Bessel Functions and Analysis of Circular Waveguides
Abstract
The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order and complex argument, and combine it with a perfectly matched layer technique to solve the relevant Bessel eigenvalue problem and deliver accurate loss factors for eigensolutions to the three-layer optical slab waveguide problem. The solutions provide a benchmark for verifying model implementations of this problem and allow for a numerical verification of the Glazman criterion that provides a foundation for the well-posedness and stability analysis of homogeneous circular waveguides with impedance boundary conditions.
Keywords
Cite
@article{arxiv.2512.04348,
title = {Bessel Functions and Analysis of Circular Waveguides},
author = {Jaime Mora-Paz and Leszek Demkowicz and Christina G. Taylor and Jacob Grosek and Stefan Henneking},
journal= {arXiv preprint arXiv:2512.04348},
year = {2025}
}
Comments
26 pages, 8 figures; changed template, corrected typos, added a remark and a paragraph on source code and reproducibility; submitted to SIAM Journal on Scientific Computing