A model for the treatment of amplified spontaneous emission (ASE) noise in semiconductor optical amplifiers (SOA) in the case of ultra-short pulse injected into SOA by taking not only interband effects but also intraband effects, such as carrier heating, spectral hole burning, two-photon absorption and ultrafast nonlinear refraction is proposed. The influence of ASE on the performance of terahertz optical asymmetric demultiplexers (TOAD) is also discussed. Numerical results show that the edge of switching window of a TOAD device becomes sharper and the over-shoot peak in the tailing edge of switching window becomes more obvious when the ASE noise is considered. Results also show that the signal noise ratio (SNR) of output signal of TOAD is larger than 25 dB when it is in the turn-on state.