Vertical coupler optimisation for 2 polarisation states of an incident source i.e. Ex and Ey

[jsco7509]

Hi gang,

How do I perform topology optimisation of a vertical coupler attempting to maximise the coupling efficiency for an incident plane wave with two orthogonal polarisation states? i.e. Source_1 = Ex and Source_2 = Ey. (For 1 frequency only )

Thanks

[jsco7509]

When optimisation is performed for different frequencies it seems like this can be simply implemented using the "frequencies" Args in:

opt = mpa.OptimizationProblem(
simulation=sim,
objective_functions=[J1],
objective_arguments=ob_list,
design_regions=[design_region],
frequencies=frequencies,
maximum_run_time=2000,
)

However this is not possible for the different polarisation states. Therefore, I believe this would need to be done by defining sources with difference components i.e.

sourceEx = [mp.Source(mp.GaussianSource(fcen, fwidth=width),
component=mp.Ex,
center=mp.Vector3(0, 0, -2),
size=mp.Vector3(3, 3, 0)),
]
sourceEy = [mp.Source(mp.GaussianSource(fcen, fwidth=width),
component=mp.Ey,
center=mp.Vector3(0, 0, -2),
size=mp.Vector3(3, 3, 0)),
]

Then I'm not sure how to update mp.Simulation and the objective list and function.

[smartalecH]

The objective function will assume the objective arguments are an array with the same shape as the frequencies parameter in your optimization configuration. You might be confusing what's going on here:

The sources are prescribed in the time domain and hence excite a continuum of frequencies in your simulation. So you can effectively simulate all frequencies (within your prescribed band) using those two polarized sources.

To do any processing on these fields in the frequency domain, however, you have to use a DTFT at a series of specified frequencies (meep does all this under the hood). And the optimization object and objective function syntax follows this logic.

The output of your objective function can still be a vector, and meep with return a full Jacobian here. But your optimizer may not know how to handle that... so we typically perform some kind of reduction in the objective function (eg a mean) and meep will properly backpropagate through that.

[jsco7509]

Thank you @smartalecH

[jsco7509]

In regards to performing optimisation for a coupler using an incident plane wave source with 2 different polarisation states I set up my simulation in the following way:

sourceEy = [mp.Source(mp.GaussianSource(fcen, fwidth=width),
                     component=mp.Ey,
                     center = source_center,
                     size = source_size),]
sourceEx = [mp.Source(mp.GaussianSource(fcen, fwidth=width),
                     component=mp.Ex,
                     center = source_center,
                     size=source_size)]

simEy = mp.Simulation(
    cell_size=cell_size,
    boundary_layers=pml_layers,
    geometry=geometry,
    sources=sourceEy,
    dimensions=3,
    resolution=resolution,
)

simEx = mp.Simulation(
    cell_size=cell_size,
    boundary_layers=pml_layers,
    geometry=geometry,
    sources=sourceEx,
    dimensions=3,
    resolution=resolution,
)

mode = 1

TEEy = mpa.EigenmodeCoefficient(
    simEy,
    mp.Volume(
        center=mp.Vector3(x=-4),
        size=mp.Vector3(0, 3, 0.3),
    ),
    mode,
)

TEEx = mpa.EigenmodeCoefficient(
    simEx,
    mp.Volume(
        center=mp.Vector3(x=-4),
        size=mp.Vector3(0, 3, 0.3),
    ),
    mode,
)


ob_list = [TEEy, TEEx]

def J1(TEEy, TEEx):
    power = npa.abs(TEEy) ** 2 + npa.abs(TEEx) ** 2
    return power

opt = mpa.OptimizationProblem(
    simulation=simEy,
    objective_functions=[J1],
    objective_arguments=ob_list,
    design_regions=[design_region],
    frequencies=frequencies,
    maximum_run_time=2000,
)

[jsco7509]

This, to me, seems like the more 'pure' way of optimising for 2 different polarisation states (Ex & Ey) of an incident plane wave. However I understand that it is more computationally expensive. (NB Here I want to couple both states into a single waveguide, similar to https://doi.org/10.1364/OL.36.000796)

I note however, that you seemed to construct your simulation in the reciprocal manner. Launching a source in the waveguide, then maximising the outcoupled efficiency using Near-to-Far-Field. Obviously you get a very nice result....

is the approach I use valid? I am also concerned about only calling 1 sim (simulation=simEy) in the optimisation problem yet using simEx and simEy in the mpa.EigenmodeCoefficient:

TEEy = mpa.EigenmodeCoefficient(
    simEy,
    mp.Volume(
        center=mp.Vector3(x=-4),
        size=mp.Vector3(0, 3, 0.3),
    ),
    mode,
)

TEEx = mpa.EigenmodeCoefficient(
    simEx,
    mp.Volume(
        center=mp.Vector3(x=-4),
        size=mp.Vector3(0, 3, 0.3),
    ),
    mode,
)

opt = mpa.OptimizationProblem(
    simulation=simEy,
    objective_functions=[J1],
    objective_arguments=ob_list,
    design_regions=[design_region],
    frequencies=frequencies,
    maximum_run_time=2000,
)