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The gain coefficient of the modulation instability in the fiber doped with two-level atoms is derived by solving the Maxwell-Bloch equations. The erbium-doped fiber is taken as an example to show the results. It is found that, the gain coefficients from the pumped erbium ions and Kerr effect are additive.
Aleksey N. Azarenkov
"Propagation of supremely short light pulses in fibers", Proc. SPIE 1983, 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, 1983A7 (23 July 1993); https://doi.org/10.1117/12.2308786
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Aleksey N. Azarenkov, "Propagation of supremely short light pulses in fibers," Proc. SPIE 1983, 16th Congress of the International Commission for Optics: Optics as a Key to High Technology, 1983A7 (23 July 1993); https://doi.org/10.1117/12.2308786