For reference, note that the near2far feature already exists for
cylindrical coordinates. It was added in
https://github.com/NanoComp/meep/pull/1090. (This implementation is
based on integrating over φ using green3d.) For a demonstration, see
this tutorial example
<https://meep.readthedocs.io/en/latest/Python_Tutorials/Cylindrical_Coordinates/#focusing-properties-of-a-binary-phase-zone-plate>.
On 11/8/20 16:47, Mandy Xia wrote:
In my problem, I have a periodic cylinder structure along z-direction
and I would like to compute the scattered field in the far field.
Using the spectral representation of PGF, I'm able to compute, for a
particular point in the simulated period, what the total contribution
summing over all the period is, without an expensive spatial sum. In
order to collect all the contributions from the cylinder, the last
step I need is to integrate over the simulated period and I was trying
to rely on the numerical integration over near-field box in MEEP to
handle that. However, I found that the computed results are off. I
suspected this was due to the staggered grid we are using. I examined
the coordinates of the discrete points on the near field box. For some
(x, y) combinations, we have z coordinates going from -period/2 to
period/2 in z and in total an odd number of points. In some other (x,
y) combinations, we have z coordinates going from -period/2+half_cell
to period/2-half_cell and in total an even number of points. So it
seems that in the above two scenarios we are integrating over
different lengths in z. However, in order to get the correct
contribution, I need to integrate over exactly one period of the
structure. I'm wondering if you have any suggestions on this. Or maybe
there is something wrong with my understanding of the staggered grid,
and it would be great if you could point it out.
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