94 CHAPTER 3. OPTICAL TRANSMITTERS
Figure 3.9: (a) Gain spectrum of a 1.3-μm InGaAsP laser at several carrier densitiesN. (b)
Variation of peak gaingpwithN. The dashed line shows the quality of a linear fit in the high-
gain region. (After Ref. [2];©c1993 Van Nostrand Reinhold; reprinted with permission.)
lower injected current. In quantum-well semiconductor lasers,σgis typically larger
by about a factor of two. The linear approximation in Eq. (3.3.1) for the peak gain
can still be used in a limited range. A better approximation replaces Eq. (3.3.1) with
gp(N)=g 0 [ 1 +ln(N/N 0 )], wheregp=g 0 atN=N 0 andN 0 =eNT≈ 2. 718 NTby using
the definitiongp=0atN=NT[5].
3.3.2 Feedback and Laser Threshold.................
The optical gain alone is not enough for laser operation. The other necessary ingre-
dient isoptical feedback—it converts an amplifier into an oscillator. In most lasers
the feedback is provided by placing the gain medium inside aFabry–Perot(FP) cavity
formed by using two mirrors. In the case of semiconductor lasers, external mirrors are
not required as the two cleaved laser facets act as mirrors whose reflectivity is given by
Rm=(
n− 1
n+ 1) 2
, (3.3.2)
wherenis the refractive index of the gain medium. Typically,n= 3 .5, resulting in 30%
facet reflectivity. Even though the FP cavity formed by two cleaved facets is relatively
lossy, the gain is large enough that high losses can be tolerated. Figure 3.10 shows the
basic structure of a semiconductor laser and the FP cavity associated with it.
The concept oflaser thresholdcan be understood by noting that a certain fraction
of photons generated by stimulated emission is lost because of cavity losses and needs
to be replenished on a continuous basis. If the optical gain is not large enough to com-
pensate for the cavity losses, the photon population cannot build up. Thus, a minimum
amount of gain is necessary for the operation of a laser. This amount can be realized