108 CHAPTER 3. OPTICAL TRANSMITTERS
Figure 3.20:P–Icurves at several temperatures for a 1.3-μm buried heterostructure laser. (After
Ref. [2];©c1993 Van Nostrand Reinhold; reprinted with permission.)
whereI 0 is a constant andT 0 is acharacteristic temperatureoften used to express
the temperature sensitivity of threshold current. For InGaAsP lasersT 0 is typically
in the range 50–70 K. By contrast,T 0 exceeds 120 K for GaAs lasers. Because of
the temperature sensitivity of InGaAsP lasers, it is often necessary to control their
temperature through a built-in thermoelectric cooler.
The rate equations can be used to understand most of the features seen in Fig.
3.20. In the case of CW operation at a constant currentI, the time derivatives in Eqs.
(3.5.1) and (3.5.2) can be set to zero. The solution takes a particularly simple form if
spontaneous emission is neglected by settingRsp=0. For currents such thatGτp<1,
P=0 andN=τcI/q. The threshold is reached at a current for whichGτp=1. The
carrier population is then clamped to the threshold valueNth=N 0 +(GNτp)−^1. The
threshold current is given by
Ith=
qNth
τc=
q
τc(
N 0 +
1
GNτp)
. (3.5.6)
ForI>Ith, the photon numberPincreases linearly withIas
P=(τp/q)(I−Ith). (3.5.7)The emitted powerPeis related toPby the relation
Pe=^12 (vgαmir)h ̄ωP. (3.5.8)The derivation of Eq. (3.5.8) is intuitively obvious if we note thatvgαmiris the rate
at which photons of energy ̄hωescape from the two facets. The factor of^12 makesPe