# Data-derived 16 um moving-pole Q campaign

Date: 2026-08-30  
Campaign: `symmetric_moving_pole_q_16um_v3`

## Hypothesis

The 8 um moving-pole campaign formed a visibly periodic one-dimensional
photonic-crystal cavity but approached a box-constrained regime: most density
coordinates were near material endpoints and most raw gradient power pointed
through active [0,1] bounds. This fork tests one controlled physical
hypothesis: the optimized mirror may simply be too short to suppress leakage.

The full design length is doubled from 8 um to 16 um while the 1 um transverse
width, 25 nm pixels, material stack, x/y/z symmetry, central dipole monitor,
moving-pole objective, and adaptive trust-region L-BFGS controller remain
unchanged. The positive simulation octant therefore grows from 160x20 to
320x20 trainable density coordinates. The source moves from x=4.25 um to
x=8.25 um and remains outside the design region.

## Immutable parent

The parent is
`invdes_fryett_symmetric_moving_pole_q_v2.pre_16um_extension_20260830.npz`.
It is an atomic copy of accepted update 103, before the original worker was
stopped. The child never overwrites or resumes that artifact. All L-BFGS
curvature is reset because the coordinate dimension changes.

## Inferring the outer mirror

Let \(\rho(x_i,y_j)\) be the parent positive-quadrant density and

\[
p_i=\frac{1}{N_y}\sum_j\rho(x_i,y_j).
\]

The longitudinal profile is convolved with the symmetric kernel
\((1,2,3,2,1)/9\). Connected intervals above 0.5 identify solid-cell centers.
The last six x rows are excluded before detection so the cell clipped by the
old design boundary cannot enter the estimate. The last five complete centers
\(c_k\) are fitted to

\[
c_k=c_0+kP
\]

by least squares. The fit must give \(8\le P\le14\) grid cells and every center
must lie within 0.75 cell of the translation model, otherwise the fork fails.

For phase \(s\in[-P/2,P/2)\), each of the five two-dimensional cells is
linearly sampled at \(c_k+s\). Their pointwise median defines the repeated
cell

\[
T(s,y)=\operatorname{median}_k\rho(c_k+s,y).
\]

Thus the extension uses the complete optimized two-dimensional cell, not a
one-dimensional duty-cycle fit. Median registration rejects a locally
imperfect cell without inventing a new mirror geometry.

The parent is copied through the midpoint between its last fitted center and
the next predicted center, which lies in the low-density part of the cell.
From that splice to x=8 um, the seed is

\[
\rho_{16}(x,y)=T\!\left(\operatorname{mod}(x-c_{\rm last}+P/2,P)-P/2,y\right).
\]

The artifact stores the inferred period, five centers, center-fit residuals,
registered adjacent-cell MSE values, splice coordinate, original 8 um density,
and complete extended seed.

## Baseline qualification

Before any adjoint update, the exact 16 um seed receives a fresh forward FDTD
replay. Field-amplitude and total-energy pole fits must both pass their
residual/window checks and agree within 25%. If the added mirrors move the pole
by one 1 THz source bandwidth, the source and fit center are rebuilt at the
measured pole and replayed, for at most three recenters. Failure leaves no
child artifact. The independently evaluated seed Q, wavelength, mode volume,
fields, trace, and source center become update zero.

## Optimization

The sole differentiated scalar remains

\[
J(\epsilon)=\log\left(\frac{2Q_EQ_U}{Q_E+Q_U}\right),
\qquad Q_{\rm trusted}=\min(Q_E,Q_U).
\]

Frequency is telemetry, not a constraint. The source follows the accepted pole
after one bandwidth of drift. Direct unfiltered 25 nm pixels remain bounded in
[0,1]; there is no projection, binarization, spatial filter, mode-volume term,
or beta term. Projected L-BFGS starts at a 0.01 raw-density trust radius and
adapts by measured/predicted objective agreement exactly as in the 8 um parent.
The persistent worker continues after Q=100,000 until explicitly stopped.