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

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-07-22 DOI:10.1016/j.cpc.2025.109772

Sravya Rao , Parry Y. Chen , T. Grossinger, Yonatan Sivan

引用次数: 0

Abstract

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.

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平板波导、光纤和球面模式的改进参数原理根搜索方法

我们更新了超越方程的根搜索方法。该方法基于柯西剩余定理，具有全局收敛性，并保证在指定的搜索域内找到所有的复根。除了阶跃折射率光纤外，我们还扩展了该实现来处理平板波导的色散关系和球体的共振。我们还实现了其他改进，例如轮廓选择过程和使用无量纲搜索变量，以确保该方法即使在具有挑战性的参数制度下也保持可靠。我们还将该算法扩展到根据传播常数特征值模式识别泄漏模式，这是我们所知的第一次揭示色散图中光线的不连续。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.