TFSF Source in anisotropic dispersive media

[ymahlau]

Since polarization-weighting is currently not implemented, a source within an ansisotropic dispersive media will not behave correctly. Currently we are taking the average of components

[ymahlau]

Some AI-generated investigation

1. The ε(ω) fed to the filter is polarization-blind. compute_eps_spectrum_from_coefficients
   returns exactly the component average (εₓ+ε_y+ε_z)/3:

┌───────┬────────────────────────┬─────────────────────────┬──────────────────────┐
│ ω/ω_c │ εₓ (correct for x-pol) │ ε_y (correct for y-pol) │ what the filter uses │
├───────┼────────────────────────┼─────────────────────────┼──────────────────────┤
│ 0.4 │ −152.8 + 19.2j │ 1 │ −50.3 + 6.4j │
├───────┼────────────────────────┼─────────────────────────┼──────────────────────┤
│ 1.0 │ −23.9 + 1.2j │ 1 │ −7.3 + 0.4j │
└───────┴────────────────────────┴─────────────────────────┴──────────────────────┘

The filter is fed neither polarization's permittivity — and _build_dispersive_H_filter has no
polarization argument at all, so it physically cannot produce the right answer.

2. The resulting H-side FIR filter is qualitatively wrong for the clean case. For a
   y-polarized wave the medium is vacuum (ε_y ≡ 1), so the correct broadband filter is the
   identity (no correction). The code instead applies a 30.9 % spurious dispersion correction —
   it mixed in the metallic x-axis:

correct y-pol filter == raw profile (identity)? True
code filter == raw profile (identity)? False (30.9% distortion)

For the x-polarized wave the error happens to be small here (2.1 %) — but that's a
coincidence: the filter is the normalized ratio √(ε(ω)/ε(ω_c)), and for a strongly metallic
Drude response the 1/3 factor and the +ε∞ largely cancel in the ratio. Change the material
(weaker pole, Lorentz resonance, ε∞ ≠ 1) and that cancellation goes away. The y-pol case is
the honest measure of the defect.

Scope and attribution (to keep the finding calibrated)

• Only the broadband correction is affected. The carrier-frequency amplitude and E/H ratio are
  correct — they project onto e_pol (linear_polarization.py:279). Single-frequency sources (no
  filter) and isotropic dispersion are both unaffected.
• The code warns, so it's flagged, not silent. But "impedance matching is approximate here"
  undersells it — for a wave along a non-dispersive axis the correction should be zero, not
  merely approximate.
• Orthogonal note: the DC rfft bin of any Drude spectrum divides by zero (nan) — I verified
  this fires for isotropic Drude too, so it's pre-existing and handled downstream, unrelated to
  this PR.

The fix

Pass the source's e_pol into _build_dispersive_H_filter and project the per-component ε onto
it (einsum("i,ijxyz,j->xyz", e_pol, eps_tensor, e_pol)), exactly mirroring what the
carrier-frequency path already does — instead of .mean(axis=1) over components in
compute_eps_spectrum_from_coefficients. For isotropic dispersion (C=1) this is a no-op, so
it's fully backward-compatible.

[MarkCunningham0410]

@ymahlau going to have a look at this