468 CHAPTER 9. SOLITON SYSTEMS
Problems
9.1 A 10-Gb/s soliton system is operating at 1.55μm using fibers withD=2 ps/(km-
nm). The effective core area of the fiber is 50μm^2. Calculate the peak power
and the pulse energy required for fundamental solitons of 30-ps width (FWHM).
Usen 2 = 2. 6 × 10 −^20 m^2 /W.
9.2 The soliton system of Problem 9.1 needs to be upgraded to 40 Gb/s. Calculate
the pulse width, peak power, and the energy of solitons usingq 0 =4. What is
the average launched power for this system?
9.3 Verify by direct substitution that the soliton solution given in Eq. (9.1.11) satis-
fies the NLS equation.
9.4 Solve the NLS equation using the split-step Fourier method (see Section 2.4 of
Ref. [10] for details on this method). Reproduce Figs. 9.1–9.3 using your pro-
gram. Any programming language, including software packages such as Mathe-
matica and Matlab, can be used.
9.5 Verify numerically by propagating a fundamental soliton over 100 dispersion
lengths that the shape of the soliton does not change on propagation. Repeat the
simulation using a Gaussian input pulse shape with the same peak power and
explain the results.
9.6 A 10-Gb/s soliton lightwave system is designed withq 0 =5 to ensure well-
separated solitons in the RZ bit stream. Calculate pulse width, peak power, pulse
energy, and the average power of the RZ signal assumingβ 2 =−1ps^2 /km and
γ=2W−^1 /km for the dispersion-shifted fiber.
9.7 A soliton communication system is designed to transmit data over 5000 km at
B=10 Gb/s. What should be the pulse width (FWHM) to ensure that the neigh-
boring solitons do not interact during transmission? The dispersion parameter
D=1 ps/(km-nm) at the operating wavelength. Assume that soliton interaction
is negligible whenB^2 LTin Eq. (9.2.10) is 10% of its maximum allowed value.
9.8 Prove that the energy of standard solitons should be increased by the factor
GlnG/(G− 1 )when the fiber lossαis compensated using optical amplifiers.
HereG=exp(αLA)is the amplifier gain andLAis the spacing between ampli-
fiers assumed to be much smaller than the dispersion length.
9.9 A 10-Gb/s soliton communication system is designed with 50-km amplifier spac-
ing. What should be the peak power of the input pulse to ensure that a funda-
mental soliton is maintained in an average sense in a fiber with 0.2 dB/km loss?
Assume thatTs=20 ps,β 2 =− 0 .5ps^2 /km andγ=2W−^1 /km. What is the
average launched power for such a system?
9.10Calculate the maximum bit rate for a soliton lightwave system designed with
q 0 = 5 ,β 2 =−1ps^2 /km, andLA=50 km. Assume that the condition (9.3.10)
is satisfied whenB^2 LAis at the 20% level. What is the soliton width at the
maximum bit rate?
