A chirped reflection grating with a perfectly
5
linear dispersion of 1310 psec/nm and a birefringence of 10 ~ at a wave-
length of 1550 nm will have a PMD of 28 psec! This result is of the order
that has been reported in apodized DCGs [50]. It is clear that even a
small birefringence causes a severe PMD penalty. Figure 7.23 shows how
the PMD changes with grating dispersion as a function of birefringence.
For high dispersion values, it may be impossible to achieve the low bire-
fringence needed for a low PMD value. For example, a dispersion of 5
8
nsec/nm and a PMD of 1 psec require a birefringence of ~6 X 10~ , a
value that may not be achievable even with gratings in standard fibers.
The problem is compounded if the DCG is unapodized. From Eq.
(7.4.3) we note that the change in the Bragg reflection wavelength is
5
~0.02 nm for a birefringence of 1 X 10~ at a wavelength of 1550 nm.
Since there is a high-frequency ripple of period —0.01 nm on the short-
wavelength side of the DCG shown in Fig. 7.10, on an overall average
dispersion slope of 1310 psec/nm, large jumps in PMD may occur, even
with very weak birefringence. These jumps could be of the order of the
amplitude of the ripple (100 psec).