Optical pulse propagation in doped fiber amplifiers.

This paper provides a general treatment of the pulse-propagation problem in doped fiber amplifiers within the rate-equation approximation. The dopants are modeled as a two-level system whose dynamic response is governed by the population relaxation time ${\mathit{T}}_{1}$ and the dipole relaxation time ${\mathit{T}}_{2}$. For incident optical pulses with a width ${\mathit{T}}_{0}$ such that ${\mathit{T}}_{1}$\ensuremath{\gg}${\mathit{T}}_{0}$\ensuremath{\gg}${\mathit{T}}_{2}$, pulse amplification is governed by a Ginzburg-Landau-type equation that includes gain saturation, gain dispersion, fiber dispersion, fiber nonlinearity, and the detuning effects occurring when the carrier frequency of the input pulse does not coincide with the gain peak. In the absence of gain saturation, this equation has solitary-wave solutions in the form of chirped solitons. Our numerical results show that the chirped solitons are stable only in the normal-dispersion regime. In the case of anomalous dispersion, as is the case for erbium-doped fiber amplifiers, the amplified pulse develops many subpulses. The effect of gain saturation on pulse amplification is also discussed.