Page 343 - Fiber Bragg Gratings

320 Chapter 7 Chirped Fiber Bragg Gratings

grating. A more detailed analysis [39] bears out the simple conclusion; a
more accurate (to 1%) fit increases the bandwidth of each step by only
40% [391. Curiously, the comparison between gratings of the same chirp
but different number of steps gets better if the total chirp is reduced by
b.\ chirp!N. The convergence to the asymptotic transfer characteristics is
faster for all SCGs with the chirp bandwidth adjustment, although this
is especially true for those with a few sections. For a large number of
sections, this really does not matter. For all the following simulations,
the bandwidth adjustment has been included.
Figures 7.4 and 7.5 show the calculated reflectivity and delay, respec-
tively, of an SCG (L g = 100 mm, &A chirp = 0.75 nm) grating with 200
sections (2 steps/mm) and an SCG with only 0.42 steps/mm [total steps =
42, according to Eq. (7.2.5)]. It is immediately apparent that the agreement
between the two spectra is good. The reflectivity spectrum has a ripple
that is characteristic of unapodized gratings, as does the group delay. The
strong ripple in the group delay plays an important role in the recompres-
sion of a dispersed pulse. While there is an average delay slope, the ripple
frequency becomes smaller toward the end from which the reflection is
measured. This is true for even continuously chirped gratings, and the
influence of apodization is examined in Section 7.3.

Figure 7.4: Reflectivity of a 100-mm-long SCG with 200 sections as well as
42 sections. The reflectivity curves have been offset to allow easy examination.