Regarding the extension of metaplectic geometrical optics to modelling evanescent waves in ray-tracing codes

TL;DR

This paper extends metaplectic geometrical optics (MGO) to model evanescent waves in ray-tracing, enabling accurate wavefield predictions near caustics including shadow regions with complex wave behavior.

Contribution

It introduces a complex-valued symplectic rotation in MGO to model evanescent waves and demonstrates its effectiveness in shadow regions, broadening MGO's applicability.

Findings

MGO accurately models evanescent waves in shadow regions.

Corrected quadrature-angle bias improves MGO performance.

Strong agreement between MGO and exact solutions in examples.

Abstract

Metaplectic geometrical optics (MGO) is a recently developed ray-tracing framework to accurately compute the wavefield behavior near a caustic (turning point or focal point), where traditional ray-tracing breaks down. However, MGO has thus far been restricted to having real-valued wavevectors. This is disadvantageous because often upon crossing a caustic from the `illuminated' region to the `shadow' region, two real-valued rays coalesce into one complex-valued ray corresponding to the transition from propagating to evanescent behavior. One can distinguish caustics as having either `illuminated shadows' or `proper shadows' -- the former corresponds to when the shadow still contains real-valued rays (albeit in a fewer quantity than in the illuminated region), while the latter corresponds to when the shadow contains no real-valued rays. Here, by means of examples, we show how MGO can be used to model both types of shadows. First, for illuminated shadows we show that MGO can actually be used `as is', provided a corrected quadrature-angle bias is used compared to that proposed in the original references. This is then implemented and demonstrated in a recently developed MGO ray-tracing code. Second, we show that for proper shadows, the MGO formalism can still be used if the symplectic rotation matrix that removes caustics along rays is allowed to be complex-valued. In both cases, strong agreement is seen between the MGO and the exact solution, demonstrating the potential of MGO for improving the predictive capability of ray-tracing codes and laying the foundations for modeling more complicated evanescent phenomena such as tunnelling with MGO.