Floquet vector should be normalized with respect to frequency when using periodic boundary conditions

[krono-i2]

Description:

When using periodic boundary conditions in palace, the Bloch/Floquet vector appears to be treated as a fixed value throughout a frequency sweep. However, for physically correct periodic (Floquet) simulations, the Bloch vector depends linearly on frequency.
If the frequency changes during a sweep but the Bloch vector in the JSON configuration remains constant, the simulation becomes inconsistent and produces incorrect results.
This prevents performing valid frequency sweeps under periodic boundary conditions unless the user manually updates the Bloch vector for each frequency—something that the current input format does not support.

Suggested improvement:

It would be better if the Bloch/Floquet vector specified in the JSON:

• were normalized to the frequency, or
• alternatively, could be expressed in terms of direction only, letting palace scale it internally using the vacuum wavenumber.

This would ensure correct behaviour when performing frequency sweeps and avoid misleading results.

Thanks for your work on the project!

[hughcars]

Hi @krono-i2,

The choice to have the floquet vector be constant valued reflects how we have been using it for periodic structures, where the shift represented by k is a measure of the periodicity in the spatial direction. Crucially, being constant valued means that the periodicity/phase shift is not a function of frequency but is constant across them. Were the shift to vary as a function of frequency, this is is akin to saying that the phase shift across a periodic boundary is different for different waves, which whilst physically possible is very different from what we had put the feature in for originally. As such, this is not a bug, this is a feature.

Having a linear dependency as you are suggesting can be done, but would be modeling a different phenomena than what had been originally requested. Additionally this would result in a more complex dependence on the frequency decomposition, so plausibly we would need to pipe that term through a few more interfaces. This is more of an engineering barrier than something show stopping though. If you could send me a link to an arxiv or paper where this type of relation is used for an EM simulation, I might be able to better appreciate it's application, and can then plan accordingly.

[krono-i2]

Hi @hughcars, thanks a lot for your feedback!

I agree that, in general, the Floquet vector is a measure of the periodicity in the spatial direction. However, in practical CEM setups it typically depends on the operating frequency. Let me clarify this with a couple of examples:

• For a plane-wave excitation, the Floquet vector is essentially the projection of the plane-wave propagation vector onto the periodicity plane. Since the magnitude of the wave vector scales linearly with frequency, so does the Floquet vector.
• More generally, any incident field can be expressed as a superposition of infinitely many plane waves, each associated with its own projected wave vector. This again implies a frequency dependence.

In other words, the Floquet vector can usually (if not always) be interpreted as a projection of a wave vector whose magnitude varies with frequency—at least in non-dispersive media.

Because of this, assuming a constant Floquet vector in the Palace configuration forces users to run separate simulations for each frequency of interest, modifying the Floquet vector manually every time. Allowing frequency-dependent Floquet vectors would remove this limitation and significantly improve workflow efficiency.