Inverse design of a Directional Coupler

[satadrudas]

Hi, first of all, I really appreciate the creators of this library. I work with MEEP for inverse design but really needed something to speed up my work. Though, I have a few questions and need your help.

I am trying to do an inverse design of a directional coupler. This is what I did with MEEP:

What I am trying to do here is using two sources, but with a pi/2 phase shift (as you can see in the amplitude in the code snippet below) and the objective function is to maximize the power output of the top-right port for a broadband source which looks something like this on MEEP:

    fcen = 1/1.55
    width = 0.2
    fwidth = width * fcen
    src = mp.GaussianSource(frequency=fcen,fwidth=fwidth)
    sources = [mp.EigenModeSource(src,
                        eig_band = 1,
                        direction=mp.NO_DIRECTION,
                        eig_kpoint=kpoint,
                        size = source_size,
                        center=source_center1,
                        amplitude=1.0),
                mp.EigenModeSource(
                        src,
                        eig_band=1,
                        direction=mp.NO_DIRECTION,
                        eig_kpoint=kpoint,
                        size=source_size,
                        center=source_center2,
                        amplitude=0.0 - 1.0j
        )]

What I wanted to know is, is it possible to use two sources with a pi/2 relative phase difference of the amplitudes? I see that there is the phase_shift in WaveCharacter. Do I use that?

And also, how do we use broadband Gaussian source? I found this: GaussianPulseProfile. So, do I use this as my source? There is a carrier phase variable here, do I use that instead of WaveCharacter?

Sorry if my questions appear naive, I am still new to inverse design.

[ymahlau]

Hi, this is definitely something you can achieve with FDTDX.

You basically already answered your own question, a phase shift of pi/2 in the wavecharacter will offset the phase of the source. By default, sources in fdtdx are continous sources, but if you set the temporal_profile attribute to a GaussianPulseProfile, you can change this to a broadband pulse.

I would suggest to also put an EnergyDetector over the whole simulation volume. If you set the as_slices=True attribute, the detector will save the mean energy of the simulation volume in an efficient way and automatically create a video of the simulation. This can be very helpful to verify that the simulation is behaving correctly.

Some important differences to meep are:

• FDTDX uses JAX, which can be a bit confusing to start with. If you run into any problems feel free to ask them here!
• In FDTDX, all units are metrical. So instead of 1.55 for a wavelenght of 1.55µm you would specify 1.55e-6 since FDTDX uses meter as a unit.

If you run into any problems or want to suggest improvements that would make your life easier post them here or in the issues section.

[satadrudas]

Thanks for the suggestions. Will try them. I also wanted to know if there is any way to do a 2D simulation? Basically, I want to do a 2D inverse design with effective index and then in the last couple of epochs I'll extrapolate the height for the design in a 3D simulation.

I have tried

partial_real_shape = (length, width)

And also:

partial_real_shape = (length, width, None)

for the SimulationVolume and UniformMaterialObject

In both cases, I am getting errors.

[ymahlau]

2D-Simulations are not really the main focus of FDTDX, but you can hack yourself one together pretty easily. Just make the third dimension very small, for example three simulation grid cells. Then place periodic boundaries at the bottom and top, which will give you a 2D-Simulation as long as all Objects are also 2D.

Out of curiosity, how do you plan to use a 2d-simulation in a 3d-domain? I would have thought your design will allways be surrounded by air or substrate in practice such that the 2d-simulation is going to give you drastically different results.

[satadrudas]

Hi, I am actually trying to replicate the work in this paper:
Inverse-designed low-index-contrast structures on a silicon photonics platform for vector–matrix multiplication

[ymahlau]

Oh that is very interesting! Feel free to post here if you get any results or run into obstacles.

[satadrudas]

Definitely. Thanks for all your help.