Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 3

Consider a WDM system that utilizes two soliton channels at wavelengths 1 and 2. Since 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
where = 1 - 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 = 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 2 L amp should be satisfied, where L amp is the amplifier spacing. What is the upper bound for L amp for the above case