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engines/majumdar_lab/package/multilayer_autonomous_optimizer/fryett_q_series_phase3/STATUS_PHASE3.md · assembled 2026-07-29 15:57 UTC.

Phase 3 status

Completed

  • Complex-frequency Dyson waveguide Green matrix with no nonanalytic Hermitian symmetrization.
  • A dimensionless outgoing Sommerfeld contour scaled by complex k_cladding(omega).
  • A scalar pole benchmark that fixes the contour orientation and residue sign.
  • Exact x and z integration for normalized constant vector modes in each elliptical hole.
  • Analytic C(-beta)^T G(beta) C(beta) projection.
  • Assembly of the first finite, geometry-dependent cavity operator and determinant diagnostics.
  • A condition-aware simple-pole refiner and the exact conversion from its complex frequency to Q.

Deliberately not claimed

  • The lowest constant-hole truncation is not a converged Maxwell solution.
  • No numerical root from it is identified with the paper's Q near 100,000.
  • The earlier paper/code geometry ambiguity remains pinned, as requested.
  • FDTD verification remains pinned, as requested.

Immediate next step

Add higher Zernike--Legendre modes inside every ellipse, derive their analytic or spectrally convergent overlap with the rectangular-waveguide basis, and run the first joint convergence table in:

  1. hole-basis degree,
  2. waveguide-basis degree,
  3. transverse momentum cutoff/order,
  4. beta-contour order/deformation, and
  5. number of mirror holes.

Only after a single lower-half-plane pole can be tracked through that table should its Q be compared with Fryett et al.