3.3. SEMICONDUCTOR LASERS 93
fibers. A relatively narrow spectral width of emitted light allows operation at high bit
rates (∼10 Gb/s), since fiber dispersion becomes less critical for such an optical source.
Furthermore, semiconductor lasers can be modulated directly at high frequencies (up
to 25 GHz) because of a short recombination time associated with stimulated emission.
Most fiber-optic communication systems use semiconductor lasers as an optical source
because of their superior performance compared with LEDs. In this section the out-
put characteristics of semiconductor lasers are described from the standpoint of their
applications in lightwave systems. More details can be found in Refs. [2]–[14], books
devoted entirely to semiconductor lasers.
3.3.1 Optical Gain
As discussed in Section 3.1.1, stimulated emission can dominate only if the condition
of population inversion is satisfied. For semiconductor lasers this condition is real-
ized by doping thep-type andn-type cladding layers so heavily that the Fermi-level
separation exceeds the bandgap [see Eq. (3.1.14)] under forward biasing of thep–n
junction. When the injected carrier density in the active layer exceeds a certain value,
known as the transparency value, population inversion is realized and the active region
exhibits optical gain. An input signal propagating inside the active layer would then
amplify as exp(gz), wheregis thegain coefficient. One can calculategby noting that
it is proportional toRstim−Rabs, whereRstimandRabsare given by Eqs. (3.1.12) and
(3.1.13), respectively. In general,gis calculated numerically. Figure 3.9(a) shows the
gain calculated for a 1.3-μm InGaAsP active layer at different values of the injected
carrier densityN.ForN= 1 × 1018 cm−^3 ,g<0, as population inversion has not yet
occurred. AsNincreases,gbecomes positive over a spectral range that increases with
N. The peak value of the gain,gp, also increases withN, together with a shift of the
peak toward higher photon energies. The variation ofgpwithNis shown in Fig. 3.9(b).
ForN> 1. 5 × 1018 cm−^3 ,gpvaries almost linearly withN. Figure 3.9 shows that the
optical gain in semiconductors increases rapidly once population inversion is realized.
It is because of such a high gain that semiconductor lasers can be made with physical
dimensions of less than 1 mm.
The nearly linear dependence ofgponNsuggests an empirical approach in which
the peak gain is approximated by
gp(N)=σg(N−NT), (3.3.1)whereNTis the transparency value of the carrier density andσgis the gain cross sec-
tion;σgis also called thedifferential gain. Typical values ofNTandσgfor InGaAsP
lasers are in the range 1.0–1.5× 1018 cm−^3 and 2–3× 10 −^16 cm^2 , respectively [2]. As
seen in Fig. 3.9(b), the approximation (3.3.1) is reasonable in the high-gain region
wheregpexceeds 100 cm−^1 ; most semiconductor lasers operate in this region. The use
of Eq. (3.3.1) simplifies the analysis considerably, as band-structure details do not ap-
pear directly. The parametersσgandNTcan be estimated from numerical calculations
such as those shown in Fig. 3.9(b) or can be measured experimentally.
Semiconductor lasers with a larger value ofσggenerally perform better, since the
same amount of gain can be realized at a lower carrier density or, equivalently, at a