Page 223 - Photonics Essentials an introduction with experiments

Optical Fibers and Optical Fiber Amplifiers

Optical Fibers and Optical FIber Amplifiers 217

average of the square of the photocurrent power (rms), and so it is pro-
portional only to GS input . Similarly, the ASE power can be expressed as

2
Bq S input G(G – 1) f
2
i ASE = (9.24)
hf·m
where B is a constant and m is the fraction of the population inversion
between states N 2 and N 1 :
N 2 – N 1
m =
N 2
Note that m
1.
Under conditions of high gain, that is G > 100,

2
2
4q S input G f
2
i ASE (9.25)
hf·m
The SNR at the output is approximated by
S input ·m
S output = (9.26)
4hf f
whereas the SNR at the input is the signal power divided by the shot
noise:
2
qS input
hf
S input
SNR input = = (9.27)
2qS input f 2hf f

hf
Now we can compare the SNR at the output to the SNR at the in-
put:

m
SNR output
= (9.28)
2
SNR input
Under the very best conditions, 100% of the population is inverted,
and the SNR at the output is reduced by 3 dB compared to the SNR at
the input after passage through each amplifier. This situation, howev-
er has been obtained so far only in the laboratory. In typical commer-
cial amplifiers, the signal-to-noise ratio is degraded by a factor of
about 3 (~ 5 dB). The actual noise penalty is comprised of additional,
but less important contributions. It is furnished by the vendor with
the specifications of the optical amplifier package. If one starts from a
transmitter with an excellent signal-to-noise ratio (typically on the or-

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