> On Oct 26, 2017, at 10:01 PM, Ardavan Oskooi <ardavan.osk...@gmail.com> wrote
> I use meep as c++ library for nanooptics and write my own code around
> it. After some fiddling around I implemented adaptive resolution using
> transformations of the material property tensors. It workes fine so far.
> Two things:
>
> 1. If anyone wants it, I can upload a short summary-pdf of how I did
> that, how the results look and a bit of example code plus
That's great to hear; I've suggested using transformation optics for variable
resolution several times on the mailing list, but I can't recall whether anyone
actually succeeded in doing it. (The formulas are all well known, but
implementing them can be tricky.)
> 2. I do scattering calculations, using dft_flux_box-es. I am a bit
> confused: do I have to watch out for something, if I put these boxes in
> the region with the transformed epsilon an mu? Transforming the fields
> back somehow before the flux is calculated?
That's a good question. Of course, transforming the fields back before the
flux is calculated will definitely work in principle, but it would be a pain to
implement.
It's possible that you could just compute the "ordinary" flux in the
transformed region and it will just work (i.e. give the same answer as the flux
in the original coordinates), but I'm not sure about this. I can think of a
couple of cases off the top of my head where it must be true, but I don't know
if it is true in general.
It should be a straightforward exercise to check this. Look at my notes on
transformation optics
http://math.mit.edu/~stevenj/18.369/coordinate-transform.pdf
and plug the transformed fields into an integral of the Poynting vector (don't
forget the Jacobian factor for the integral itself), and see if you can show
that it is invariant under the transformation. (Note the tricks with the
Levi-Civita tensor and identity after equation (17), for example.)
> shows some more dips/wriggles. (I calculated the scattering of a metal
> nano-cylinder in 2D, where already the non-adaptive mesh leads to a
> spectrum that has a bit more wriggles than in Mie-calculations).
You should check whether these are just a resolution artifact, i.e. whether
they go away as you increase the overall resolution.
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