Gain dynamics in doped-fiber amplifiers for added and dropped signals

Sun e2 al. [l] reduced the set of coupled iirst order nonlinear partial differential equations determining the wavelength-dependent, time-varying doped-fiber amplifier gain into a single ordinary differential equation (ODE). In this paper we further simplify the ODE, greatly enhancing its utility as an analysis and design tool. We find that the gain dynamics are completely specified by the total number of excited ions. We demonstrate that channel addition causes much faster transients than channel dropping in wavelength division multiplexing networks. We approximate the solution of the ODE by an exponential with time constant given as a function of amplifier parameters.