9.2. SOLITON-BASED COMMUNICATIONS 413
Figure 9.6: Evolution of a soliton pair over 90 dispersion lengths showing the effects of soliton
interaction for four different choices of amplitude ratiorand relative phaseθ. Initial spacing
q 0 = 3 .5 in all four cases.
One can understand the implications of soliton interaction by solving the NLS equa-
tion numerically with the input amplitude consisting of a soliton pair so that
u( 0 ,τ)=sech(τ−q 0 )+rsech[r(τ+q 0 )]exp(iθ), (9.2.6)whereris the relative amplitude of the two solitons,θis the relative phase, and 2q 0
is the initial (normalized) separation. Figure 9.6 shows the evolution of a soliton pair
withq 0 = 3 .5 for several values of the parametersrandθ. Clearly, soliton interaction
depends strongly both on the relative phaseθand the amplitude ratior.
Consider first the case of equal-amplitude solitons (r=1). The two solitons at-
tract each other in the in-phase case (θ=0) such that they collide periodically along
the fiber length. However, forθ=π/4, the solitons separate from each other after an
initial attraction stage. Forθ=π/2, the solitons repel each other even more strongly,
and their spacing increases with distance. From the standpoint of system design, such
behavior is not acceptable. It would lead to jitter in the arrival time of solitons because
the relative phase of neighboring solitons is not likely to remain well controlled. One
way to avoid soliton interaction is to increaseq 0 as the strength of interaction depends
on soliton spacing. For sufficiently largeq 0 , deviations in the soliton position are ex-
pected to be small enough that the soliton remains at its initial position within the bit
slot over the entire transmission distance.