Analytical characterization of optical pulse propagation in polarization-sensitive semiconductor optical amplifiers

In this paper, we perform analytical characterization of optical pulses propagating through a polarization-sensitive semiconductor optical amplifier (SOA). We derive analytical expressions for the carrier density, gain and phase evolution along the SOA and show how these expressions prove useful in optical signal processing applications. The propagation of counter-propagating pulses as well as pulse streams across SOAs have been analysed and expressions for energy gain have been derived in all these cases. We also show that our analytical results reduce to corresponding results of polarization insensitive SOAs already published. The analytical results are in excellent agreement with detailed numerical simulations done in MATLAB using the NIMROD portal. The analytical calculations lead to significant savings with regard to simulation time and processing capacity requirements. We further prove that the energy gain difference for counter-propagating pulse streams is directly proportional to the difference delay between in them and hence can be used as a measure of the delay difference. This theoretical result agrees well with experimental results.