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从描述F-P型半导体光放大器(FPSOA)腔内光强I_(av)与输入光强I_(in)、输出光强I_(out)之间关系的方程组出发,证明了I_(in)是I_(av)的单值函数。将I_(in)近似表示为I_(av)的三阶泰勒级数,则I_(in)对I_(av)的导数可以表示为一个关于变量I_(av)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。
From the equations describing the relationship between the intensity I_ (av) and the input intensity I_ (in) and the output intensity I_ (out) in the cavity of an FP type semiconductor optical amplifier (FPSOA), it is proved that I_in is I_ (av) single-valued function. By approximating I_ (in) as the third-order Taylor series of I_ (av), the derivative of I_ (in) versus I_ (av) can be expressed as a quadratic quadratic equation with respect to variable I_ (av). Furthermore, it is theoretically proved that FPSOA is in a bistable working area only when the quadratic equation has two real roots. In this way, the necessary conditions for FPSOA bistability can be mathematically expressed as the discriminant of the quadratic equation is greater than zero. Numerical experiments agree well with the analytical results. The results of this study have certain reference value for the study of bistable phenomena with similar structure devices.