We deal with one of the computationally most critical steps of the Phase-Only synthesis of aperiodic reflectarrays, namely the fast evaluation of the radiation operator. We present an approach exploiting the use of a fast numerical algorithm using 2D Non-Uniform FFTs (NUFFTs) of NED (Non-Equispaced Data) and NER (non equispaced results) type and of parallel processing on Graphic Processing Units (GPUs). We extend the approach in K. Fourmont, J. Fourier Anal. Appl., vol. 9, n. 5, pp. 431-540, 2013 for implementing NUFFT routines to the 2D case and illustrate the parallel strategies to accelerate the approach. In particular, we show how the two levels of parallelism intrinsic in the interpolation step of the 2D NED-NUFFT can be fruitfully exploited by adopting dynamic parallelism, a feature made available in one of the latest architecture of NVIDIA cards. The presented synthesis results show that the introduction of further degrees of freedom (positions) allows improving the performance with respect to periodic reflectarrays. Also, the possibility of adopting aperiodic reflectarrays of reduced number of elements for fixed performance is demonstrated.
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