Nonlinear Fiber Optics - 4 ed. Agrawal

170 Chapter 5. Optical Solitons
5.13 A soliton system is designed to transmit a signal over 5000 km at B = 5 Gb/s.
What should the pulse width (FWHM) be to ensure that the neighboring solitons
do not interact during transmission? The dispersion parameter D = 2 ps/(km-nm)
at the operating wavelength.
5.14 Follow Ref. [167] and derive the moment equations for the pulse parameters
given as Eqs. (5.5.3)–(5.5.6).
5.15 Verify by direct substitution that the solution given in Eq. (5.5.12) is indeed the
solution of Eq. (5.5.11) with (b = 40δ 4 ) −1/2 .
5.16 What is intrapulse Raman scattering? Why does it lead to a shift in the carrier
frequency of solitons? Derive an expression for the frequency shift of a fundamental
from Eqs. (5.5.3)–(5.5.6) assuming that α = 0, β 3 = 0 and C p = 0.
Neglect also the self-steepening terms containing ω 0 .
5.17 Verify by direct substitution that the solution given in Eq. (5.5.21) is indeed the
solution of Eq. (5.5.8) when δ 3 =0,s =0,andN = 3/(4τ R ).
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