阵列波导光栅中自由传播区模式的有效折射率

针对阵列波导光栅设计中自由传播区模式有效折射率的确定问题，提出了一种采用加权等效模式折射率作为自由传播区模式有效折射率的方法。通过引入慢变包络近似条件并采用吸收边界条件的一阶Galerkin有限元法，给出了阵列波导光栅自由传播区仅含有磁场分量的全矢量波动方程组。在此基础上，基于三维全矢量束传播法对自由传播区光场进行了模式分析，并结合导模传输分析法，推导给出了加权等效模式折射率的表达式，为阵列波导光栅设计中自由传播区模式折射率的确定提供了一个理论依据。

Determination problem of mode effective refractive index in the free propagation region of AWG

Considering the determination of mode effective refractive index in the free propagation region of AWG, a new method using weighted equivalent mode refractive index as the mode effective refractive index in the free propagation region was proposed. The vector wave equation of magnetic field in the free propagation region of AWG was demonstrated using Galerkin finite element method with absorbing boundary condition under the slowly-vary-envelope approximation. On this basis, the mode of free propagation region was analyzed based on 3D full-vector beam propagation method, and the equation of weighted equivalent mode refractive index was deduced with guided-mode propagation analysis method. This method provides a useful theoretical tool for the determination of mode effective refractive index in the free propagation region of AWG.