采用解析方法分析讨论泵浦消耗情形下的准相位匹配范围以及相位匹配条件的变化, 并给出相位匹配条件的表达式.比较分析小信号近似和泵浦消耗两种情形下四波混频增益演化过程.研究表明, 在泵浦消耗情形下, 随转移功率的增大, 满足总相位匹配的线性失配因子从负值逐渐趋于0, 准相位匹配范围也越来越小; 确定四波混频的准相位匹配范围, 可简化波分复用或空分复用系统中级联四波混频的分析过程; 小信号近似模型只适合于转移功率远小于泵浦功率的情形, 满足总相位匹配的线性失配因子不依赖于光纤长度.

The analytic method is used to analyze the range of quasi-phase matching and the evolution of the phase matching in the case of pump depletion, and the expression for the phase matching is given. The evolution process of four-wave mixing gain under pump depletion is compared to the case in small-signal approximation. In the case of pump depletion, with the increase of the transfer power, the linear mismatch factor corresponding to the total phase matching gradually tends to 0 and the quasi-phase matching range also becomes narrower. By determining the quasi-phase matching rang, the cascaded four-wave mixing process in wavelength division multiplex or space division multiplexing systems can be simplified for analysis. The small signal approximation model is only suitable for the case that the transfer power is far less than the pump power, and the linear mismatch factor at the total phase matching is not dependent on the length of the fiber.