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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。
Aiming at the problem of determining the effective refractive index of free-propagation mode in arrayed waveguide grating design, a method of using the weighted equivalent mode refractive index as the effective refractive index in the free-propagation mode is proposed. By introducing the first-order Galerkin finite element method with slowly changing envelope approximation conditions and absorbing boundary conditions, a full vector wave equation system containing only the magnetic field component in the free-propagation region of the arrayed waveguide grating is given. On the basis of this, the mode of the light field in the free propagation area is analyzed based on the 3D full vector beam propagation method, and the expression of the refractive index of the weighted equivalent mode is deduced in combination with the guided mode transmission analysis method. The design of the arrayed waveguide grating In free-propagation mode refractive index to provide a theoretical basis.