272 CHAPTER 6. OPTICAL AMPLIFIERS
were orthogonally polarized for reducing the nonlinear effects resulting from a rela-
tively small channel spacing of 42 GHz. This technique is referred to as polarization
multiplexing and is quite useful for WDM systems.
The two major nonlinear phenomena affecting the performance of WDM systems
are the cross-phase modulation (XPM) and four-wave mixing (FWM). FWM can be
avoided by using dispersion management such that the GVD is locally high all along
the fiber but quite small on average. The SPM and XPM then become the most limiting
factors for WDM systems. The XPM effects within an EDFA are normally negligible
because of a small length of doped fiber used. The situation changes for the L-band
amplifiers, which operate in the 1570- to 1610-nm wavelength region and require fiber
lengths in excess of 100 m. The effective core area of doped fibers used in such am-
plifiers is relatively small, resulting in larger values of the nonlinear parameterγand
enhanced XPM-induced phase shifts. As a result, the XPM can lead to considerable
power fluctuations within an L-band amplifier [155]–[160]. A new feature is that such
XPM effects are independent of the channel spacing and can occur over the entire band-
width of the amplifier [156]. The reason for this behavior is that all XPM effects occur
before pulses walk off because of group-velocity mismatch. The effects of FWM are
also enhanced in L-band amplifiers because of their long lengths [161].
Problems
6.1 The Lorentzian gain profile of an optical amplifier has a FWHM of 1 THz. Cal-
culate the amplifier bandwidths when it is operated to provide 20- and 30-dB
gain. Neglect gain saturation.
6.2 An optical amplifier can amplify a 1-μW signal to the 1-mW level. What is the
output power when a 1-mW signal is incident on the same amplifier? Assume
that the saturation power is 10 mW.
6.3 Explain the concept of noise figure for an optical amplifier. Why does the SNR
of the amplified signal degrade by 3 dB even for an ideal amplifier?
6.4 A 250-μm-long semiconductor laser is used as an FP amplifier by biasing it
below threshold. Calculate the amplifier bandwidth by assuming 32% reflectivity
for both facets and 30-dB peak gain. The group indexng=4. How much does the
bandwidth change when both facets are coated to reduce the facet reflectivities
to 1%?
6.5 Complete the derivation of Eq. (6.2.3) starting from Eq. (6.2.1). What should
be the facet reflectivities to ensure traveling-wave operation of a semiconductor
optical amplifier designed to provide 20-dB gain. Assume thatR 1 = 2 R 2.
6.6 A semiconductor optical amplifier is used to amplify two channels separated by
1 GHz. Each channel can be amplified by 30 dB in isolation. What are the
channel gains when both channels are amplified simultaneously? Assume that
Pin/Ps= 10 −^3 ,τc= 0 .5 ns, andβc=5.
6.7 Integrate Eq. (6.2.19) to obtain the time-dependent saturated gain given by Eq.
(6.2.20). PlotG(τ)for a 10-ps square pulse usingG 0 =30 dB andEs=10 pJ.