利用有效折射率法计算聚合物脊形光波导的横向折射率分布,将三维光传播问题简化为二维问题;从导模满足的标量波动方程出发,采用慢变包络和傍轴近似,得出传播光场满足的单步传输约束关系;运用微分算子的级数展开得到相应的递归公式,考虑微分算子的差分近似得出基本的计算格式;运用对称矩阵的相似变换对算子展开法进行加速处理。在此基础上,对马赫-曾德尔(M-Z)型光波导中TM模的传播特性进行理论分析,研究了脊宽、分支角等结构参数对插入损耗的影响。研究表明,算子展开束传播法可以较好地解决聚合物脊形M-Z波导的理论分析和设计问题。该方法精度高、计算量小,为聚合物电光调制器的制备提供了理论依据。

By using effective index method to calculate the transverse refractive index distribution of polymer rib waveguide,3D lightwave propagation is successfully simplified into a 2D one. Starting from the scalar wave equation,the one-step restriction on beam propagation is obtained by exploiting the slowly varying envelope and the paraxial approximation. The recursive formula is deduced using the series expansion of exponential differential operator,and the basic computing scheme is derived from the differential approximation. Considering the similar transformation of the symmetric matrix,the calculation speed of this algorithm is greatly improved. Based on the algorithm,the propagation characteristics of the TM lightwave in the Mach-Zenhder (M-Z) waveguide are systematically analyzed,including optical loss and the effect of structural parameters such as rib width,Y branch angle on the insertion loss. It is demonstrated that the operator expansion beam propagation method can be applied for the theoretical analysis and design of polymer M-Z waveguides with high precision,small computation complexity and high efficiency. The approach provides an alternative method for the design of polymer electro-optic modulators.