The first acoustic diode (AD), which is composed by integrating a super lattice (SL) with a nonlinear medium (NLM), has recently been proposed to make a one-way street for the acoustic energy flux. This device prohibits the acoustic waves from one direction, but allows the transmission of the second harmonic wave (generated from the NLM) from the other direction. To improve its performance, it is crucial to transfer more acoustic energy from the stop-band of the acoustic filter (i.e., the SL) to its pass-band with the help of the NLM. In this work, a finite difference time domain model is developed to study the dynamic behaviors of the AD, in which a micro-bubble suspension takes the role of the NLM. Based on this model, the method of optimizing the nonlinearity-based AD is investigated by examining its performance with respect to several parameters, such as the periodicity number of the SL, the bubble size distribution, the bubble shell parameters, and the bubble concentration. It is also suggested that, instead of the rectification ratio, it might be more reasonable to characterize the performance of the AD with the energy attenuation coefficients (or transmission loss) for both incident directions.