在考虑光纤损耗的情况下,以两载频以及混频过程中产生的边带频率成分为研究对象,给出了研究群速度色散(GVD)、自相位调制(SPM)、交叉相位调制(XPM)综合作用下混频过程中调制不稳定性(MI)的耦合模分析法。导出了当某一相位匹配较好、其他相位失配严重时,两载频自相位调制或交叉相位调制引起的调制不稳定性增益的解析表达式。分析发现,当调制不稳定性主要由自相位调制或交叉相位调制引起时,增益的最大值与色散无关,交叉相位调制在各边带引起的调制不稳定性最大增益相等。同时,考虑损耗后,幅度增益减小的大小受功率、非线性系数、色散情况、损耗系数和传输距离等因素共同影响,调制不稳定性产生的增益只有当频率偏移量足够大时才会出现,载频自相位调制引起的最大增益对应的频率偏移量减小。

Considering the fiber loss, focusing on the two carried frequencies and sideband frequencies generated in the frequency-mixing process, the coupled-mode method was used to investigate the modulation instability (MI) under the effect of group velocity dispersion (GVD), self-phase modulation (SPM) and cross-phase modulation (XPM). The expressions of gain caused by SPM or XPM of carried frequencies were given when one phase matched perfectly and others mismatched seriously. The maxima of gain are independent of GVD when the MI is caused by SPM or XPM mainly. The maxima of gain at different sidebands are equal when MI is caused by XPM. After considering the fiber loss, the decreased degree of gain is affected by power, nonlinear coefficient, dispersion, loss coefficient and transmission distance, and only when the frequency shift is large enough, the MI gain occurs. The frequency shift corresponding to the maximal gain caused by SPM decreases after considering the fiber loss.