11.3 Erbium-Doped Fiber Amplifiers
453
The maximum value of QCE is unity, in which case all the pump photons are
converted to signal photons.
One also can rewrite Eq. (11.16) in terms of the amplifier gain G. Assuming there
is no spontaneous emission, then
G =
P s,out
P s,in
≤ 1 +
λ p
λ s
P p,in
P s,in
(11.19)
This shows an important relationship between signal input power and gain. When
the input signal power is very large so that P s,in (λ p /λ s )P p,in , then the maximum
amplifier gain is unity. This means that the device is transparent to the signal. From
Eq. (11.19), it can be seen that in order to achieve a specific maximum gain G, the
input signal power cannot exceed a value given by
P s,in ≤
λ p
λ s
P p,in
(G − 1)
(11.20)
Example 11.3 Consider an EDFA being pumped at 980 nm with a 30-mW pump
power. If the gain at 1550 nm is 20 dB, what are the maximum input and output
powers?
Solution: From Eq. (11.20), the maximum input power is
P s,in ≤
980
1550
30 mW
(100 − 1)
= 190 μW
From Eq. (11.16), the maximum output power is
P s,out (max) = P s,in (max) +
λ p
λ s
P p,in
= 190 μW + 0.63(30 mW)
= 19.1 mW = 12.8 dBm
Drill Problem 11.3 Consider an EDFA being pumped with a 36-mW pump
power at 1480 nm. (a) If the gain is 23 dB at 1550 nm, show that the maximum
input power is 0.172 mW = −7.6 dBm. (b) Show that the maximum output
power is 34.5 mW = 15.4 dBm.
In addition to pump power, the gain also depends on the fiber length. The maximum
gain in a three-level laser medium of length L, such as an EDFA, is given by
G max = exp(ρσ e L)
(11.21)