在小信号条件下, 结合相位补偿, 推导了四波混频耦合方程, 得出了级联光纤参量放大器(CFOPA)的理论输出增益和相位表达式, 借以对CFOPA带宽增益特性进行分析, 并与单段光纤参量放大器(SFOPA)相关特性做了比较。分段数N=10时, CFOPA的3 dB带宽可以达到67.2 nm, 而SFOPA则只有12.6 nm, 即通过级联增加了54.6 nm。同时, 若考虑光纤损耗及级联熔接损耗后, CFOPA的3 dB带宽将保持不变, 而峰值增益降低。研究表明, 将色散位移光纤(DSF)进行多段级联相位补偿可有效提高其放大带宽；在DSF长度、抽运光功率或闲频光初始功率给定时, CFOPA的增益带宽较SFOPA有明显增加, 且具有更好的增益平坦度。

Considering phase compensation and small signal condition, we derive the four-wave-mixing coupling equations of the cascaded fiber optical parametric amplifier (CFOPA), from which the expressions of the output gain and phase are obtained. Utilizing the obtained expressions, the gain and bandwidth characteristics of CFOPA are analyzed and further compared with the single-segment fiber optical parametric amplifier(SFOPA). The 3 dB bandwidth of the CFOPA can reach 67.2 nm when the dispersion-shifted fiber (DSF) is dividing into ten segments, but the SFOPA is just 12.6 nm. So the bandwidth is increased 54.6 nm through cascading compensation. And then, the 3 dB bandwidth of the CFOPA will remain the same, but the gain decreases when considering the fiber loss and splice loss. Results show that the bandwidth can be broadened significantly by introducing multi-segments cascading compensation to DSF, and the obtained bandwidth is observed much broader and flatter when compared with that of SFOPA for a given DSF length, pumping power, or idle power.