Add subpixel smoothing example for metagrating problem #62
Conversation
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Nice! FYI if you use |
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@mfschubert I wonder if there is a clean way to directly compute the vector fields from this formulation, which has a level set. In other words, we know the normal direction and distance to the nearest interface at every point, so perhaps this doesn't require solving a mini optimization problem? |
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@smartalecH This is an interesting thought, and in general a level set view may be fruitful to take. However, my sense is that we will still have to solve an optimization problem---recall that when computing the vector fields, we balance smoothness with alignment to the permittivity gradient. So, in some cases the optimal field is not aligned with the gradient, and a direct calculation from the permittivity (however it may be parameterized) may not produce such a field. But, maybe there is some cleverness that I am not thinking of this morning. Let's chat about it further. |
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The optimal designs reported in the testbed paper (Section F and Fig. 8) have a diffraction efficiency of ~93%. What are the values for the two designs shown above? What are the values of the designs computed using Meep? Note: there is already a Meep script (metagrating_meep.py) which can be used for validation. The input is a CSV file of the design. |
Here, we use fmmax, the invrs.io gym, along with some handy autograd-wrapper functions to take meep's recently added subpixel smoothing functionality, and optimize the metagrating example.
Importantly, this example shows how one can use fmmax (an RCWA/FMM tool) and still evolve β→∞.
We have an explicit shape optimization example (β=∞):
As well as an explicit topology optimization example (β=16, 64, ∞):
Everything was very straightforward thanks to all the existing code!
(note that we need to merge the corresponding PR in meep first)
(cc @oskooi, @mfschubert, @stevengj, @mochen4, @hammy4815)