Page 339 - Fiber Bragg Gratings

316 Chapter 7 Chirped Fiber Bragg Gratings

Note the stipulation on the bandwidth of the pulse, since dispersion
compensation is only valid for the bandwidth of the grating. If the pulse
bandwidth is larger, then the pulse recovery is

For perfect recompression, DfZ = —DgL g, and the pulse remains unal-
tered at the output of the fiber, so long as the bandwidth of the pulse is
smaller than the bandwidth of the grating. We can now define a figure
of merit (FOM) for the bandwidth of the grating, since the maximum
compression ratio that can be achieved is

We can redefine Eq. (7.1.13) by recognizing that the dispersion D g of
the grating is almost exactly 10 nsec/m/AA chirp, so that

We note that the FOM is proportional to the square root of the length
and the chirped bandwidth of the grating. Here, we remind ourselves that
we have used the 1/e bandwidth of the grating. The conversion from the
Gaussian l/e width to its FWHM width, which is more commonly used,
may be done by using the following relationship:

It is clear from Eq. (7.1.13) that the pulse broadening, which can be
compensated for, is

As an example, a 1-meter-long grating with a bandwidth of 10 nm will
have M = 280. This means that an input pulse can undergo a pulse
broadening of —280 times its initial pulse width and be recompressed.
The dependence of the FOM on the grating bandwidth for maximum