  The design and optimization of radiofrequency-wave systems for fusion
applications is often performed using ray-tracing codes, which rely on the
geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and
caustics. To accurately model the wave behavior in these regions, more advanced
and computationally expensive "full-wave" simulations are typically used, but
this is not strictly necessary. A new generalized formulation called
metaplectic geometrical optics (MGO) has been proposed that reinstates GO near
caustics. The MGO framework yields an integral representation of the wavefield
that must be evaluated numerically in general. We present an algorithm for
computing these integrals using Gauss-Freud quadrature along the
steepest-descent contours. Benchmarking is performed on the standard Airy
problem, for which the exact solution is known analytically. The numerical MGO
solution provided by the new algorithm agrees remarkably well with the exact
solution and significantly improves upon previously derived analytical
approximations of the MGO integral.
