The performance of a terahertz optical asymmetric demultiplexer (TOAD) operating with an ordinary fiber and with a DDF and DIF (dispersion decreasing and increasing fiber) configurations, for three lengths of fiber ( ξ=π/2,2π and 5π) and using soliton and quasi-soliton laser profiles for the control pulse, was studied. The numerical simulations show that the increase of the fiber length leads to the decrease of the power for the first and second demultiplexed pulses and leads to a broadening of these pulses, with the exception of the TOAD operating with the DDF fiber. For the TOAD operating with a basic telecommunication fiber one see that the increase of the power of the control power lead to a strong compression of the demultiplexed pulse. Operating the TOAD using a DDF fiber one can say that the control power necessary to demultiplex the signal pulse is always lower compared with the TOAD with the normal telecommunication fiber. This is a strong suggestion that the use of the DDF fiber will allow the use of less control power. Our simulations considering the TOAD operating with a DDF and DIF with a linear profile conclude that it is possible to operate the TOAD with lower control power using a DDF fiber setup. For this device the demultiplexed pulses will present a compression on time duration and will be insensitive to the time profile of the control pulse. We also did simulations with the TOAD operating with DDF in four different profiles: hyperbolic, exponential, linear and Gaussian. For all the profiles the increase of the length of the fiber also decreases the pump power of the three first peaks for the soliton and quasi-soliton regimes. The first critical power is always lower for the quasi-soliton regime compared to the soliton regime for all profiles under consideration and all lengths of the TOAD under consideration. It was also observed that for all the profiles and lengths of fiber one has pulse compression for the switched pulse. For the ξ=2π fiber with the hyperbolic profile, both soliton and quasi-soliton profiles present the lowest critical power and the highest compression factors for all the considered profiles.