The dynamic characteristics of semiconductor optical amplifiers (SOA) and the performance of switching window of terahertz optical asymmetric demultiplexers (TOAD) are investigated numerically by taking into account not only interband effects but also intraband effects, such as carrier heating, spectral hole burning, two-photon absorption, and ultrafast nonlinear refraction. Two cases are considered. 1) change the frequency of signal pulse while let the wavelength of control pulse unchanged. 2) change the frequency of control and signal pulse on the condition that the frequency of control pulse is the same as that of signal pulse. Numerical results show that in order to obtain flat and narrow switching window, the wavelength of control and signal pulse should be the same, and the difference between the wavelength of control pulse and the center wavelength of SOA's gain spectral should be little larger.