114 CHAPTER 3. OPTICAL TRANSMITTERS
integrated electroabsorption modulator or an external LiNbO 3 modulator (see Section
3.6). One can even design a modulator to reverse the sign of chirp such thatβ 2 C<0,
resulting in improved system performance.
Lightwave system designed using the RZ format, optical time-division multiplex-
ing, or solitons often require mode-locked lasers that generate short optical pulses
(width∼10 ps) at a high repetition rate equal to the bit rate. External-cavity semi-
conductor lasers can be used for this purpose, and are especially practical if a fiber
grating is used for an external mirror. An external modulator is still needed to impose
the data on the mode-locked pulse train; it blocks pulses in each bit slot corresponding
to 0 bits. The gain switching has also been used to generate short pulses from a semi-
conductor laser. A mode-locked fiber laser can also be used for the same purpose [79].
3.5.4 Relative Intensity Noise
The output of a semiconductor laser exhibits fluctuations in its intensity, phase, and
frequency even when the laser is biased at a constant current with negligible current
fluctuations. The two fundamental noise mechanisms arespontaneous emissionand
electron–hole recombination(shot noise). Noise in semiconductor lasers is dominated
by spontaneous emission. Each spontaneously emitted photon adds to the coherent field
(established by stimulated emission) a small field component whose phase is random,
and thus perturbs both amplitude and phase in a random manner. Moreover, such
spontaneous-emission events occur randomly at a high rate (∼ 1012 s−^1 ) because of a
relatively large value ofRspin semiconductor lasers. The net result is that the intensity
and the phase of the emitted light exhibit fluctuations over a time scale as short as
100 ps. Intensity fluctuations lead to a limitedsignal-to-noise ratio(SNR), whereas
phase fluctuations lead to a finite spectral linewidth when semiconductor lasers are
operated at a constant current. Since such fluctuations can affect the performance of
lightwave systems, it is important to estimate their magnitude [80].
The rate equations can be used to study laser noise by adding a noise term, known
as theLangevin force, to each of them [81]. Equations (3.5.1), (3.5.2), and (3.5.16)
then become
dP
dt=
(
G−
1
τp)
P+Rsp+FP(t), (3.5.26)dN
dt=
I
q−
N
τc−GP+FN(t), (3.5.27)dφ
dt=
1
2
βc[
GN(N−N 0 )−
1
τp]
+Fφ(t), (3.5.28)whereFp(t),FN(t), andFφ(t)are the Langevin forces. They are assumed to be Gaus-
sian random processes with zero mean and to have a correlation function of the form
(theMarkoffian approximation)
〈Fi(t)Fj(t′)〉= 2 Dijδ(t−t′), (3.5.29)