对随机折射率调制的光纤光栅进行了理论建模,将随机光纤光栅看作是长、短周期均匀光纤光栅的随机线性组合.分别利用传输矩阵法和光束传播法计算了随机间距均值为20 μm的随机光栅的反射和透射特性,证实了随机光栅中同时具有前后向纤芯基模的耦合以及纤芯基模与包层模式之间的耦合,验证了所提出的线性组合的理论模型.文中还进行了随机光栅的实验研究,采用飞秒激光器在1 cm的单模光纤中写入了具有500个随机间距在10~20 μm的折射率调制点的随机光栅,并测量了该随机光栅的反射和透射光谱.实验结果进一步验证了理论模型的准确性.

Analysis model of the fiber gratings with random spaced index modulations was established. The random spaced index modulated fiber grating can be treated as the random combinations of long period uniform gratings and short period uniform gratings. The reflective and transmissive characteristics of a random fiber grating with the averaged random modulation space 20 μm were calculated with transmission matrix method and beam propagation method. The results confirmed the coexistence of the coupling between the forward and backward propagated fundamental core modes and the coupling between the fundamental core modes and cladding mode. A random fiber grating with 500 modulation points was fabricated by femto-second laser, the spaces between the adjacent random modulation points were about 10~20 μm. The reflective and transmissive spectra of the grating were measured experimentally. The experimental results further validated the numerical analysis.