A numerical simulation of Semiconductor Optical amplifiers is proposed, which self-consistently solves the vertical transport and the bidirectional propagation for both coherent signals and amplified spontaneous emission. A realistic account of taper sections is obtained in deriving the confinement factor in all component sections. Microscopic equations are used, as far as possible, for both gain and spontaneous emission rates. With few adjustable parameters we nevertheless obtain a good fit to experimental data which remains stable with geometry and active material changes.