Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions

Radjen, A. M. R.; Tew, R. H.; Gradoni, G.

Abstract

The standard approach to applying ray theory to solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have (i) an oscillatory exponential with a phase term that is linear in the wave-number and (ii) has an amplitude profile expressed in terms of inverse powers of that wave-number. The Friedlander–Keller modification includes an additional power of this wave-number in the phase of the wave structure, and this additional term is crucial when analysing certain wave phenomena such as creeping and whispering gallery wave propagation. However, other wave phenomena necessitate a generalisation of this theory. The purposes of this paper are to provide a ‘generalised’ Friedlander–Keller ray ansatz for Maxwell’s equations to obtain a new set of field equations for the various phase terms and amplitude of the wave structure; these are then solved subject to boundary data conforming to wave-fronts that are either specified or general. These examples specifically require this generalisation as they are not amenable to classic ray theory.

Citation

Radjen, A. M. R., Tew, R. H., & Gradoni, G. (2023). Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions. European Journal of Applied Mathematics, 34(6), 1187-1208. https://doi.org/10.1017/s0956792522000249

• Journal Article Type: Article
• Acceptance Date: Jul 6, 2022
• Online Publication Date: Oct 10, 2022
• Publication Date: 2023-12
• Deposit Date: Nov 3, 2022
• Publicly Available Date: Nov 3, 2022
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 6
• Pages: 1187-1208
• DOI: https://doi.org/10.1017/s0956792522000249
• Keywords: Applied Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/13176431
• Publisher URL: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/friedlanderkeller-ray-expansions-in-electromagnetism-monochromatic-radiation-from-arbitrary-surfaces-in-three-dimensions/57D42B26956A4EBC5D6A2240817AC7BB
• Additional Information: Copyright: © The Author(s), 2022. Published by Cambridge University Press; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.; Free to read: This content has been made available to all.