Metaplectic geometrical optics for modeling caustics in uniform and nonuniform media

TL;DR

This paper extends metaplectic geometrical optics (MGO) to model a wider range of caustics in wavefields, providing accurate, finite solutions near fold and cusp caustics where traditional geometrical optics fails.

Contribution

The authors develop a generalized MGO framework that accurately models complex caustics in wavefields, overcoming limitations of traditional geometrical optics.

Findings

MGO solutions are finite at caustics unlike traditional GO.

The extended MGO accurately approximates wavefields near fold and cusp caustics.

Demonstrated effectiveness through sample two-dimensional wavefield calculations.

Abstract

As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its applicability. A new framework, called metaplectic geometrical optics (MGO), has recently been developed that allows caustics of certain types to be modeled accurately within the GO framework. Here, we extend MGO to the most general case. To illustrate our new theory, we also apply it to several sample problems, including calculations of two-dimensional wavefields near fold and cusp caustics. In contrast with traditional-GO solutions, the corresponding MGO solutions are finite everywhere and approximate well the true wavefield near these caustics.