The performance of terahertz optical asymmetric demultiplexer (TOAD) has been studied by modelling the semiconductor optical amplifier (SOA) in which the intraband effects had been taken into account. Numerical results are coincident with the experiment results. We interpret why there are three peaks in the switching window, which has never been reported before. In addition, we put forward the definition of the flatness of the switching window of TOAD for the first time By analysing the different phase of clockwise and counter clockwise signal pulse changed by SOA, appropriate peak power of control pulseand wavelength of signal and control pulse have been calculated in order to obtain large output power and flat switching window of TOAD.