Validation of straight-line signal propagation for radio signals of very inclined cosmic ray air showers

An ongoing challenge for radio-based detectors of high-energy cosmic particles is the accurate description of radio signal propagation in natural nonuniform media. For radio signals originating from extensive air showers, the current state of the art simulations often implicitly assume straight-line signal propagation. The refraction due to a nonuniform atmosphere is however expected to have an effect on the received signal and associated reconstruction. This effect is currently not completely understood for the most inclined geometries. Here, we present a study regarding the validity of straight-line signal propagation when simulating radio emission associated with very inclined air shower geometries. To this end, the calculation of the electric field based on the end point formalism used in coreas was improved by use of tabulated ray tracing data. We find a difference of 2% in radiation energy and a difference of $O(0.01\ifmmode^\circ\else\textdegree\fi{})$ on direction reconstruction when working at frequencies below 600 MHz. We thus find that, for frequencies up to 600 MHz and zenith angles up to 88\ifmmode^\circ\else\textdegree\fi{}, the current straight-line based simulation approaches are accurate.