Page 336 - Fiber Bragg Gratings

7.1 General characteristics of chirped gratings 313

Despite the large dispersion, unchirped gratings have symmetrical delay
characteristics, so that the dispersion changes sign when detuning from
one side of the bandgap to the other [33]. With the several possibilities
of using unchirped gratings for the management of dispersion, chirped
gratings are even more attractive for this application, despite their use
in reflection.
The application of reflective chirped gratings for dispersion compensa-
tion was originally suggested by Ouellette [34]. The group delay through
a fiber is large in comparison with the dispersion of standard optical fibers
at 1550 nm. A grating reflecting a band of wavelengths distributed over
its length benefits from the large group delay in the fiber. We now assess
the performance of chirped gratings as a dispersive filter specifically for
the compensation of chromatic dispersion.
Figure 7.1 shows a schematic of a chirped grating, of length L g and
chirped bandwidth AA chirp. Referring to Fig. 7.1, we note that the chirp
in the period can be related to the chirped bandwidth, AA chirp of the fiber
grating as

The reflection from a chirped grating is a function of wavelength,
and therefore, light entering into a positively chirped grating (increasing
period from input end) suffers a delay ron reflection that is approximately

where A 0 is the Bragg wavelength at the center of the chirped bandwidth
of the grating, and v g is the average group velocity of light in the fiber.

Figure 7.1: The chirped grating.