Page 265 - Optical Communications Essentials

Performance Impairments

Performance Impairments 255

system. Section 15.5.4 presents the origins of SPM and XPM and shows their
degradation effect on system performance. The mechanisms giving rise to FWM
and the resultant physical effects on link operation are outlined in Sec. 15.5.5.
As noted in Sec. 15.3, FWM can be suppressed through clever arrangements of
fibers having different dispersion characteristics.

15.5.1. Effective length and area
Modeling the nonlinear processes can be quite complicated, since they depend
on the transmission length, the cross-sectional area of the fiber, and the optical
power level in the fiber. The difficulty arises from the fact that the impact of the
nonlinearity on signal fidelity increases with distance. However, this is offset by
the continuous decrease in signal power along the fiber due to attenuation. In
practice, one can use a simple but sufficiently accurate model that assumes the
power is constant over a certain fiber length, which is less than or equal to the
actual fiber length. This effective length L eff , which takes into account power
absorption along the length of the fiber (i.e., the optical power decays exponen-
tially with length), is given by
1 e αL
L eff (15.5)
α

Given a typical attenuation of α 0.22dB/km (or, equivalently, α 5.07
1
10 2 km ) at 1550nm, this yields an effective length of about 20km when L eff
1/α. When there are optical amplifiers in a link, the signal impairments owing
to the nonlinearities do not change as the signal passes through the amplifier. In
this case, the effective length is the sum of the effective lengths of the individual
spans between optical amplifiers. If the total amplified link length is L A and the
span length between amplifiers is L, the effective length is approximately
1 e αL
L A
L eff (15.6)
α L
Figure 15.4 illustrates the effective length as a function of the actual system
length. The two curves shown are for a nonamplified link with α 0.22dB/km
and an amplified link with a 75-km spacing between amplifiers. As indicated by
Eq. (15.6), the total effective length decreases as the amplifier span increases.
The effects of nonlinearities increase with the light intensity in a fiber. For a
given optical power, this intensity is inversely proportional to the cross-sectional
area of the fiber core. Since the power is not distributed uniformly over the
fiber-core cross section, for convenience one can use an effective cross-sectional
area A eff . Although this can be calculated accurately from mode-overlap integrals,
in general the effective area is close to the actual core area. As a rule of thumb,
2
standard nondispersion-shifted single-mode fibers have effective areas of 80µm ,
2
dispersion-shifted fibers have effective areas of 55µm , and dispersion-compen-
2
sated fibers have effective areas on the order of 20µm .

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.