中文摘要：

详细描述了泵浦消耗情形下高非线性光纤中（HNLF）简并四波混频（DFWM）的解析求解过程，结合第1类、第3类椭圆积分和雅阁比椭圆函数给出了个导波光的输出功率和相位的表达式。为了方便计算和分析，给出了特殊函数在Matlab中的计算命令。利用解析式分析了基于DFWM实现多电平再生的必要条件，研究了相敏放大过程中泵浦光初始相位和初始功率对MPSK信号相位转移曲线的影响。研究表明，调节泵浦光初始相位可使相敏放大器（PSA）的相位转移曲线与输入信号的多电平相位匹配，优化光纤长度或泵浦光初始功率可获得最大的多电平相位再生抖动抑制性能，且优化的初始泵浦光功率与光纤长度近似呈反比。采用OptiSystem软件仿真了基于PSA的8PSK信号再生器的性能，仿真结果与理论分析一致；当归一化输入相位抖动为0．1时，该相位再生器的抖动抑制比为4．62，能够使系统的符号错误率降低2个数量级。

英文摘要：

The analytic solution to the coupled-mode equations for degenerate four-wave mixing （DFWM） in nonlinearity optical fiber （HNLF） under pump depletion is described in detail. The expressions of out- put phase and power for every waves are given by the first and third kind elliptic integrals,as well as the Jacobian elliptic functions. In order to facilitate the calculation and analysis, we give the commands of the special functions in Matlab. The condition of multi-level phase regeneration based on DFWM and the in- fluence of initial pump phase and power on phase transfer curves for phase-sensitive amplifiers （PSAs） are analyzed by using the analytic expressions. Adjusting the initial pump phase allows the phase transfer curve of the PSA to match the multi-level phase of the input signal. The phase fluctuation suppression performance can be optimized by appropriately choosing the fiber length or pump power, in which the op- timized initial pump power is inversely proportional to the fiber length approximately. The performance of the 8 phose shift kein4g （8PSK） signal regenerator based on PSAs is simulated by Optisystem optical simulation software, which is consistent with the theoretical analysis. The phase fluctuation suppression ratio is up to 4. 62 for the normalized input phase fluctuation of 0.1, and the symbol error rate without forward error correction can be reduced by two orders of magnitude.