从描述F-P型半导体光放大器（FPSOA）腔内光强Iav与输入光强Iin、输出光强Iout之间关系的方程组出发, 证明了Iin是Iav的单值函数。将Iin近似表示为Iav的三阶泰勒级数, 则Iin对Iav的导数可以表示为一个关于变量Iav的一元二次方程。进一步地, 从理论上论证了只有当该一元二次方程具有两个实数根时, FPSOA才处于双稳工作区。这样, FPSOA双稳现象的必要条件在数学上可以表示为该一元二次方程的判别式大于0。数值实验与解析结果吻合得很好。该研究结果对于具有类似结构器件的双稳现象研究具有一定的参考价值。

Starting from the equations describing the relationship between the intracavity Iav, the incident Iin and the output beam Iout of a FPSOA, it is demonstrated that Iin is a single valued function of Iav. After expanding Iin into a third-order Taylor’s series in terms of Iav approximately, the derivative of Iin with respect to Iav can be expressed as a quadratic equation in terms of Iav. Furthermore, it is verified that only when the quadratic equation owns two real roots, the FPSOA enters into bistable operation region. In other words, the discriminant of the quadratic equation being positive can be described as the necessary condition of bistability in FPSOAs. Numerical results agree well with the analytical formula. The results will afford a novel way for studying the bistability in other devices owning similar structures.