Asymptotic Expansions of Solutions To The Helmholtz and Maxwell’s Equations Advancements in Ray Theory

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Radjen, A. M. R. (2023) Asymptotic Expansions of Solutions To The Helmholtz and Maxwell’s Equations Advancements in Ray Theory. PhD thesis, University of Nottingham.

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Abstract

The standard approach to ray theory in solving the Helmholtz and Maxwell’s equations in the short wave limit involves seeking solutions that have (i) an oscillatory exponential with a phase term linear in the wavenumber and (ii) have an amplitude profile expressed in terms of inverse powers of the wavenumber. The Friedlander-Keller ray expansion includes an additional variable term within the phase of the wave structure; this new exponent term is proportional to a specific power of the wavenumber. However, many wave phenomena require a generalisation of the Friedlander-Keller ray expansion.

The work presented within this thesis provides physical motivations requiring generalised ray expansions of exponential terms of fractional order for the ansatz of the solutions of the Helmholtz, Navier’s, and Maxwell’s equations. Furthermore, it derives a new set of field equations for the new wave structure’s individual exponent and amplitude terms. It then solves those equations subject to provided data conforming to arbitrary general boundaries.

To demonstrate the applicability of the generalised ray theory, this thesis also presents classes of wave phenomena associated with high-frequency reflection, refraction, and radiation within a two or three-dimensional medium, which is either homogeneous or inhomogeneous.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: van der Zee, Kris
Keywords: ray theory, wave theory of light, differential equations
Subjects: Q Science > QA Mathematics > QA299 Analysis
Q Science > QA Mathematics > QA801 Analytic mechanics
Q Science > QC Physics > QC350 Optics. Light, including spectroscopy
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 73420
Depositing User: Radjen, Anthony
Date Deposited: 26 Jul 2023 04:40
Last Modified: 26 Jul 2023 04:40
URI: https://eprints.nottingham.ac.uk/id/eprint/73420

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