Milestone 5: resonance tracking, artifact rejection, and physical restart
Outcome
This milestone closes the first implementation loop from free-form LDOS optimization to a mode-tracked 3D resonance optimizer. It also demonstrates why three independent gates are necessary: pole/linewidth agreement, PML invariance, and mode identity.
The current physically corrected coarse candidate was generated from a reflection-symmetric taper with a full one-wavelength air strip. A mirror-cell sweep nucleated a Q~66 pole; fixed-frequency optimization moved it to Q~76; direct implicit pole-Q ascent moved the tracked branch to Q~162. The protected strip remains exactly air.
This is not yet a quantitative cavity result. The Q~139 checkpoint passes the coarse PML gate, but the Q~162 checkpoint has pole Q~162 and fitted linewidth Q~194. The 19% mismatch is above the acceptance threshold.
New components
pole_validation.py- retarded real-axis
dA/df, including both mirror derivatives; - source-residue and modal-overlap pole selection;
- relaxed real-center continuation;
- frozen-self-energy diagnostic;
- real-frequency LDOS sweep;
- variable-projection Fano-Lorentzian fit; and
- pole field, history, metrics, and validation plots.
shifted_optimizer.py- resonance-shifted LDOS and direct pole-Q objectives;
- exact implicit log-Q gradient for the local nonlinear pole;
- fixed-point center-motion correction from
d2A/df2; - persistent pole-field tracking between checkpoint files; and
- reflection-symmetric topology updates.
pml_convergence.py- tracked PML-strength and onset perturbations;
- modal-overlap, frequency-shift, and Q-span metrics; and
- a coarse automated acceptance gate.
Numerical checks
Corrected default grid (20 x 13 x 11):
- vector unknowns: 8,580;
- topology variables: 168;
- surface-plane unknowns: 429;
- maximum density in the air strip: zero;
- y/z PML clearances: 0.24 / 0.40 lambda0;
- complex-symmetry error:
9.94e-14; - curl-gradient error: exactly zero;
- two-period boundary-translation error:
6.03e-12; - surface Dyson residual:
2.44e-13; and - LDOS directional-gradient error:
6.05e-7.
Pole machinery:
- implicit pole-Q directional-gradient error:
6.04e-4; - Q=556 development pole versus linewidth: 556.3 versus 554.1 (
0.395%); - derivative step-halving error for that pole:
5.69e-6; - mirror derivative modal fraction: 2.37; and
- freezing the mirror derivative gives Q=3.71.
Corrected Q~139 PML gate:
- maximum relative pole-frequency shift:
2.96e-4; - minimum modal overlap:
0.99025; - relative Q span:
0.1765; and - coarse gate: pass.
Corrected Q~162 linewidth gate:
- continued first-order pole Q: 162.4;
- fitted real-frequency linewidth Q: 193.7;
- fit R-squared: 0.99964; and
- gate: not yet passed because Q differs by about 19%.
Artifact discovered and removed
The compact milestone-4 topology produced an apparently excellent Q=24,867 and a matching real-frequency line. A new PML perturbation test showed that the pole was absorber dependent. The causes were a design/PML overlap and an asymmetric material mask caused by exact floating-point comparisons. The default transverse domain is now larger, every material/PML interface has a cladding buffer, and mask/source reflection symmetry is regression tested.
The artifact is scientifically useful: even pole/linewidth agreement can validate the same nonphysical discretized PML mode. PML invariance must be an independent gate.
Decision
The 3D optimizer architecture is ready for continued research development, but not for a full-resolution fabrication run. The next blocking item is a higher-order rational continuation (or equivalent multi-pole real-axis model) of the frequency-dependent mirror boundary. After that, the same candidate should be enlarged and grid/PML converged before adding waveguide beta factor and fabrication robustness.