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I like to simulate the free-space propagation of an electric field (beam radius ~ 1-10 cm) over extremely short distances (~ 5-10 cm). The reason is that the field is focused by a lens with a very small focal distance (~ 30 cm). For larger distances, the FFT based method works but it fails for short distances due to aliasing (and I tried extremely high spatial resolutions without success). So I tried to compute the Rayleigh-Sommerfeld diffraction integral directly, but the highly oscillating term in it demands an extremely high spatial resolution as well once the propagation distance becomes too short. The only other method I can think of at the moment is a finite-differences solver for the wave equation itself. But before I try to implement it, I thought about asking if anyone has experience with this kind of problem? And maybe even some advice what I can try to solve it?

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