506 CHAPTER 10. COHERENT LIGHTWAVE SYSTEMS
the limiting value ofB^2 Lby noting that the power penalty can be reduced to below
1 dB in most cases if the system is designed such that|β 2 |B^2 L< 0 .1. For standard
fibers withβ 2 =−20 ps^2 /km near 1.55μm,B^2 Lis limited to 5000 (Gb/s)^2 -km, andL
should be<50 km atB=10 Gb/s. Clearly, dispersion becomes a major limiting factor
for systems designed with standard fibers when transmission distance is increased us-
ing optical amplifiers. Dispersion management would solve this problem. Electronic
equalization can be used for compensating dispersion in coherent systems [100]. The
basic idea is to pass the intermediate-frequency signal through a filter whose transfer
function is the inverse of the transfer function associated with the fiber (see Section
7.2). It is also possible to compensate fiber dispersion through optical techniques such
as dispersion management [101]. PMD then becomes a limiting factor for long-haul
coherent systems [102]–[104].
10.5.5 Other Limiting Factors.....................
Several other factors can degrade the performance of coherent lightwave systems and
should be considered during system design. Reflection feedback is one such limiting
factor. The effect of reflection feedback on IM/DD systems has been discussed in
Section 5.4.5. Essentially the same discussion applies to coherent lightwave systems.
Any feedback into the laser transmitter or the local oscillator must be avoided as it can
lead to linewidth broadening or multimode operation of the semiconductor laser, both
of which cannot be tolerated for coherent systems. The use of optical isolators within
the transmitter may be necessary for controlling the effects of optical feedback.
Multiple reflections between two reflecting surfaces along the fiber cable can con-
vert phase noise into intensity noise and affect system performance as discussed in
Section 5.4.5. For coherent systems such conversion can occur even inside the re-
ceiver, where short fiber segments are used to connect the local oscillator to other re-
ceiver components, such as an optical hybrid (see Fig. 10.10). Calculations for phase-
diversity receivers show that the reflectivity of splices and connectors should be below
−35 dB under typical operating conditions [105]. Such reflection effects become less
important for balanced receivers, where the impact of intensity noise on receiver per-
formance is considerably reduced. Conversion of phase noise into intensity noise can
occur even without parasitic reflections. However, the power penalty can be reduced
to below 0.5 dB by ensuring that the ratio∆ν/Bis below 20% in phase diversity ASK
receivers [106].
Nonlinear effects in optical fibers discussed in Section 2.6 also limit the coher-
ent system, depending on the optical power launched into the fiber [107]. Stimulated
Raman scattering is not likely to be a limiting factor for single-channel coherent sys-
tems but becomes important for multichannel coherent systems (see Section 7.3.3). On
the other hand, stimulated Brillouin scattering (SBS) has a low threshold and can af-
fect even single-channel coherent systems. The SBS threshold depends on both the
modulation format and the bit rate, and its effects on coherent systems have been stud-
ied extensively [108]–[110]. Nonlinear refraction converts intensity fluctuations into
phase fluctuation through self- (SPM) and cross-phase modulation (XPM) [107]. The
effects of SPM become important for long-haul systems using cascaded optical am-
plifiers [111]. Even XPM effects become significant in coherent FSK systems [112].