Source
Engine design23_v1 · package package/design23_recentered_optimizer · assembled 2026-07-29 15:57 UTC.
Design 23 continuous-radiation gate¶
Date: 2026-07-22
Answer first¶
The failed Design 23 improvement is reproduced without an EME cell library. When the saved cavity currents are projected onto the physical open channels of the full air/SiN/anthracene/PVA/substrate stack, the predicted loss rises by 1.54% from optimizer iteration 0 to 30. The corresponding Q proxy falls by 1.51%. FDTD is flat (+0.076% Q), whereas the former analytical objective incorrectly predicts +260% Q.
The optimizer did not suppress the dominant physical radiation. It slightly reduced the bound TE film branch, but increased both much larger half-space continua.
| Iteration | FDTD Q / initial | Old analytical Q / initial | Continuous-channel loss / initial | Channel Q proxy / initial |
|---|---|---|---|---|
| 0 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
| 15 | 1.000428 | 1.670096 | 1.009082 | 0.991000 |
| 30 | 1.000763 | 3.604590 | 1.015362 | 0.984871 |
The gate therefore rejects the old objective's false improvement and agrees with the FDTD direction. The channel score is not yet an independently normalized absolute Q; its validated use here is the relative ranking of the saved geometries.
Dominant physical channels¶
At iteration 0, the total open-channel score separates as follows.
| Physical channel | Share of total loss | Iteration 0 to 30 |
|---|---|---|
| Half-space TE continuum | 70.62% | +1.71% |
| Half-space TM continuum | 25.05% | +1.40% |
| Bound planar-film TE branch, n_eff = 1.552 | 4.33% | -0.49% |
The ordinary TE continuum is the first optimization target. The bound film mode is real and was missing from a naive real-axis Gaussian quadrature, but it is not the dominant loss in this design.
The continuum is also localized in longitudinal momentum. Define
For iteration 0:
- 85.6% of TE-continuum power lies in 0.5 < u < 0.7;
- 91.0% of TM-continuum power lies in 0.5 < u < 0.7;
- the largest TE packet is near u = 0.618, or |kx| = 0.896 k0;
- the largest TM packet is near u = 0.582, or |kx| = 0.844 k0;
- a secondary TE packet occurs around u = 0.66, or |kx| about 0.96 k0.
These are collective radiation packets formed by coherent emission from all 84 holes. They are not independent per-hole losses. Iteration 30 leaves the same packets in place and slightly increases their integrated weight.
What was wrong in the previous radiation treatment¶
Two outgoing-channel effects were incomplete.
- The multilayer planar stack has a real-qy bound TE pole. Generic Gaussian
nodes avoid the zero-width pole, so its outgoing
i*pi*residuecontribution was omitted or made contour-dependent. - A fixed qy rule does not resolve the square-root singularities at the air and substrate light lines. At high beta order this produced a visibly non-passive radiation density.
The repaired projector:
- finds every bound TE/TM branch of the exact planar stack;
- extracts its positive-semidefinite residue;
- subtracts the real-axis pole in principal value and restores the outgoing residue explicitly;
- splits the half-space integral at every physical light line;
- uses endpoint-clustered qy quadrature for the grazing singularities;
- separates the TE and TM spectral densities;
- Dyson-dresses each density by the finite-width SiN strip;
- projects the result onto the coherently phased full-cavity current;
- integrates beta separately over each physical channel interval.
The background optical theorem closes below 3e-16 and the dressed-strip identity closes below 9e-13 over the 256-point campaign. The extracted film residue is positive semidefinite and more than 0.9999999998 rank one.
Convergence¶
The 84-hole current creates fine beta interference fringes, so very low-order beta rules are useful only as qualitative gates. The final campaign used 256 Gauss-Legendre points per physical beta interval. Increasing the endpoint calculations to 512 points changed the absolute scores by 0.28% and changed the endpoint Q-proxy ratio from 0.984871 to 0.984800.
The qy continuum is integrated on separate air and substrate light-line panels with a sine endpoint map. TE and TM components are individually checked for passivity before they are combined.
Architectural decision¶
Do not build a paid EME cell library yet. This result shows that the existing cavity-current representation contains enough information to recover the correct Design 23 direction once it is coupled to the physical outgoing spectrum. The immediate production path is therefore:
- insert this pole-aware, light-line-resolved Green operator into the actual QNM determinant rather than using it only as a saved-field diagnostic;
- differentiate the channel amplitudes or the equivalent loss quadratic form;
- optimize the dominant TE continuum packets while retaining total-channel loss as an adaptive guardrail;
- verify several central finite differences and then one or two FDTD geometry perturbations before restarting a long optimization;
- retain the film TE branch and TM continuum even though they are smaller, so the optimizer cannot redirect power into an omitted channel.
A useful reduced basis can now be constructed by SVD of the complex radiation amplitudes in the dominant momentum window across the baseline and perturbed geometries. Reduction should be accepted only when both total loss and its geometry gradient are stable. A scalar loss per cell is still insufficient.
Reproduction¶
python run_radiation_channel_gate.py /path/to/run_state.json \
--iterations 0 15 30 \
--beta-order 256 \
--workers 2 \
--output radiation_channel_gate.json
This is a local calculation and uses no Tidy3D credits. The checkpoint schema is the actual 128-value Design 23 schema: 42 positive gaps, 42 longitudinal radii, 42 transverse radii, SiN width, and SiN thickness.
The offline regression command is:
All 12 tests pass.