This dissertation is a contribution toward developing all-optical binary delta sigma modulator (BDSM) [‎27] by changing its bistability to proteretic bistability in order to increase the modulator bandwidth frequency. An innovative delta sigma modulator called proteretic binary delta sigma modulator (PBDSM), which is optically compatible, is investigated theoretically and by modeling and simulation and its bandwidth superiority is proven. The time interval of PBDSM Δt calculation is driven and dynamic performance measure of PBDSM comparing to previous related work is computed, modeled and simulated. Modeling and simulations are based on Matlab-Simulink for ideal environment testing. The basic components of BDSM are the leaky integrator and the bi-stable device. Thus, the focus was on improving the bi-stable device to overcome the bandwidth limitation toward THz modulation frequency in optical domain. Consequently, proteresis bistability was investigated in semi-practical domain, using Matlab-Simulink function, for clear realization of its input-output characteristics and compared with the corresponding hysteresis bistability. The contribution in this research, regarding proteresis bi-stable device design, can be implemented in current technologies, both optical and electrical, of continuous-time delta sigma modulation. Furthermore, the new design showed capability and more flexibility in manipulating its output form and it showed more control on the way of conducting delta sigma modulator error correction.