Page 344 - Fiber Bragg Gratings

7.2 Chirped and step-chirped gratings 321

Figure 7.5: Comparison of the delay characteristics of the SCGs shown in
Fig. 7.4. For the 200-section grating, N/L g = 2 steps/mm, while for the 42-section
grating, N/L g = 0.42 steps/mm.

We now examine a 4-mm-long SCG with a chirp of 1 nm. The minimum
number of sections of this grating according to Equation (7.2.5) is 2.
Simulations of the reflectivity and delay are shown in Figs. 7.6 and 7.7,
respectively, for two and three sections. Along with these gratings the
characteristics of a 50-section grating is also shown. The grating charac-
teristics are surprisingly similar despite the few sections, especially noting
the positions of the zeroes and the central part of the reflection spectrum.
The agreement is equally valid for apodized fiber Bragg gratings [39].
For convenience, it may be simple to double the minimum number of
calculated sections for good linearly chirped gratings.
The design of quasi-linearly chirped gratings has been represented
graphically in Fig. 7.8. This design diagram shows that a grating must
be divided into a minimum number of sections per millimeter for a given
chirp, irrespective of the length of the grating. The criterion used for the
design is that the total group delay of a continuously chirped grating with
the same coupling constant and length as the step-chirped grating should
differ by less than 1% of its maximum value. For example, the maximum
deviation in the delay ripple in a 100-mm-long unapodized grating should
be less than 10/psec across 90% of the available bandwidth. This result