Bessel Functions and Analysis of Circular Waveguides

TL;DR

This paper develops a method to accurately compute Bessel functions of complex order and argument, applying it to analyze the stability and loss factors of circular waveguides, with implications for optical and acoustical applications.

Contribution

It introduces a combined approach using variable change, Frobenius method, and PML technique to solve Bessel eigenvalue problems for circular waveguides, providing benchmarks and stability analysis.

Findings

Accurate computation of Bessel functions for complex parameters.

Benchmark solutions for three-layer optical slab waveguides.

Verification of the Glazman criterion for waveguide stability.

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.