7.9. HIGH-CAPACITY SYSTEMS 317
slot is required for a RZ system making use of 1-ps pulses, transmission at bit rates as
high as 500 Gb/s appears to be feasible using DCFs or chirped fiber gratings designed
to provide compensation ofβ 3 over a 4-nm bandwidth. In a 1996 experiment [181],
a 400-Gb/s signal was transmitted by managing the fiber dispersion and transmitting
0.98-ps pulses inside a 2.5-ps time slot. Without compensation of the third-order dis-
persion, the pulse broadened to 2.3 ps after 40 km and exhibited a long oscillatory tail
extending over 5–6 ps, a characteristic feature of the third-order dispersion [106]. With
partial compensation of third-order dispersion, the oscillatory tail disappeared, and the
pulse width reduced to 1.6 ps, making it possible to recover the 400-Gb/s data with
high accuracy. Optical pulses as short as 0.4 ps were used in 1998 to realize a bit rate
of 640 Gb/s [182]. In a 2001 experiment, the bit rate was extended to 1.28 Tb/s by
transmitting 380-fs pulses over 70 km of fiber [183]. Propagation of such short pulses
requires compensation of second- third- and fourth-order dispersion simultaneously.
It turns out that if sinusoidal phase modulation of the right kind is applied to the lin-
early chirped pulse before it is transmitted through a GVD-compensated fiber, it can
compensate for both the third- and fourth-order dispersion.
7.9.4 PMD Compensation
As discussed in Section 2.3.5, PMD leads to broadening of optical pulses because
of random variations in the birefringence of an optical fiber along its length. This
broadening is in addition to GVD-induced pulse broadening. The use of dispersion
management can eliminate GVD-induced broadening but does not affect the PMD-
induced broadening. For this reason, PMD has become a major source of concern for
modern dispersion-managed systems [184]–[196].
Before considering the techniques used for PMD compensation, we provide an
order-of-magnitude estimate of the system length in uncompensated systems. Equa-
tion (2.3.17) shows that the RMS pulse broadening for a link of lengthLis given by
σT≡〈(∆T)^2 〉^1 /^2 =Dp
√
L, whereDpis the PMD parameter and∆Tis the relative delay
along the two principal states of polarization (PSPs). It is important to note thatσTde-
notes an average value. The instantaneous value of∆Tfluctuates with time over a wide
range because of temperature and other environmental factors [192]. If∆Texceeds the
bit slot even for a short time interval, the system will stop functioning properly; this
is referred to as fading oroutagein analogy with a similar effect occurring in radio
systems [184].
The performance of a PMD-limited system is quantified using the concept of the
outage probability, which should be below a prescribed value (often set near 10−^5 or
5 minutes/year ) for the system [184]. This probability can be calculated noting that
∆Tfollows a Maxwellian distribution. In general, the RMS valueσTshould only be a
small fraction of the bit slotTBat a certain bit rateB≡ 1 /TB. The exact value of this
fraction varies in the range 0.1–0.15 depending on the modulation format (RZ, CRZ, or
NRZ) and details of the input pulse. Using 10% as a conservative criterion, the system
length and the bit rate should satisfy the condition
B^2 L<( 10 Dp)−^2. (7.9.7)