Wave asymptotics and their application to astrophysical plasma lensing

Plasma lensing events can have significant observational consequences, including flux density modulations and perturbations in pulse arrival times. In this paper we develop and apply a formalism that extends geometrical optics to describe the effects of two dimensional plasma lenses of arbitrary shape. We apply insights from catastrophe theory and the study of uniform asymptotic expansions of integrals to describe the lensing amplification close to fold caustics and in shadow regions, and explore the effects of image appearance and disappearance at caustics in the time of arrival (TOA) perturbations due to lensing. The enhanced geometric optics approach successfully reproduces the predictions from wave optics and can be efficiently used to simulate multifrequency TOA residuals during lensing events. Lensing will introduce perturbations both in the way the residuals change as a function of frequency and also in the magnitude and sign of the residuals averaged over a frequency band. The deviations from the expected dispersive $\nu^{-2}$ scaling will be most significant when including observations at low frequencies. We examine the consequences of lensing in the context of precision pulsar timing and touch on its potential relevance to the study of FRBs.