7.2. PRECOMPENSATION SCHEMES 283
of the optical carrier can be realized by modulating the current injected into the DFB
laser by a small amount (∼1 mA). Although such a direct modulation of the DFB laser
also modulates the optical power sinusoidally, the magnitude is small enough that it
does not interfere with the detection process.
It is clear from Fig. 7.1 that FM of the optical carrier, followed by external AM,
generates a signal that consists of chirped pulses. The amount of chirp can be deter-
mined as follows. Assuming that the pulse shape is Gaussian, the optical signal can be
written as
E( 0 ,t)=A 0 exp(−t^2 /T 02 )exp[−iω 0 ( 1 +δsinωmt)t], (7.2.4)
where the carrier frequencyω 0 of the pulse is modulated sinusoidally at the frequency
ωmwith a modulation depthδ. Near the pulse center, sin(ωmt)≈ωmt, and Eq. (7.2.4)
becomes
E( 0 ,t)≈A 0 exp[
−
1 +iC
2(
t
T 0) 2 ]
exp(−iω 0 t), (7.2.5)where the chirp parameterCis given by
C= 2 δωmω 0 T 02. (7.2.6)Both the sign and magnitude of the chirp parameterCcan be controlled by changing
the FM parametersδandωm.
Phase modulation of the optical carrier also leads to a positive chirp, as can be
verified by replacing Eq. (7.2.4) with
E( 0 ,t)=A 0 exp(−t^2 /T 02 )exp[−iω 0 t+iδcos(ωmt)] (7.2.7)and using cosx≈ 1 −x^2 /2. An advantage of the phase-modulation technique is that
the external modulator itself can modulate the carrier phase. The simplest solution is
to employ an external modulator whose refractive index can be changed electronically
in such a way that it imposes a frequency chirp withC>0 [6]. As early as 1991,
a 5-Gb/s signal was transmitted over 256 km [7] using a LiNbO 3 modulator such that
values ofCwere in the range 0.6–0.8. These experimental values are in agreement with
the Gaussian-pulse theory on which Eq. (7.2.3) is based. Other types of semiconduc-
tor modulators, such as an electroabsorption modulator [8] or a Mach–Zehnder (MZ)
modulator [10], can also chirp the optical pulse withC>0, and have indeed been used
to demonstrate transmission beyond the dispersion limit [11]. With the development
of DFB lasers containing a monolithically integrated electroabsorption modulator, the
implementation of the prechirp technique has become quite practical. In a 1996 exper-
iment, a 10-Gb/s NRZ signal was transmitted over 100 km of standard fiber using such
a transmitter [12].
7.2.2 Novel Coding Techniques
Simultaneous AM and FM of the optical signal is not essential for dispersion compen-
sation. In a different approach, referred to asdispersion-supported transmission, the
frequency-shift keying (FSK) format is used for signal transmission [13]–[17]. The
FSK signal is generated by switching the laser wavelength by a constant amount∆λ