12.10 Principles of Solitons
503
Note that for a given value of s 0 , this is independent of the bit rate. For example,
if the data rate is 20 Gb/s, then the FWHM pulse width is 5.5 ps, which also occupies
11 percent of the bit slot.
12.11 Summary
For low optical signal power levels, an optical fiber behaves as a linear transmission
medium. This means three things: (a) The properties of a fiber do not change as
the optical signal power varies, (b) the wavelength does not change as the signal
propagates along the fiber, and (c) a specific signal does not interact with other
simultaneously propagating signals at different wavelengths. However, for power
levels that are higher than about +3 dBm (2 mW) the fiber material starts to exhibit
nonlinear power-dependent properties. These nonlinear effects are manifested as
interactive changes and power loss in the propagating signal. The optical power loss
gives rise to a nonlinear power penalty.
Optical nonlinearities can be classified into scattering-related and refractive indexrelated categories. The nonlinear inelastic scattering processes include stimulated
Raman scattering (SRS) and stimulated Brillouin scattering (SBS). The second category of nonlinear effects arises from intensity-dependent variations in the refractive
index in a silica fiber, which is known as the Kerr effect. These effects include selfphase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing
(FWM). Note that certain nonlinear effects are independent of the number of WDM
channels.
SBS, SRS, and FWM result in gains or losses of signal power in a wavelength
channel. The power variations depend on the optical signal intensity. These three
nonlinear processes provide gains to some channels while depleting power from
other channels, thereby producing crosstalk between the wavelength channels. SPM
and XPM affect only the phase of signals, which causes chirping in digital pulses.
This can worsen pulse broadening due to dispersion, particularly in very high-rate
systems. FWM can be suppressed by avoiding the use of fibers with both positive
and negative chromatic dispersion values in the operating wavelength band.
Problems
12.1 A 50-km single-mode fiber has an attenuation of 0.55 dB/km at 1310 nm and
0.28 dB/km at 1550 nm. Compare the effective lengths of this fiber at 1310
and 1550 nm.
12.2 Consider a 1550-nm optical source that has a 40-MHz linewidth. Suppose a
given single-mode fiber has a 72-μm
2 effective area and a 0.2-dB/km attenuation at 1550 nm. Assuming that the polarization factor b = 2 and that the
Brillouin gain coefficient is g B = 4 × 10
−11 m/W, what is the threshold power
503
Note that for a given value of s 0 , this is independent of the bit rate. For example,
if the data rate is 20 Gb/s, then the FWHM pulse width is 5.5 ps, which also occupies
11 percent of the bit slot.
12.11 Summary
For low optical signal power levels, an optical fiber behaves as a linear transmission
medium. This means three things: (a) The properties of a fiber do not change as
the optical signal power varies, (b) the wavelength does not change as the signal
propagates along the fiber, and (c) a specific signal does not interact with other
simultaneously propagating signals at different wavelengths. However, for power
levels that are higher than about +3 dBm (2 mW) the fiber material starts to exhibit
nonlinear power-dependent properties. These nonlinear effects are manifested as
interactive changes and power loss in the propagating signal. The optical power loss
gives rise to a nonlinear power penalty.
Optical nonlinearities can be classified into scattering-related and refractive indexrelated categories. The nonlinear inelastic scattering processes include stimulated
Raman scattering (SRS) and stimulated Brillouin scattering (SBS). The second category of nonlinear effects arises from intensity-dependent variations in the refractive
index in a silica fiber, which is known as the Kerr effect. These effects include selfphase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing
(FWM). Note that certain nonlinear effects are independent of the number of WDM
channels.
SBS, SRS, and FWM result in gains or losses of signal power in a wavelength
channel. The power variations depend on the optical signal intensity. These three
nonlinear processes provide gains to some channels while depleting power from
other channels, thereby producing crosstalk between the wavelength channels. SPM
and XPM affect only the phase of signals, which causes chirping in digital pulses.
This can worsen pulse broadening due to dispersion, particularly in very high-rate
systems. FWM can be suppressed by avoiding the use of fibers with both positive
and negative chromatic dispersion values in the operating wavelength band.
Problems
12.1 A 50-km single-mode fiber has an attenuation of 0.55 dB/km at 1310 nm and
0.28 dB/km at 1550 nm. Compare the effective lengths of this fiber at 1310
and 1550 nm.
12.2 Consider a 1550-nm optical source that has a 40-MHz linewidth. Suppose a
given single-mode fiber has a 72-μm
2 effective area and a 0.2-dB/km attenuation at 1550 nm. Assuming that the polarization factor b = 2 and that the
Brillouin gain coefficient is g B = 4 × 10
−11 m/W, what is the threshold power