__Baoli Yao__^{1}, Dalun Xu^{1}, Xun Hou^{1}, Kunsheng Hu^{2}, and Aojin Wang^{2}

^{1}State Key Laboratory of Transient Optics and Technology, Xi´an Institute of Optics and Precision Mechanics, The Chinese Academy of Sciences, Xi´an 710068, China, and ^{2}Institute of Biophysics, The Chinese Academy of Sciences, Beijing 100101, China

**e-mail: yaobl@dns.opt.ac.cn
**

Bacteriorhodopsin (BR), a natural photoreceptor and photoenergy converter embedded in the purple membrane of *Halobacterium salinarium*, is a unique nanobionic protein material. Since its finding in 1970s, it has been widely investigated into the structure, function and various photochemical and photophysical properties. Now it is well known as an excellent photochromic and photoelectric biomolecular material having greatly technical applications in optical memory, optical information processing and artificial retinas. As a photoelectric material, the differential response of BR to light intensity is quite unique compared to other photoelectric materials, i.e., semiconductor. This characteristics is attribute to the carrier dynamics of BR, e.g., the primary charge separation of the chromophore and the proton transportation have opposite displacements. Based on this knowledge, here we try to analyze the differential property from a mathematical method. To obtain analytical solution, we simplify the BR photocycle to a two-level model. The photon excites the BR from ground state exciting state with a negative charge displacement and then relaxing to ground state with a positive charge displacement. Two-level rate equations are established. According to three differently initial conditions, e.g., positive step, constant and negative step of the light intensity, we can solve the rate equations and than obtain the photovoltage waveform. The derived functions give a good description to the differential signals, which are measured from our preparing BR oriented film sandwiched between two electrodes. This theory can also explain why the amplitude and decay rate of the positive peak are larger than those of the negative peak.