Page 221 - Fiber Bragg Gratings

198 Chapter 5 Apodization of Fiber Gratings

Commonly used functions are as follows:

1. Raised cosine:

2. Gaussian:

3. Tanh:

where the phase offset has been set to zero.

4. Blackman:

5. Sine:

6. Cauchy:

Three of these apodisation functions, the Tanh, raised cosine, and
cosine, are shown in Fig. 5.1 for a grating that has a full chirped bandwidth
of O.Snm and is 100 mm long. The reflectivity has been adjusted to be
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~90%, with a peak-to-peak refractive index modulation of 8 X 10~ .
The beneficial effect of apodization is in the removal of a strong ripple
in the group delay. The corresponding effect on the relative group delay as

Figure 5.1: The reflectivity spectrum of a 100-mm-long, 0.8-nm bandwidth
chirped grating, designed to compensate the dispersion of 80 km of standard fiber,
2
with tanh, cos , and cosine apodization envelopes.