Thank you and I will try increasing the resolution. My research lies in physically-based rendering in Computer Graphics, where I would like to apply wave optics to improve the accuracy of ray-based material models used in computer graphics. We are making the assumption that we are in the far-field of the scatterer so that the scattering distribution is only dependent on direction, and that can be conveniently fit into a modern rendering system that is based on ray tracing. I see that for a periodic structure we get a finite number of diffraction orders. I was thinking of having a proper period length (eg 18um in length) and that can give us a relatively good sampling amount in the longitudinal direction (~90) at visible light wavelength, which I could potentially interpolate on. This project is at an early stage though. In previous work, we used BEM and solve for the cross-section scattering (assuming infinitely long cylinders) and then applied a longitudinal blurring to get 3D scattering function. Now we’d like to move to full 3D and try with FDTD first but I guess we would still like to study the far field scattering distribution first.
On Mon, Nov 9, 2020 at 3:14 PM Steven G. Johnson <stevenj....@gmail.com> wrote: > If it is just a problem with the precise grid, then it should go away as > you increase the resolution. If the problem doesn't disappear with > increasing resolution, then you have a bug somewhere else. > > (However, I'm curious about what you hope to learn from the far field. In > a periodic structure, there's not usually anything interesting happening in > the far field that you can't easily see/compute directly in the near field > as well, since the scattered wave is just a superposition of a set of > planewaves at a finite number of diffraction orders.) > > On Nov 8, 2020, at 7:47 PM, Mandy Xia <m...@cornell.edu> 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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