Page 262 - Optical Communications Essentials

Performance Impairments

252 Chapter Fifteen

Here L is the length of the operational fiber, D TX is the dispersion of the opera-
tional fiber, and D DCF is the dispersion of the DCF.

15.3.2. Bragg grating compensators
Another way of viewing dispersion is to consider the propagation speed of the
different wavelength constituents of an optical pulse. When an optical pulse
travels along a fiber in the anomalous-dispersion region (where D TX 0), the
shorter-wavelength (higher-frequency) components of the pulse travel faster
than the longer-wavelength (shorter-frequency) components. This is a disper-
sive effect which broadens the pulse.
To compensate for the difference in arrival times of the various frequency
components resulting from anomolous dispersion, one can use a chirped fiber
Bragg grating that provides normal dispersion. As shown in Fig. 15.3, in such a
dispersion compensator the grating spacing varies linearly over the length of the
grating. This results in a range of wavelengths (or frequencies) that satisfy the
Bragg condition for reflection. In the configuration shown, the spacings decrease
along the fiber which means that the Bragg wavelength decreases with distance
along the grating length. Consequently the shorter-wavelength components of
a pulse travel farther into the fiber before being reflected. Thereby they experi-
ence greater delay in going through the grating than the longer-wavelength
components. The relative delays induced by the grating on the different frequency
components of the pulse are the opposite of the delays caused by the fiber. This
results in dispersion compensation, since it compresses the pulse.
Prior to the year 2000, manufacturing difficulties limited gratings to lengths
of about 10cm. Since the round-trip time T inside the grating of length L G is
R
given by T R 2n G L G c, where n G is the refractive index of the grating fiber, the
maximum round-trip delay time of light through a 10-cm-long grating is 10µs.
The delay per unit length is 500ps/nm, which corresponds to the product of the
dispersion D G of the grating and the spectral width ∆λ of the light being
delayed, that is,
D G ∆λ (15.3)
T R
L G

λ 1 λ 2 λ 3
Incident pulse
Other wavelengths
pass through
Decreasing grating spacing

Reflected pulse
Figure 15.3. Chromatic dispersion compensation can be accom-
plished through the use of a chirped fiber Bragg grating.

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