By using a meshless finite cloud method, a full-vector mode solver in terms of transverse-magnetic-field components for optical dielectric waveguide bends is developed in a local cylindrical coordinate system. To construct the interpolation function, both the point collocation and the fixed reproducing kernel technique are utilized, and then with the help of the continuity conditions of the longitudinal field components and the perfectly matched layer absorbing boundary conditions, a standard matrix eigenvalue is obtained. Compared with the conventional meshed numerical techniques, the distributions of solution points of the present meshless method can be applied to the area of complexity in a completely free manner. Consequently, excellent convergence with high accuracy can be realized. Moreover, the present method can be applied to both the uniform and non-uniform nodal distributions, thus the computational procedure is relatively flexible. To validate the proposed method, both fundamental and high-order leaky modes for a typical rib bending waveguide are analyzed and their modal field distributions and corresponding effective refractive indexes are presented. Results are in good agreement with those published earlier, showing the effectiveness of the present method.

中文翻译：

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局部柱坐标系中无网格有限云法弯曲波导的全矢量分析


通过使用无网格有限云方法，在局部圆柱坐标系中开发了光学介质波导弯曲的横向磁场分量的全矢量模式求解器。构造插值函数时，采用点配置和固定再现核技术，借助纵向场分量的连续性条件和完美匹配层吸收边界条件，得到标准矩阵特征值。与传统的网格数值技术相比，本无网格方法的解点分布可以完全自由地应用于复杂区域。因此，可以实现高精度的良好收敛。而且，该方法既适用于均匀节点分布，也适用于非均匀节点分布，计算过程相对灵活。为了验证所提出的方法，对典型肋弯曲波导的基频和高阶漏模进行了分析，并给出了它们的模场分布和相应的有效折射率。结果与之前发表的结果非常吻合，表明了本方法的有效性。