Metaplectic geometrical optics for ray-based modeling of caustics

The 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 caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite. This is a critical shortcoming of GO-based methods, as often the wave intensity at a caustic is precisely the quantity being optimized, for example, when a wave is focused on a resonance to provide plasma heating. It is commonly believed that accurate modeling of waves in such regions is impossible without full-wave simulations, which are computationally expensive and thereby limit the speed at which such optimizations can be performed. We show that there is a less expensive alternative that we call metaplectic geometrical optics (MGO) [1, 2]. Instead of evolving the electric field E in the usual x (coordinate) or k (spectral) representation, MGO uses a mixed q = Ax + Bk representation. By continuously adjusting the matrix coefficients A and B along the rays, one can ensure that GO remains valid in the q variables, so E(q) can be calculated efficiently and without caustic singularities. The result is then mapped back onto the original x space using integrals (called metaplectic transforms) that can be efficiently computed using Gauss—Freud quadrature along the steepest-descent contours [3]. Our MGO-based calculations successfully reproduce wave structures in paradigmatic (e.g., Airy and cusp) caustics with high fidelity. These results open a path toward speeding up radiofrequency-wave simulations and might also be useful for modeling intensity-dependent laser-plasma interactions.

[1] N. A. Lopez and I. Y. Dodin, New J. Phys. 22, 083078 (2020)

[2] N. A. Lopez and I. Y. Dodin, J. Opt. 23, 025601 (2021)

[3] S. M. Donnelly, N. A. Lopez, and I. Y. Dodin, arXiv:2104.13307 (2021)