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12 Nonlinear Processes in Optical Fibers
The mutual interactive force between in-phase solitons thus results in periodic
attraction, collapse, and repulsion. The interaction distance L I is
L I = L disp = L period exp(s 0 )
(12.25)
This interaction distance, and particularly the ratio L I /L disp , determine the
maximum bit rate allowable in soliton systems.
These types of interactions are not desirable in a soliton system, because they
lead to jitter in the soliton arrival times. One method for avoiding this situation is
to increase s 0 , because the interaction between solitons depends on their spacing.
Because Eq. (12.23) is accurate for s 0 > 3, this equation together with the criterion
that L disp > > L T , where L T is the total transmission distance, is suitable for system
designs in which soliton interaction can be ignored.
Using Eq. (12.20) for L disp , Eq. (12.23) for T 0 , and Eq. (3.25) for D, the design
condition L disp > > L T becomes
B
2 L T <<
2π
s 0 λ
2 c
16D
ex p(s 0 ) =
π
8s
2
0 |β 2 |
ex p(s 0 )
(12.26)
When written in this form, Eq. (12.26) shows the effects on the bit rate B or the
total transmission distance L T for selected values of s 0 .
Example 12.7 Suppose a link needs to transmit information at a rate of 10 Gb/s over
an 8600 km soliton link across the Pacific Ocean.
(a) Because this is a high data rate over a long distance, one can start by selecting
a value of s 0 = 8. Then, from Eq. (12.24) it follows that = 4682. Given that
the dispersion length is at least 100 km, then L disp > 4.7 × 10
5 km, which for
all practical purposes satisfies the condition L disp > > L T = 8600 km.
(b) If D = 0.5 ps/(nm · km) at 1550 nm then for a 10-Gb/s data rate Eq. (12.26)
yields
L T << 2.87 × 10
5 km
This is satisfied, because the right-hand side is 33 times greater than the desired
length.
(c) Using Eq. (12.23), the FWHM soliton pulse width is found to be
T s =
0.881
s 0 B
=
0.881
8
10 × 10 9 b/s
= 11ps
(d) The fraction of the bit slot occupied by a soliton when s 0 = 8 is
T s
T B
=
0.881
s 0
=
0.881
8
= 11%
12 Nonlinear Processes in Optical Fibers
The mutual interactive force between in-phase solitons thus results in periodic
attraction, collapse, and repulsion. The interaction distance L I is
L I = L disp = L period exp(s 0 )
(12.25)
This interaction distance, and particularly the ratio L I /L disp , determine the
maximum bit rate allowable in soliton systems.
These types of interactions are not desirable in a soliton system, because they
lead to jitter in the soliton arrival times. One method for avoiding this situation is
to increase s 0 , because the interaction between solitons depends on their spacing.
Because Eq. (12.23) is accurate for s 0 > 3, this equation together with the criterion
that L disp > > L T , where L T is the total transmission distance, is suitable for system
designs in which soliton interaction can be ignored.
Using Eq. (12.20) for L disp , Eq. (12.23) for T 0 , and Eq. (3.25) for D, the design
condition L disp > > L T becomes
B
2 L T <<
2π
s 0 λ
2 c
16D
ex p(s 0 ) =
π
8s
2
0 |β 2 |
ex p(s 0 )
(12.26)
When written in this form, Eq. (12.26) shows the effects on the bit rate B or the
total transmission distance L T for selected values of s 0 .
Example 12.7 Suppose a link needs to transmit information at a rate of 10 Gb/s over
an 8600 km soliton link across the Pacific Ocean.
(a) Because this is a high data rate over a long distance, one can start by selecting
a value of s 0 = 8. Then, from Eq. (12.24) it follows that = 4682. Given that
the dispersion length is at least 100 km, then L disp > 4.7 × 10
5 km, which for
all practical purposes satisfies the condition L disp > > L T = 8600 km.
(b) If D = 0.5 ps/(nm · km) at 1550 nm then for a 10-Gb/s data rate Eq. (12.26)
yields
L T << 2.87 × 10
5 km
This is satisfied, because the right-hand side is 33 times greater than the desired
length.
(c) Using Eq. (12.23), the FWHM soliton pulse width is found to be
T s =
0.881
s 0 B
=
0.881
8
10 × 10 9 b/s
= 11ps
(d) The fraction of the bit slot occupied by a soliton when s 0 = 8 is
T s
T B
=
0.881
s 0
=
0.881
8
= 11%