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Summary form only given. The nonlinear optical loop mirror (NOLM) and the nonlinear amplifying loop mirror (NALM) have been shown to possess optical switching properties when they are unbalanced by an asymmetric coupler and by an asymmetrically placed gain element, respectively. Self-switching in these types of Sagnac interferometers is achieved by breaking the loop symmetry for counter-propagating pulses in the optical fiber. To do this the NOLM uses an asymmetric coupler to induce different phase-shifts by self phase modulation (SPM). However the symmetric coupler can be used in a NOLM if a gain element is placed asymmetrically in the loop (NALM). In this paper, we report numerical studies of the demultiplexing of short optical soliton and quasi-soliton pulses in the basic terahertz optical asymmetric demultiplexer (TOAD) and in a version composed with a dispersion decreasing and increasing fiber (DDF and DIF respectively) considering a linear profile. From our study of the dispersion profiles, we suggest the optimum profile, to operate the TOAD.