
159Optical Direct and External Modulation
of photon density S(t). Similarly in (5.3), the photon density S(t) is increased by stimu-
lated and spontaneous emission S(t) and decreased by internal and mirror losses with
a photon lifetime τ
p
given by
τ
α α
p
g i m
v
=
+
( )
1
(5.5)
where
α
i
and α
m
denote the waveguide loss coefcients and the mirror loss, respectively.
The
carrier
lifetime,
τ
n
is related to the loss of electrons due to both spontaneous emission
and
n
onradiative
r
ecombination
[
3]
g
iven
b
y
τ
n
sp nr
N t
R R
=
+
( )
(5.6)
where
R
sp
denotes rate of spontaneous emission
R
nr
denotes nonradiative recombination
The
t
ime
v
ariations
o
f
t
he
o
ptical
po
wer
o