A brief section in "Multiwavelength Optical Networks:" (Stern and Bala) on Solitons (reiterates much of what Bernard said in his earlier post, but I figured I'd put my OCR software to some use<g>):
"Well before the advent of fiber optic communications, it was known that a special type of solitary wave or soliton could exist in certain types of media that are both dispersive and nonlinear. Although each of these effects by itself tends to distort and broaden a propagating pulse, the right combination of dispersion and nonlinearity produces a narrow, stable pulse that propagates over long distances without any distortion whatsoever, with one effect compensating for the other. This, of course, is the ideal situation for long-distance communication.
The form of a soliton can be deduced by modifying the wave equation, Equation 4.10, to include a nonlinear and time-dispersive refractive index. For a wave propagating in the z direction we can write
[equation omitted]
where n in Equation 4.25 is of the form of Equation 4.23.
By assuming a quadratic dependency of beta on omega (corresponding to a linear dependence of group velocity on omega), assuming that the nonlinearities and dispersive effects are weak, and dropping "small" terms, it can be shown (e.g., see [Kazovsky+96]) that the complex envelope u(z, t) of a soliton satisfies the nonlinear Schrodinger equation:
[equation omitted]
A solution of Equation 4.26, called the fundamental soliton solution, is
[equation omitted]
The fundamental soliton is stable in the sense that if a pulse approximating a soliton in shape and amplitude is launched on a fiber it tends toward a soliton as it propagates, and thereafter retains the soliton form. Furthermore, solitons propagating in opposite directions pass through each other "transparently."
To maintain solitons over long distances, fiber amplification is required. Many soliton experiments using EDFAs and picosecond pulses were carried out in the 1990s."
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This book was published in 1999, so the authors apparently don't feel they are currently worthy of practical discussions in any great detail, FWIW
other references:
amazon.com
Nakazawa, et al, reported a 10Gbps soliton system operating over a total distance of 1,000,000 km.(1993 Optical Fiber Commun Conf paper PD7) |
