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

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 integration scheme 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 tunneling with MGO.