In this paper, the theory of linear stability analysis is used in analyzing the complex amplitude of vibration of multi-photon optical bistability which was described by semiolassical Maxwell-Blooh equations. The results of analysis show that after the adiabatio elimination being acted to atomic polarization there is no instability on cooperation branch and one single branch of multi-photon optical bistability characteristic, showing that there is no chaos of multi-photon optical bistability which was caused by the instability of the soft mode at the same time. It has been indicated that the third condition of stability is related to bistable characteristic of multi-photon optical bistability.
In this paper a quantum mechanics model for describing multiphoton optical bistability is given. Based on this molel, the state equation of multi-photon option1 bistability is obtained. The method which for calculating the threshold of multi-photon optical bistability is also given. After analyzing the potential function, we obtain the statics stability criterion and the explanation of switching characteristics. The stable region and the inferior stable region in the bistability characteristic curve are separated. In fact, multiphoton optical stable states are actually multi-photon optical stable-inferior stable states. We also discuss the phase transition problem of multi-photon optical bistability and multi-photon lasers.