"Introduction". In: Fiber-Optic Communication Systems

432 CHAPTER 9. SOLITON SYSTEMS

Distance (km)

012345678910

Pulse width (ps)

-2

-1

0

1

2

3

4

5

Chirp

-2

-1

0

1

2

3

4

5

Distance (km)

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Pulse width (ps)

-2

-1

0

1

2

3

4

5

Chirp

-2

-1

0

1

2

3

4

5

(a) (b)

Figure 9.16: (a) Variations of pulse width and chirp over one map period for DM solitons with
the input energy (a)E 0 Ec= 0 .1 pJ and (b)E 0 close toEc.

9.4.3 Design Issues

Figures 9.15 and 9.16 show that Eqs. (9.4.7)–(9.4.9) permit periodic propagation of
many different DM solitons in the same map by choosing different values ofE 0 ,T 0 ,
andC 0. How should one choose among these solutions when designing a soliton sys-
tem? Pulse energies much smaller thanEc(corresponding to the minimum value ofT 0 )
should be avoided because a low average power would then lead to rapid degradation of
SNR as amplifier noise builds up with propagation. On the other hand, whenE 0 Ec,
large variations in the pulse width in each fiber section would enhance the effects of
soliton interaction if two neighboring solitons begin to overlap. Thus, the region near
E 0 =Ecis most suited for designing DM soliton systems. Numerical solutions of Eq.
(9.4.5) confirm this conclusion.
The 40-Gb/s system design shown in Figs. 9.15 and 9.16 was possible only because
the map periodLmapwas chosen to be much smaller than the amplifier spacing of
80 km, a configuration referred to as thedensedispersion management. WhenLmap
is increased to 80 km usingla≈lb=40 km while keeping the same value of average
dispersion, the minimum pulse width supported by the map increases by a factor of

3. The bit rate is then limited to about 20 Gb/s. In general, the required map period
   becomes shorter as the bit rate increases.
   It is possible to find the values ofT 0 andTmby solving the variational equations
   (9.4.7)–(9.4.9) approximately. Equation (9.4.7) can be integrated to relateTandCas

T^2 (z)=T 02 + 2

∫z

0

β 2 (z)C(z)dz. (9.4.10)

The chirp equation cannot be integrated but the numerical solutions show thatC(z)
varies almost linearly in each fiber section. As seen in Fig. 9.16,C(z)changes from
C 0 to−C 0 in the first section and then back toC 0 in the second section. Noting that
the ratio( 1 +C^2 )/T^2 is related to the spectral width that changes little over one map