Page 340 - Fiber Bragg Gratings

7.2 Chirped and step-chirped gratings 317

recompression is shown in Fig. 7.2. In the simple analysis just given, it
is necessary to recognize that the chirped grating response is far from
ideal. The actual reflection and detailed delay characteristics can have a
profound influence on the performance, especially when the grating is to
be used for compensation of large dispersion in ultrahigh-bit-rate systems.
However, the FOM is a good indicator of the best possible performance
of a grating and may be used to compare the performance achieved with
gratings. Ultimately, the most important parameters that characterize a
transmission link's performance are the bit-error rate (BER), loss penalty,
and error floor. The influence of deviations from ideal transfer characteris-
tics on the BER and loss penalty is considered in Section 7.5.

7.2 Chirped and step-chirped gratings

We have seen the theory of fiber Bragg gratings in Chapter 4. Although
it is possible to mathematically express the coupled modes in a way that
exactly mimics the grating function, the methods of computation are
numerical, since no suitable analytical solutions are available. The trans-
fer matrix method (TMM) is ideally suited to chirped gratings, since the
grating may be broken up into smaller sections of uniform period and/or
refractive index profile. While there are other methods for extracting the

me
Figure 7.2: The maximum pulse re-compression FOM per V( ter) of grat-
ing length. For optimum compression, the bandwidth of the pulse is the same as
the chirped grating bandwidth. As the bandwidth gets smaller, the pulse width
becomes larger, so that the figure of merit drops.