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The design and optimization of radiofrequency-wave systems for fusionapplications is often performed using ray-tracing codes, which rely on thegeometrical-optics (GO) approximation. However, GO fails at wave cutoffs andcaustics. To accurately model the wave behavior in these regions, more advancedand computationally expensive "full-wave" simulations are typically used, butthis is not strictly necessary. A new generalized formulation calledmetaplectic geometrical optics (MGO) has been proposed that reinstates GO nearcaustics. The MGO framework yields an integral representation of the wavefieldthat must be evaluated numerically in general. We present an algorithm forcomputing these integrals using Gauss-Freud quadrature along thesteepest-descent contours. Benchmarking is performed on the standard Airyproblem, for which the exact solution is known analytically. The numerical MGOsolution provided by the new algorithm agrees remarkably well with the exactsolution and significantly improves upon previously derived analyticalapproximations of the MGO integral.

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics