adding directional coupler example

[FilipeFcp]

Hi all,

I added a quick example using the directional coupler GDS, as @e-g-melo suggested.

Today, I noticed that there's a very similar notebook in the parameter sweep tutorial, so I focused more on the simulation setup and post-processing in this case.

If you have any suggestions to make it more interesting, feel free to let me know!

[alec-flexcompute]

Great example as always, @FilipeFcp! A couple small points:

1. Also mention that you're creating a field monitor to check out the profile in the middle of the waveguides

2. Above cell 9, add "(if the field decays before the runtime, the simulation will auto shut-off and we will only be billed for the Flex credits used to run)" since this will probably be one of the first examples a new user looks at

3. In the interpolation cell, it might be helpful to add a legend in the plot

That's it, thanks for making these examples very easy to review!

[e-g-melo]

Thanks for this new notebook @FilipeFcp! It is pretty didactic.

Some suggestions:

1. "and create the td.Structures with those material properties" -> "and create the td.Structure with each of those material properties".
2. We don't need the plt.show() after sim.plot_3d() in cell [8].
3. I suggest using dB in the chart of cell [11] to display the -3dB crossing point. The current method also works, though.

Emerson

[tomflexcompute]

Thanks @FilipeFcp . Definitely make sense to have this addition in the example library.

1. The simulation domain size in y can probably be shrunk a bit more to reduce cost?
2. In the plotting, does setting edgecolor="k" actually do anything to the plot?
3. Might be better to plot transmission as a function of wavelength instead of frequency.
4. For printing the transmission, might be better to only show something like 4 significant digits?
5. Probably don't need to add the notebook to docs/features/parameter_sweep.rst?

[FilipeFcp]

Thank you all.

I believe everything has been addressed.

[daquinteroflex]

Let's merge when ready!

[github-actions]

Spell Check Report

DirectionalCoupler.ipynb:

Cell 1, Line 3: 'wavelength-division'
  > Directional couplers are fundamental components in photonic integrated circuits, enabling efficient splitting and combining of optical signals. By placing two parallel waveguides in close proximity, these passive devices exploit evanescent field coupling to control how light is distributed between channels. It is also possible to control the output by adjusting the relative phase between the inputs, enabling flexible power splitting ratios and switching behavior. Their design and compatibility with silicon-on-insulator technology have made them a popular choice for applications ranging from wavelength-division multiplexing to optical switching and signal processing.
Cell 18, Line 1: 'shut-off'
  > Before running the simulation, we can check the **maximum** possible Flexcredit cost. If the field decays before the runtime, the simulation will auto shut-off and we will only be billed for the Flexcredits of the effective runtime.
Cell 32, Line 4: 'viridis'
  > sc = ax.scatter(sidewall_angles, td.C_0 / np.array(freqs), c=transmittance, cmap="viridis")

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