504
12 Nonlinear Processes in Optical Fibers
for stimulated Brillouin scattering at 1550 nm for a 40-km link? If the attenuation for this fiber is 0.4 dB/km at 1310 nm and all other parameters are
the same, what is the threshold power for stimulated Brillouin scattering at
1310 nm?
12.3 Consider three copropagating optical signals at frequencies v 1 , v 2 , and v 3 .
If these frequencies are evenly spaced so that ν 1 = ν 2 − ν and ν 3 = ν 2 +
ν, where v is an incremental frequency change, list the third-order waves
that are generated due to FWM and plot them in relation to the original three
waves. Note that several of these FWM-generated waves coincide with the
original frequencies.
12.4 A soliton transmission system operates at 1550 nm with fibers that have a
dispersion of 1.5 ps/(nm · km) and an effective core area of 50 μm
2 . Find
the peak power required for fundamental solitons that have a 16-ps FWHM
width. Use the value n 2 = 2.6 × 10
−16 cm
2 /W. What are the dispersion length
and the soliton period? What is the required peak power for 30-ps pulses?
12.5 A telecommunications service provider wants a single-wavelength soliton
transmission system that is to operate at 40 Gb/s over a 2000-km distance.
How would you design such a system? You are free to choose whatever
components and design parameters are needed.
12.6 Consider a WDM system that utilizes two soliton channels at wavelengths λ 1
and λ 2 . Because different wavelengths travel at slightly different velocities
in a fiber, the solitons of the faster channel will gradually overtake and pass
through the slower-channel solitons. If the collision length L coll is defined
as the distance between the beginning and end of the pulse overlap at the
half-power points, then
L coll =
2T s
Dλ
where λ = λ 1 − λ 2 , T s is the pulse FWHM, and D is the dispersion
parameter.
(a) What is the collision length for T s = 16 ps,
D = 0.5 ps/(nm·km), and λ = 0.8 nm?
(b) Four-wave mixing effects arise between the soliton pulses during their
collision, but then collapse to zero afterward. To avoid amplifying these
effects, the condition L coll ≥ 2L amp should be satisfied, where L amp is the
amplifier spacing. What is the upper bound for L amp for the above case?
12.7 Based on the conditions described in Prob. 12.6, what is the maximum number
of allowed wavelength channels spaced 0.4 nm apart in a WDM soliton system
when L amp = 25 km, T s = 20 ps, and D = 0.4 ps/(nm · km)?
12 Nonlinear Processes in Optical Fibers
for stimulated Brillouin scattering at 1550 nm for a 40-km link? If the attenuation for this fiber is 0.4 dB/km at 1310 nm and all other parameters are
the same, what is the threshold power for stimulated Brillouin scattering at
1310 nm?
12.3 Consider three copropagating optical signals at frequencies v 1 , v 2 , and v 3 .
If these frequencies are evenly spaced so that ν 1 = ν 2 − ν and ν 3 = ν 2 +
ν, where v is an incremental frequency change, list the third-order waves
that are generated due to FWM and plot them in relation to the original three
waves. Note that several of these FWM-generated waves coincide with the
original frequencies.
12.4 A soliton transmission system operates at 1550 nm with fibers that have a
dispersion of 1.5 ps/(nm · km) and an effective core area of 50 μm
2 . Find
the peak power required for fundamental solitons that have a 16-ps FWHM
width. Use the value n 2 = 2.6 × 10
−16 cm
2 /W. What are the dispersion length
and the soliton period? What is the required peak power for 30-ps pulses?
12.5 A telecommunications service provider wants a single-wavelength soliton
transmission system that is to operate at 40 Gb/s over a 2000-km distance.
How would you design such a system? You are free to choose whatever
components and design parameters are needed.
12.6 Consider a WDM system that utilizes two soliton channels at wavelengths λ 1
and λ 2 . Because different wavelengths travel at slightly different velocities
in a fiber, the solitons of the faster channel will gradually overtake and pass
through the slower-channel solitons. If the collision length L coll is defined
as the distance between the beginning and end of the pulse overlap at the
half-power points, then
L coll =
2T s
Dλ
where λ = λ 1 − λ 2 , T s is the pulse FWHM, and D is the dispersion
parameter.
(a) What is the collision length for T s = 16 ps,
D = 0.5 ps/(nm·km), and λ = 0.8 nm?
(b) Four-wave mixing effects arise between the soliton pulses during their
collision, but then collapse to zero afterward. To avoid amplifying these
effects, the condition L coll ≥ 2L amp should be satisfied, where L amp is the
amplifier spacing. What is the upper bound for L amp for the above case?
12.7 Based on the conditions described in Prob. 12.6, what is the maximum number
of allowed wavelength channels spaced 0.4 nm apart in a WDM soliton system
when L amp = 25 km, T s = 20 ps, and D = 0.4 ps/(nm · km)?