Page 268 - Optical Communications Essentials

Performance Impairments

258 Chapter Fifteen

System impairment starts when the amplitude of the scattered wave is com-
parable to the signal power. For typical fibers the threshold power for this
process is around 10mW for single-fiber spans. In a long fiber chain containing
optical amplifiers, there are normally optical isolators to prevent backscattered
signals from entering the amplifier. Consequently, the impairment due to SBS
is limited to the degradation occurring in a single amplifier-to-amplifier span.

15.5.4. Self-phase modulation and cross-phase modulation
The refractive index n of many optical materials has a weak dependence on op-
tical intensity I (equal to the optical power per effective area in the fiber) given by

P
n n 0 n 2 I n 0 n 2 (15.8)
A eff
where n 0 is the ordinary refractive index of the material and n 2 is the nonlinear
2
index coefficient. In silica, the factor n 2 varies from 2.2 to 3.4 10 8 µm /W.
The nonlinearity in the refractive index is known as the Kerr nonlinearity. This
nonlinearity produces a carrier-induced phase modulation of the propagating
signal, which is called the Kerr effect. In single-wavelength links, this gives rise
to self-phase modulation (SPM), which converts optical power fluctuations in a
propagating light wave to spurious phase fluctuations in the same wave.
To see the effect of SPM, consider what happens to the optical pulse shown
in Fig. 15.7 as it propagates in a fiber. Here the time axis is normalized to the
parameter t 0 , which is the pulse half-width at the 1/e intensity point. The edges
of the pulse represent a time-varying intensity, which rises rapidly from zero to
a maximum value and then returns to zero. In a medium that has an intensity-
dependent refractive index, a time-varying signal intensity will produce a time-
varying refractive index. Thus the index at the peak of the pulse will be slightly
different from the value in the wings of the pulse. The leading edge will see a
positively changing index change (represented by dn/dt), whereas the trailing
edge will see a negative change (represented by dn/dt).
This temporally varying index change results in a temporally varying phase
change, shown by dφ/dt in Fig. 15.7. The consequence is that the instantaneous
optical frequency differs from its initial value across the pulse. That is, since the
phase fluctuations are intensity-dependent, different parts of the pulse undergo
different phase shifts. This leads to what is known as frequency chirping, in that
the rising edge of the pulse experiences a shift toward higher frequencies
whereas the trailing edge of the pulse experiences a shift toward lower fre-
quencies. Since the degree of chirping depends on the transmitted power, SPM
effects are more pronounced for higher-intensity pulses.
For some types of fibers, the time-varying phase may result in a power penalty
owing to a spectral broadening of the pulse as it travels along the fiber. In the
wavelength region where chromatic dispersion is negative, the leading edge of
the pulse travels faster and thus moves away from the center of the pulse. The

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