Doped-fiber amplifier dynamics: a system perspective

Sun et al. [see Electron. Lett., vol. 32, p. 1490, Aug. 1996] succeeded in reducing the set of coupled first-order nonlinear partial differential equations determining the wavelength-dependent, time-varying amplifier gain into a single ordinary differential equation (ODE). In this paper, we further simplify the ODE bringing into greater evidence the physical meaning of the amplification process, and greatly enhancing the utility of the ODE as an analysis and design tool. We find that the gain dynamics of a doped-fiber amplifier are completely specified by its total number of excited ions r, whose time behavior is described by a simple first-order differential equation. We exploit this new understanding of amplifier gain dynamics: 1) to develop an equivalent circuit model for amplifier gain dynamics, 2) to identify that channel addition causes much faster transients than channel dropping in wavelength division multiplexing networks, and 3) to demonstrate that gain excursions can be significant in multichannel packet switching applications, which unlike time-multiplexed signals are characterized by bursts and lulls in communications. We are also able to revisit the most significant previously published results on both steady-state and dynamic analysis of doped-fiber amplifiers with a much more concise and more intuitive derivation