标题： 一种改进的幅角原理根搜索方法用于平板波导、光纤和球体的模式 显示英文标题

标题： An improved argument principle root-search method for modes of slab waveguides, optical fibers, and spheres

摘要： 我们更新了求解超越方程的根搜索方法。 我们的方法是全局收敛的，并且保证能够在指定的搜索区域内找到所有复数根，因为它基于柯西留数定理。 我们扩展了实现，以处理平板波导的色散关系和球体的共振，除了阶跃折射率光纤之外。 我们还实现了其他改进，例如对轮廓选择过程的改进以及使用无量纲搜索变量，以确保即使在具有挑战性的参数范围内，该方法仍然可靠。 我们还将算法扩展为以传播常数特征值模式识别泄漏模态，首次揭示了光线下色散图中的不连续性。 显示英文摘要

摘要： We update our root-search method for transcendental equations. Our method is globally convergent and is guaranteed to locate all complex roots within a specified search domain, since it is based on Cauchy's residue theorem. We extend the implementation to treat the dispersion relations of slab waveguides and the resonances of a sphere, in addition to step-index fibers. We also implement other improvements, such as to the contour selection procedure and using non-dimensional search variables, to ensure the method remains reliable even in challenging parameter regimes. We also extend the algorithm to identify leaky modes in terms of propagation constant eigenvalue modes, revealing, to the first time to our knowledge, a discontinuity across the light line in the dispersion plot.