Multiple-scale Analysis of Optical Amplifiers

Short-pulse propagation in optical amplifiers has been widely studied for applications in optical signal processing and optical communications areas. Even though it is possible to integrate differential equations numerically, such implementations may not provide adequate insight into the device operation. We propose a systematic way to construct analytical solutions under pulsed conditions and show excellent agreement with numerically integrated results. Our approach makes use of the multiple-scale technique in which different time scales associated with physical processors are cleverly used to partition amplifier response to different regions where analytical solution can be found using simple techniques.