Thank you Ardavan for the reference. My understanding of the near2far feature in cylindrical coordinate and the example is that we have rotational symmetry of the problem. In my case, I'm interested in a general cylinder that is periodic in the cylinder axis direction but does not necessarily have rotational symmetry, e.g an elliptical cylinder or cylinder with arbitrary cross-section. If there is a connection to what already in MEEP that I'm not seeing, it would be great if you could point out. It's very possible that I'm not seeing the connection.
Thanks! On Sun, Nov 8, 2020 at 9:43 PM Mandy Xia <m...@cornell.edu> wrote: > Hmm I was trying to efficiently compute contribution from a periodic > cylinder structure and avoid the expensive spatial sum used in MEEP. I > don’t think this functionality was implemented MEEP currently. > > On Sun, Nov 8, 2020 at 9:36 PM Ardavan Oskooi <ardavan.osk...@gmail.com> > wrote: > >> 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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