"Introduction". In: Fiber-Optic Communication Systems

3.5. LASER CHARACTERISTICS 109

the power emitted from each facet for a FP laser with equal facet reflectivities. For FP
lasers with coated facets or for DFB lasers, Eq. (3.5.8) needs to be suitably modified [2].
By using Eqs. (3.5.4) and (3.5.7) in Eq. (3.5.8), the emitted power is given by

Pe=

h ̄ω

2 q

ηintαmir

αmir+αint

(I−Ith), (3.5.9)

where the internal quantum efficiencyηintis introduced phenomenologically to indi-
cate the fraction of injected electrons that is converted into photons through stimulated
emission. In the above-threshold regime,ηintis almost 100% for most semiconductor
lasers. Equation (3.5.9) should be compared with Eq. (3.2.2) obtained for an LED.
A quantity of practical interest is the slope of theP–Icurve forI>Ith; it is called
theslope efficiencyand is defined as

dPe

dI

=

h ̄ω

2 q

ηd with ηd=

ηintαmir

αmir+αint

. (3.5.10)

The quantityηdis called thedifferential quantum efficiency, as it is a measure of the
efficiency with which light output increases with an increase in the injected current.
One can define the external quantum efficiencyηextas

ηext=

photon-emission rate

electron-injection rate

=

2 Pe/h ̄ω

I/q

=

2 q

h ̄ω

Pe

I

. (3.5.11)

By using Eqs. (3.5.9)–(3.5.11),ηextandηdare found to be related by

ηext=ηd( 1 −Ith/I). (3.5.12)

Generally,ηext<ηdbut becomes nearly the same forIIth. Similar to the case of
LEDs, one can define the total quantum efficiency (or wall-plug efficiency) asηtot=
2 Pe/(V 0 I), whereV 0 is the applied voltage. It is related toηextas

ηtot=

h ̄ω

qV 0

ηext≈

Eg

qV 0

ηext, (3.5.13)

whereEgis the bandgap energy. Generally,ηtot<ηextas the applied voltage exceeds
Eg/q. For GaAs lasers,ηdcan exceed 80% andηtotcan approach 50%. The InGaAsP
lasers are less efficient withηd∼50% andηtot∼20%.
The exponential increase in the threshold current with temperature can be under-
stood from Eq. (3.5.6). The carrier lifetimeτcis generallyNdependent because of
Auger recombination and decreases withNasN^2. The rate of Auger recombination
increases exponentially with temperature and is responsible for the temperature sen-
sitivity of InGaAsP lasers. Figure 3.20 also shows that the slope efficiency decreases
with an increase in the output power (bending of theP–Icurves). This decrease can
be attributed to junction heating occurring under CW operation. It can also result
from an increase in internal losses or current leakage at high operating powers. De-
spite these problems, the performance of DFB lasers improved substantially during the
1990s [10]–[12]. DFB lasers emitting>100 mW of power at room temperature in the
1.55μm spectral region were fabricated by 1996 using a strained MQW design [61].
Such lasers exhibited<10 mA threshold current at 20◦C and emitted∼20 mW of
power at 100◦C while maintaining a MSR of>40 dB. By 2001, DFB lasers capable of
delivering more than 200 mW of power were available commercially.