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

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


A. M. R. Radjen


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.


Radjen, A. M. R., Tew, R. H., & Gradoni, G. (2022). Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions. European Journal of Applied Mathematics, 1-22.

Journal Article Type Article
Acceptance Date Jul 6, 2022
Online Publication Date Oct 10, 2022
Publication Date Oct 10, 2022
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
Pages 1-22
Keywords Applied Mathematics
Public URL
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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 (, 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.


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