Match the PML properties to beam path material

[amorimd]

Feature request 💡

The Perfect Matching Layer currently assumes that the beam is going through vacuum. If the material is changed to something with $\sigma \neq 0$ S/m or $\epsilon_r \neq 1$ and $\mu_r \neq 1$ then the PML layers are not adapted to the simulation domain, creating discontinuities in the field computation.

🔍 Describe the solution you'd like

The $\sigma$, $\epsilon^{-1}$ and $\mu^{-1}$ tensors should have the layers corresponding to the PML automatically adapting their parameters with respect to the beam path material.

[amorimd]

When using a non-vacuum material for the beam path, the PML cell properties computation remain the same as for vacuum. This creates discontinuities in the field propagation.

Here with $\epsilon_r = 10, \mu_r=1, \sigma=0.2\ S/m$ we clearly see the discontinuity in the $E_z$ field

The discontinuity in $\sigma$ over the PML domain can clearly be seen:

Now with the same material for the beam path, but with the adapted PML, the $E_z$ field looks nicer:

The conductivity of the PML cells is now correctly adapted: