  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.
