Page 350 - Fiber Bragg Gratings

7.2 Chirped and step-chirped gratings 327

rear end is higher than in the unapodized grating. The broadband reflec-
tion from the input of the grating has now been reduced significantly due
to apodization. Hence, the ripple should disappear on the long-wavelength
end. However, we notice that the ripple is of the order of that of the
unapodized grating, but now of higher frequency at the input end, Fig.
7. lib, A. This is indicative of interference from the reflection off the rear
end of the grating. Note, too, that the ripple has the lowest frequency
and disappears at the shortest wavelengths, quite the reverse of the
unapodized grating, with reduced interference from the launch end (due
to apodization). The corresponding measured result for this type of a
grating is shown in Fig. 7.lib, B [42].
On the other hand, when light is launched into the short-wavelength
end, the reflected delay ripple is almost identical to that of an unapodized
grating (Fig. 7.lib, C and D). The apodized long-wavelength end does not
play a role in generating the delay ripple.
This result is of particular importance for long chirped gratings. When
one half of a grating remains unapodized while the other half is cosine
apodized, the results are even more dramatic, as shown in Fig. 7.12.
Shown in curve A is the group delay of an unapodized grating, while B
and C refer to the grating profiles shown above the figure in (B) and (C)
with light launched in the directions shown for each grating. The group
delay ripple measured from the long wavelength end, B, has all but disap-
peared for the long-wavelength apodized grating, and the residual ripple
at the long-wavelength edge is again due to the interference from the
short-wavelength end. For light launched into the long-wavelength end
in the short-wavelength apodized grating (C), the group delay ripple C is
as for the unapodized grating, A.
The implication of the apodization is as follows: Long chirped gratings
for dispersion compensation require apodization only on the long wave-
length end of the grating. The type of apodization (see Chapter 5) will
determine the bandwidth reduction in the reflectivity spectrum. The una-
podized short wavelength end, provides extra bandwidth, with a small
penalty on the long wavelength end due to the residual ripple.
An important factor, that influences the performance of chirped grat-
ings in dispersion compensation is the deviation of the delay from linearity
and group delay ripple. Symmetrically apodized gratings offer the prospect
of excellent dispersion compensation [43]. The group delay differences
from linear delay and reflectivity for commonly found cosine and raised
cosine profile apodized gratings are shown in Fig. 7.13. The gratings have