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Historical derivation — preserved in full

Source: design23_autonomous_optimizer_v1.0.0/design23_autonomous_optimizer/multilayer_nanobeam_phase1/README.md
Snapshot: design23-v1.0.0. The body below is unabridged.

Multilayer nanobeam track — Phase 1

This directory starts a separate analytical track for the supplied Si3N4 Majumdar cavity with substrate, 200 nm anthracene, and 200 nm PVA. It does not modify the confirmed Quan implementation.

Implemented:

  • exact reconstruction of the 50-hole FDTD benchmark and its actual ellipse axes;
  • the Q = 5793.918446, wavelength = 780.443613 nm benchmark record;
  • exact generalized TE/TM reflection of the planar material stack;
  • reciprocal vertical scalar Green kernels retaining film poles;
  • complex-step film-thickness sensitivities;
  • an x/y-only symmetry projector that retains both z parities.

Not yet claimed:

  • a full vector dyadic layered Green tensor;
  • the asymmetric Si3N4 strip guided mode;
  • a multilayer cavity Q, mode volume, or feed-coupling prediction;
  • geometry gradients of those final observables.

Run the dependency-light checks and write the audit result with:

python -m unittest multilayer_nanobeam_phase1/test_phase1.py -v
python multilayer_nanobeam_phase1/run_phase1_benchmark.py \
  --output multilayer_nanobeam_phase1/RESULTS_PHASE1.json

The next phase is the mixed-representation TE/TM dyadic Green tensor \(G(\beta,q_y;z,z')\), projected onto an asymmetric cross-section basis. Once that uniform-waveguide operator converges, the existing longitudinal pole, QNM-residue, implicit differentiation, and constrained optimizer layers can be reconnected above it.