Sponsor
This research was funded in part by the AFOSR, United States grant FA9550-23-1-0103 and the Austrian Science Fund (FWF) under grant 10.55776/J4824. This work also benefited from activities organized under the auspices of NSF RTG grant DMS-2136228.
Published In
Wave Motion
Document Type
Article
Publication Date
11-1-2025
Subjects
Helical coiling, Bent waveguide, Optical fiber, Eigenvalue, Dimension reduction Torsion
Abstract
This paper studies guided transverse scalar modes propagating through helically coiled waveguides. Modeling the modes as solutions of the Helmholtz equation within the three-dimensional (3D) waveguide geometry, a propagation ansatz transforms the mode-finding problem into a 3D quadratic eigenproblem. Through an untwisting map, the problem is shown to be equivalent to a 3D quadratic eigenproblem on a straightened configuration. Next, exploiting the constant torsion and curvature of the Frenet frame of a circular helix, the 3D eigenproblem is further reduced to a two-dimensional (2D) eigenproblem on the waveguide cross section. All three eigenproblems are numerically treated. As expected, significant computational savings are realized in the 2D model. A few nontrivial numerical techniques are needed to make the computation of modes within the 3D geometry feasible. They are presented along with a procedure to effectively filter out unwanted non-propagating eigenfunctions. Computational results show that the geometric effect of coiling is to shift the localization of guided modes away from the coiling center. The variations in modes as coiling pitch is changed are reported considering the example of a coiled optical fiber.
Rights
Copyright (c) 2026 The Authors Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
DOI
10.1016/j.wavemoti.2025.103621
Persistent Identifier
https://archives.pdx.edu/ds/psu/44602
Publisher
Elsevier BV
Citation Details
Gopalakrishnan, J., & Neunteufel, M. (2025). Guided modes of helical waveguides. Wave Motion, 139, 103621.