A drawback of the finite difference (FD) method in solving waveguide eigenmodes exists in the difficulty to accurately describe the field singularities at sharp edges. In this paper, we incorporate the boundary conditions proposed previously into the FD method to solve this problem. An alternative form of the boundary condition at the edge of a wedge with external angle 2/spl pi/ is also derived, which is more flexible for field eigenvalue problems. Numerical results show the validity and accuracy of the proposed treatments. Compared with the traditional treatment, our methods are more accurate and numerically more stable, especially for the computation of field distributions near edges.
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机译：有限差分（FD）方法在求解波导本征模方面存在一个缺点，即难以准确描述尖锐边缘处的场奇点。在本文中，我们将先前提出的边界条件合并到FD方法中以解决此问题。还导出了具有外部角度为2 / spl pi /的楔形边缘处边界条件的另一种形式，这对于场特征值问题更加灵活。数值结果表明了所提方法的有效性和准确性。与传统的处理方法相比，我们的方法更准确，在数值上更稳定，尤其是在计算边缘附近的场分布时。
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