A Systematic Way of Approximating Gain Recovery Dynamics in SOAs

Short picosecond pulse propagation in semiconductor optical amplifiers (SOAs) has been widely studied for applications in optical signal processing and optical communications areas. Even though it is possible to fully numerically integrate differential equations describing the dynamics of SOAs, such implementations may not provide adequate insight into the device operation. We propose a systematic way to construct analytical solutions for the gain recovery dynamics of SOAs with excellent agreement with numerically integrated results. Our approach is a formalization of an heuristic technique used by researchers in the past for constructing an approximate analytical solution of carrier dynamics in a two level system by first treating stimulated emission process as instantaneous. Just after the stimulated emission-induced carrier depletion, it is assumed in this approach that carriers will replenish themselves to the initial steady-state population through carrier injection, with a carrier-recovery lifetime. The main contribution of this work is to put this heuristic approach into a firm theoretical base so that approximate analytical solutions for carrier recovery dynamics for different variants of SOA models can be systematically constructed. We derive analytical solutions for modal signal gain and pulse energy gain at an arbitrary point of the SOA waveguide. Surpassing previous work in this area, we also show that it is possible to construct analytical solutions to described gain recovery dynamics when waveguide attenuation is not negligible.