Metaplectic geometrical optics for modeling caustics in uniform and non-uniform media

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 the true wavefield well near these caustics.