| Summary: | 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.
|
|---|