In this paper, an all-optical logic gate based on 2x2 (MMI) multimode interference coupler is theoretically designed and simulated using three-dimensional beam propagation method (3D-BPM) and effective index method (EIM) to analyze and evaluate the performance of the device. The proposed device is used to convert phase information of input optical signals to amplitude at the output ports of MMI. With this mechanism, the device can operates as a logical half adder. Simulation results show that the optical half adder archives with insertion loss and extinction ratio from ON to OFF logiclevel below 0.7 dB and over 40 dB, respectively. Furthermore, wide bandwidth of 100 nm is also an advantage of this devices. Therefore, it can be applied to all optical signal processing in next generation optical networks as well as in photonic integrated circuits.Index Terms-Multimode interference, all-optical logic gates, logical half adder. ! Nguyen Tan Hung was born in Danang, Vietnam, in 1980.