6.5. SYSTEM APPLICATIONS 265
Figure 6.21: Variation of the signal powerPsand the ASE powerPASEalong a cascaded chain of
optical amplifiers. The total powerPTOTbecomes nearly constant after a few amplifiers. (After
Ref. [119];©c1991 IEEE; reprinted with permission.)
amplifier spacing. The signal and ASE powers become comparable after 10,000 km,
indicating the SNR problem at the receiver.
To estimate the SNR associated with a long-haul lightwave system, we assume
that all amplifiers are spaced apart by a constant distanceLA, and the amplifier gain
G≡exp(αLA)is just large enough to compensate for fiber losses in each fiber section.
The total ASE power for a chain ofNAamplifiers is then obtained by multiplying Eq.
(6.5.3) withNAand is given by
Psp= 2 NASsp∆νopt= 2 nsphν 0 NA(G− 1 )∆νopt, (6.5.18)where the factor of 2 accounts for the unpolarized nature of ASE. We can use this equa-
tion to find the optical SNR using SNRopt=Pin/Psp. However, optical SNR is not the
quantity that determines the receiver performance. As discussed earlier, the electrical
SNR is dominated by the signal-spontaneous beat noise generated at the photodetector.
If we include only this dominant contribution, the electrical SNR is related to optical
SNR as
SNRel=R^2 Pin^2
NAσsig^2 −sp=
∆νopt
2 ∆f
SNRopt (6.5.19)if we use Eq. (6.5.8) withG=1 assuming no net amplification of the input signal.
We can now evaluate the impact of multiple amplifiers. Clearly, the electrical SNR
can become quite small for large values ofGandNA. For a fixed system lengthLT,
the number of amplifiers depends on the amplifier spacingLAand can be reduced by
increasing it. However, a longer amplifier spacing will force one to increase the gain
of each amplifier sinceG=exp(αLA). Noting thatNA=LT/LA=αLT/lnG, we find
that SNRelscales withGas lnG/(G− 1 )and can be increased by lowering the gain of
each amplifier. In practice, the amplifier spacingLAcannot be made too small because