非线性驻波的研究

Nonlinear Standing Wave

提出了由两个相反方向光同时在三阶非线性介质中传输而引起的非线性驻波的概念;导出了这种非线性驻波的功率分布、节距、驻波比以及单向非线性相移分布的解析表达式,并进行了仿真计算。结果表明,当非线性较弱时,驻波的功率分布仍然呈余弦形式,但将出现节距随功率增大而变小的节距调制效应,并正比于最大和最小折射率的几何平均值。当非线性较强时,不仅存在节距调制效应,而且还出现功率分布函数曲线从余弦形式过渡到周期性尖脉冲形式的驻波波形调制效应。其非线性相移不再与距离成正比,变成一条周期性的单增曲线。对于非线性介质谐振腔的激光器、选频放大器、多波长激光器以及其他非线性光学器件的研究,具有重要的意义。

The conception of nonlinear standing wave （NSW）, which is produced by two beams with bi-directions in nonlinear medium, is proposed. The analytical formulas for power distribution, pitch and standing wave ratio of this NSW and phase shift of single-direction beam are deduced. The simulation results show, that when the nonlinearity is weak, the NSW power distribution maintains its cosine type, but there is a pitch modulation effect, which will be shorten when the power increases, and it is proportional to the geometric mean of maximum and minimum indices. When the nonlinearity is stronger, there are two nonlinear effects, including pitch modulation and waveform of NSW modulation effects, the distribution function curve of which is changed from cosine to periodic sharp pulses. The nonlinear phase shift is not proportional to distance, but it changes to periodic monotonic increasing function. The results of this paper are very important to nonlinear medium cavity of laser, frequency selected amplifier, multi- wavelength laser and other nonlinear optical devices.