
365EDF Ampliers and Simulink
®
Models
in
s
tate
2. H
ence,
t
he
t
ransition
r
ate
W
1−3
should be very close to transition W
3−2
due to the
shorter
l
ifetime.
W
e
t
hus
h
ave
W
3−2
≅ W
1−3
. Substituting this into Equation (9.2) we have
∂
∂
= ∗ − ∗ + ∗ −
− − −
−
n
t
W n W n W n
n
2
1 2 1 2 1 2 1 3 3
2
2 1
τ
(9.4)
In fact, n
3
, n
2
, and n
1
are independent. However, as mentioned earlier, the erbium ions
are accumulated in state 2 and the population density in n
3
thus can be negligible.
The total population density ρ of the ber is a constant value. Therefore, if n
3
≈ 0, then
n
1
and n
2
are no longer independent of each other and are under the constraint that the
sum of th