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