adds topology optimized bend

[tylerflex]

#175 got too crazy, so this will be the PR to merge and deploy before Monday's seminar.

Need to re-run one more time.

[e-g-melo]

Hi @tylerflex! Thanks, the notebook is very nice!

Why is the final permittivity in [16] smoother than the density plot in step 25?
I suggest replacing "Conclusion" with "More Examples" or something similar.

[tylerflex]

Thanks, Emerson! I'll look into the density plot.

By the way, is there a good link for me to put near the top in case people want to sign up for an account?

[tylerflex]

it's a bit confusing, but I think it's just the difference between how custom medium are plotted in sim.plot_eps() and using matplotlib to plot the raw data directly.

[yaugenst-flex]

wow but those plotting differences are...pretty significant? like, the plot_eps version looks like it has another filter applied to it. could it be a design region resolution thing?

edit: could it be related to the mesh override only having a third of the resolution of the design parameters?

td.MeshOverrideStructure(
                geometry=design_region_geometry,
                dl=3*[pixel_size]
            )

if that's the case, I guess it should be noted that the design that is plotted is not actually what's being simulated

[e-g-melo]

How about calling get_sim instead of get_density and plotting the permittivity?

[yaugenst-flex]

looks nice, the below are basically all typos and nitpicks

I'd suggest running ruff format on the notebook, there are a few formatting inconsistencies (like spaces between operators, single and double quotes, etc.) that I won't list here

otherwise, going from top to bottom:

• pixellated -> pixelated
• min_steps_per_wvl = wvl0 / pixel_size / np.sqrt(eps_mat) / 1: why divide by 1? also, this is more of a general thing, feel free to ignore, but I find the 1 / x / y / z syntax really confusing. much prefer parentheses.
• This array will go through convolution with a conic filter and a tanh projection to express larger spatial features. -> this is ok but I guess it would be a bit clearer, especially for beginners, to understand that the filter is what's doing the feature sizes and the tanh is a soft threshold to give two material classes in the device.
• "The filter and projection functions are included in our tidy3d.plugins.autograd plugin"
• could also use FilterAndProject instead of make_filter_and_project, but doesn't matter
• in get_sim(), why do you copy twice? i.e. there is sim = sim_base.copy() before doing sim.updated_copy(). I guess just sim_base.updated_copy() should be fine?
• minor, but in cell 9 you give the figure a name (f, ... = plt.subplots()) whereas in cell 7 you don't (also I guess f is quite confusing in this context, fig might be better)
• cell 10: I'd suggest calling .values as early as possible, otherwise this is a bit hidden and I have the impression that it frequently gets lost on users. so rather mode_amps = data['mode'].amps.sel(direction='-').values
• another nitpick on the same line, but I think it's kind of confusing to mix numpy and non-numpy, i.e. doing np.sum(abs(...)). how about np.sum(np.abs(...))? I feel like it's relying on an implementation detail that abs() calls __abs__ which calls np.abs() on an array...
• "Let's construct this function now and get read to use it in the main optimization loop." --> "get ready"
• val_grad = autograd.value_and_grad(objective) -> maybe val_grad_fn?
• learning_rate = 1: I guess it works here but can we really still call this topology optimization 😆, like, this forces the design to be perfectly binary at the first iteration, no tanh needed
• plt.imshow(np.flipud(1 - params.squeeze().T), cmap='gray', vmin=0, vmax=1): pretty confusing, even if it's "just" for plotting, I suggest: plt.imshow(params.squeeze().T, cmap='gray_r', vmin=0, vmax=1, origin="lower")
• # compute and apply updates to the optimizer based on gradient --> compute and apply updates to the parameters (instead of optimizer)?
• I think the params = np.clip(params, 0, 1) needs a comment too. on that note, do we need the explicit np.array() when using np.clip()? still better to include it for illustration I guess
• "Let's add a multi-frequency mode monitor and a field monitor to inpsect the performance.": inpsect --> inspect
• fname="./misc/invdes_bend.gds",: just a question, but does this create the folder misc if it doesn't exist? I've had many notebooks crash this way 😬
• cell 21: # use the final parameters to start this optmization --> optimization
• cell 22: I know this is only a bonus, but still - it really doesn't show how to make a gif easily 😅 you can pretty easily save gifs directly from a matplotlib FuncAnimation, so maybe we should show how to do that here? may be beyond the scope of this notebook

[yaugenst-flex]

How about calling get_sim instead of get_density and plotting the permittivity?

adds a little bit of overhead but would probably be the easiest solution

[tylerflex]

Thanks @yaugenst-flex made all changes. re-running now.