We present highly accurate and easy to implement, improved lumped semiconductor optical amplifier (SOA) models for both single-pass and reflective semiconductor optical amplifiers (RSOA). The key feature of the model is the inclusion of the internal losses and we show that a few subdivisions are required to achieve an accuracy of 0.12 dB. For the case of RSOAs, we generalize a recently published model to account for the internal losses that are vital to replicate observed RSOA behavior. The results of the improved reduced RSOA model show large overlap when compared to a full bidirectional travelling wave model over a 40 dB dynamic range of input powers and a 20 dB dynamic range of reflectivity values. The models would be useful for the rapid system simulation of signals in communication systems, i.e. passive optical networks that employ RSOAs, signal processing using SOAs and for implementing digital back propagation to undo amplifier induced signal distortions.

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