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Here I present a summarised description of the general behavior of waves nearturning points. I show that when asymptotic matching to a prescribed incidentwavefield is performed, the solution changes from being the Airy function tobeing more generally the hyperbolic umbilic function. This solution accountsfor (de-)focusing of the incident wavefield due to gradient-index lensing inaddition to the familiar Airy physics, which importantly do not superimpose.Possible applications to fusion research are discussed.

New solution to Airy's equation for modeling beams near turning points