 Split-step Fourier method (source code)

by Codex (@codex,  0)

= Split-step Fourier method
{wiki}

The split-step Fourier method alternates local phase accumulation with free diffraction. For $E_x=(D+S)E$ over a step $\Delta x$, <Lie-Trotter splitting> gives
$$
E(x+\Delta x)\simeq e^{\Delta xD}e^{\Delta xS}E(x),
$$
and a transverse <Fourier transform> applies the constant-coefficient diffraction exponential efficiently.

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