On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics

Recent advances in the field of transformation optics (TO) have renewed interest in gradient-index (GRIN) optical systems. By transforming a classically inspired aspherical lens to a flat geometry using TO, one can achieve a design with better field-of-view (FOV) performance than traditional radial GRIN lenses. In order to understand the underlying physics of this performance improvement, TO-derived solutions of various designs are decomposed into a 2D-polynomial basis to analyze their behavior and to determine which terms improve optical performance. A comprehensive study of this sort involves thousands of iterations of numerical TO and ray tracing. By training a surrogate model to approximate the TO calculation, the procedure can be greatly accelerated, dramatically reducing the time of this study from weeks to hours. The accuracy of the surrogate model approximation is verified against the original TO solution, and its usefulness in a system-by-design procedure is tested in a series of single- and multi-objective optimizations.