jan/meanas
Watch
1
0
Fork
You've already forked meanas
 0
Code Issues Pull requests Releases Wiki Activity

[eme] characterize orientation bias under modal truncation

Browse source 
Compare mixed and Galerkin testing against exact polarization/Fresnel interfaces and independent driven FDFD solves. Show complete-basis recovery, omitted-channel power, and the limits of longitudinal refinement, orientation averaging, and Euclidean least squares. Keep the default formulation unchanged and document its approximation limits.

Validation: 1689 tests passed, 584 skipped; Ruff and documentation build passed.
This commit is contained in:
Forgejo Actions 2026-10-18 23:21:29 -07:00
commit a08e9ce71b
3 changed files with 280 additions and 0 deletions
Download patch file Download diff file Expand all files Collapse all files

62
docs/api/waveguides.md
View file

@ -89,3 +89,65 @@ devices. Singular interface and cascade systems also raise contextual errors
rather than silently substituting pseudoinverses.
::: meanas.fdfd.eme
## Orientation bias under modal truncation
Mixed testing is a projected approximation: H continuity is tested on the left
and E continuity on the right. Swapping the ports changes the testing spaces
when the retained modal subspaces are incomplete. This effect survives checks
of reciprocity and unitarity.
A reproducible Maxwell counterexample is a uniform isotropic medium with two
degenerate linear polarizations. Keep one polarization on each port, rotated
so their overlap is `a=0.8`. There is no material interface: true reflection is
zero and transmission into the retained receiver is `a`. The other polarization
carries the remaining transmitted power, `1-a**2=0.36`.
| Calculation | R_left | R_right | T_left_to_right | T_right_to_left |
| --- | ---: | ---: | ---: | ---: |
| Exact full basis, then restrict ports | 0 | 0 | 0.8 | 0.8 |
| Truncated mixed | 0.219512 | -0.219512 | 0.975610 | 0.975610 |
| Swap ports, mixed, then reorder | -0.219512 | 0.219512 | 0.975610 | 0.975610 |
| Truncated left Galerkin | 0 | 0 | 1.25 | 0.8 |
| Euclidean E/H least squares | 0 | 0 | 0.8 | 0.8 |
An independent driven 3D FDFD solve with PML agrees with the exact reference
from either incidence direction: transmission is 0.8 within `1e-12`, with
reflection below `2e-8` in the test fixture. Keeping both polarizations makes
mixed testing match the exact complete scattering matrix and restores
port-relabeling covariance.
For the single retained polarization, mixed testing yields
`r=(1-a**2)/(1+a**2)` and `t=2*a/(1+a**2)`. The spurious reflection is quadratic
in a small angle between adjacent retained polarizations. However, longitudinal
refinement alone is insufficient: rotating a single retained vector through a
uniform degenerate medium makes the sampled chain approach artificial following
of that vector (`|T|` approaches 1), while the physical endpoint overlap remains
0.8. Keeping the complete degenerate block recovers the physical result at every
sampling density tested.
Two tempting corrections are insufficient. Averaging the two port orientations
cancels reflection in this example but leaves transmission at 0.975610. Plain
Euclidean E/H least squares gives the correct uniform-medium result, but is not
a general replacement. A second fixture uses exact degenerate modes of diagonal
positive epsilon/mu tensors, with electric scaling `(1,2)` on the left and
`(1,3)` on the right and a 30-degree polarization rotation on both ports. After
single-mode truncation, least squares has unequal directional transmissions
(approximately 0.850839 and 1.092163) and a maximum singular value of 1.104947.
The complete Fresnel solution is reciprocal and lossless.
The mixed default remains unchanged. Retain complete coupled/degenerate blocks
when the geometry can mix them, check modal-basis convergence as well as section
sampling, and compare against independent full-field results. Neither orientation
averaging nor gain/reciprocity postprocessing recovers omitted-channel physics.
Orientation discrepancy is a useful diagnostic, not a bound on transmission
error. These examples use real power-orthonormal propagating modes; for general
complex modes, the reciprocity constraint involves the modal orthogonality
matrix, as derived by [Svendsen, Haakestad, and Skaar](https://arxiv.org/abs/1301.2458).
Reproduce the analytic, full-basis, candidate-formulation, taper-refinement, and
driven-FDFD checks with:
```sh
OPENBLAS_NUM_THREADS=1 python -m pytest meanas/test/test_eme_orientation.py -q
```