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GME-1D paper workbench

Public working draft. Historical performance values are provisional. This authoring surface is accessible without a login but remains excluded from search indexing; it is not a reviewer or public data release.

This repository turns the successful Quan–Lončar and Design23 optimization lineages into one auditable paper: a differentiable outgoing mode expansion, tested in two materially distinct nanobeam cavities and qualified independently with FDTD.

Read the current PDFs Open the publication outline Review claim status Read the method in sequence

Current state

Main draft

Complete 11-page two-column manuscript: the operator construction, the closed-form geometry gradient, both devices, and the direction-versus- magnitude transfer result, with every quoted number carrying its ringdown condition.

Supplement

Nineteen sections, 37 pages, self-contained. Theory rewritten in one notation from Maxwell to the optimizer; evidence including the full trajectory table, the audited legacy-value table, and a catalogue of rejected approaches.

Evidence

Exact historical endpoints, the 105-step Design23 history, a ringdown audit of all 35 retained FDTD observations, endpoint geometry metrics, and 69 external raw artifacts indexed by SHA-256.

Two drafts

A — two devices, one operator (manuscript/): the method paper, 11 pages plus a 37-page supplement.

B — one device, in full (manuscript-quan/): a separate, narrower draft giving the simplest complete account of a single optimization — the Quan–Lončar campaign, 45 variables, 56 accepted steps, field profiles before and after, quality factor against iteration, and an independent solver holding a veto outside the loop. It draws on the 56-step indefinite campaign rather than the 3-step Phase-58 endpoint that paper A quotes, so the two sets of numbers are not interchangeable.

The paper in one sentence

A reduced analytical expansion of guided, aperture, and radiation-continuum modes can be differentiated through its outgoing complex pole and proposes large-Q cavity improvements that transfer to independent FDTD as directions even though its absolute linewidth drifts by more than an order of magnitude along the very trajectory it is driving.

The number that matters

Along one Design23 trajectory the ratio \(Q_\text{ana}/Q_\text{FDTD}\) runs from 0.472 (under-prediction) to 12.31 (over-prediction) — a drift of 27.5× — while the rank correlation between the two observables within a fixed FDTD protocol is 0.911 over 23 observations. Ordering transfers; values do not. Per- step sign agreement is 19/31 (p = 0.28) and is explicitly not claimed.

Hard gates

  • No FDTD job is submitted by a build or website command.
  • Final device gains require the predeclared matched endpoint panels.
  • Design23 uses the exact step-0/step-105 pure-BFGS lineage; the unrelated \(Q=20{,}942.06\) seed cannot replace its initial endpoint.
  • The working site is published through the approved public /gme-1d/ route.
  • Three of the four quoted endpoints were fitted over less than one photon lifetime; the predeclared Quan panel axis is itself under one lifetime at the optimized endpoint and must be extended before promotion.
  • No number is typed into the LaTeX: 193 macros and 6 tables are generated from JSON, and the test suite pins them.
  • Public code/data and reviewer packages are intentionally deferred until the manuscript and final evidence are settled.