不均匀磁场的Faraday旋光效应研究

The Faraday Rotation Effect for Non-uniform Magnetic Field

为解决不均匀磁场中磁光效应特性在数学上难以准确刻画的问题,该文建立感应不均匀介质的琼斯矩阵模型,并据此研究感应不均匀介质特性和不均匀磁场的Faraday旋光效应。研究发现,不均匀磁场和应力场共同作用下致使旋光介质感应角不守恒,感应不均匀介质琼斯矩阵级联形式是复非对角元酉矩阵,可通过本征变换为基于介质感应角、介质不均匀角和整体相移差为整体物理量的无冗余的三元解析式。建立不均匀磁场的Faraday旋光效应的光强测量模型并进行数值仿真与实验验证。与均匀磁场情形相比,不均匀磁场对琼斯矩阵、输出光强均有明显影响:琼斯矩阵出现了介质不均匀角,光强公式出现了不均匀系数。论证实际测量磁场是关于光程磁场的加权积分磁场,对提高光学电流互感器精准测量的实际应用具有参考价值。

This paper proposed the Jones-matrix-based model of non-uniformly induced medium, in order to deal with the difficulty of mathematically depicting Faraday rotation of the non-uniform magnetic field with high accuracy. On the basis of the proposed model, the characteristics of non-uniformly induced medium and Faraday rotation of the non-uniform magnetic field were studied. It’s found that the rotation medium induction angle is non-conservative under the combined effect of non-uniform magnetic field and stress field. The cascade form of the Jones matrix for the non-uniformly induced medium is a complex non-diagonal element unitary matrix. Through the eigen transformation, it can be deformed into a non-redundant analytic expression of 3 variables, namely induction angle, uneven angle and phase shift difference. It’s indicated that these 3 variables are respectively. The model of light intensity measurement for Faraday rotation of non-uniform magnetic field is established which is proved by numerical simulations and experiments. The non-uniformity of magnetic field has great impact on Jones matrix and output light intensity that the average uneven angle appears in Jones matrix and the different non-uniformity coefficient appears in the light intensity formula, which is different from that in uniform magnetic field. Besides, the magnetic field sensed actually is the weighted integral of the optical path magnetic field, it provides reference for the practical application in terms of improving the measurement accuracy of optical current transformers.