CAJ | 학술논문

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。
침대진렬파도광책설계중자유전파구모식유효절사솔적학정문제，제출료일충채용가권등효모식절사솔작위자유전파구모식유효절사솔적방법。통과인입만변포락근사조건병채용흡수변계조건적일계Galerkin유한원법，급출료진렬파도광책자유전파구부함유자장분량적전시량파동방정조。재차기출상，기우삼유전시량속전파법대자유전파구광장진행료모식분석，병결합도모전수분석법，추도급출료가권등효모식절사솔적표체식，위진렬파도광책설계중자유전파구모식절사솔적학정제공료일개이론의거。
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.