Online Supplement for Fast and Accurate Propagation of Coherent Light

We observed in §2.1 that if the propagation distance z is small, then the propagation problem may be accurately and efficiently solved in the Fourier domain. This is not a new observation—see, e.g., [16, 14]—so our objective here is simply to demonstrate how this propagation method (the so-called angular spectrum method) can be implemented using the quadratures from Theorem 2 to ensure any user-specified accuracy. Given boundary data f and a propagation distance z, the angular spectrum method amounts to the numerical evaluation of the integral