The dynamic gain responses of the semiconductor optical amplifier (SOA) in a terahertz optical asymmetric demultiplexer (TOAD) to intense control pulses with different input energies and pulse widths are investigated. The influences on the switching characteristics of TOAD for control pulse energies, widths, loop′s time asymmetry, and time delays between the signal and control pulses are studied and optimized in detail. The theoretical analysis is compared with the experimental result.