# XYZ-symmetric y-atom SiN temporal-to-pole campaign

Date: 2026-08-31  
Campaign: `sin300_xyz_y_atom_hole_12x4_temporal_qv_v1`

## Purpose

This campaign transfers atom-centered temporal discovery to an even,
two-sided cavity and then optimizes reciprocal guided Purcell enhancement.
Three physical
mirror planes reduce a full 12 um by 4 um design to one 6 um by 2 um in-plane
quadrant. The atom is y polarized, so the retained bright channel is the
fundamental TE-like waveguide mode.

## Immutable physical contract

- Vacuum discovery wavelength: 780 nm.
- Material: nondispersive SiN with index 2 in air.
- Slab: 300 nm thick.
- Full design region: 12 um along x and 4 um along y.
- Atom: at the origin, polarized along y.
- Opening: a through-slab air disk of diameter at least 1 um. Every 50 nm
  square intersecting the exact radius-0.5 um disk is fixed to air.
- Ports: a 500 nm-wide x-directed SiN feedthrough on both sides. The retained
  +x source has amplitude `1/sqrt(2)`; x unfolding supplies its coherent
  counterpropagating partner, giving unit total incident power.
- Symmetry: x magnetic, y electric, and z magnetic mirror planes,
  `symmetry=(1,-1,1)`. Reduced energy is multiplied by eight.
- Parameterization: 4,800 stored direct 50 nm pixels before the hard aperture,
  outer-air guard, and exact port pin are removed. There is no filter,
  projection, binarization, periodic template, or density penalty.
- Initialization: density 0.5 on trainable pixels, zero in fixed air, and one
  in the pinned waveguide attachment.

The non-PML interior is 13.1 um by 4.5 um by 1.5 um. Ten 50 nm PML cells are
added per full-domain face. The 0.60 um air distance from either slab surface
to z PML is retained from the same-material one-sided campaign's explicit
padding audit, where increasing that distance to 1.55 um changed temporal
residual by 0.000075% and field Q by -0.00497%. Full xyz symmetry makes this
longer design's reduced Maxwell grid smaller than the prior 8 um square run.

## Stage A: absolute temporal discovery

Let `s_k` be the analytically delayed complex Gaussian bright-channel field at
the atom. The exact discrete normalized target pole is

\[
 a_{k+1}=e^{-(\gamma+i\omega_0)\Delta t}a_k
          +(1-e^{-\gamma\Delta t})s_k,
 \qquad \gamma=\frac{\omega_0}{2Q_t}.
\]

The target uses `Q_t=10,000`, beta one, `V_t=0.1 um^3`, and y-polarized unit
overlap. Its Purcell factor is

\[
 F_t=\frac{3}{4\pi^2}\lambda_0^3\frac{Q_t}{V_t}.
\]

The fixed trace is the prompt bright mode plus `sqrt(beta F_t)` times the
causal pole coordinate. It is never rescaled to fit the simulation. The sole
discovery objective is

\[
 J_t=-\frac{\sum_k\|\mathbf E(\mathbf r_a,t_k)-\hat y E_{t,k}\|^2}
              {\sum_k|E_{t,k}|^2}.
\]

Raw Adam uses learning rate 0.01 with persistent first and second moments.
One 2 ps forward/adjoint pair is one applied update; there is no line search or
rejected Adam step. Stage A runs for at least 150 applied updates. Handoff also
requires a valid pole, field/energy Q agreement within 25%, and conservative Q
at least 100. In short, the handoff requires Q at least 100; the iteration
clock alone is insufficient.

For this exact live branch, the operator observed saturation and explicitly
authorized an early handoff at applied update 130. A fresh replay passed all
pole gates before the stage changed; the ordinary automatic gate remains 150
for a new campaign.

## Pole, Q, and atom-volume telemetry

After the pulse clears, Ey at the atom is fitted twice, recentering the second
fit on the first. Total electromagnetic energy is fitted independently at the
same pole frequency. Trusted Q is `min(Q_E,Q_U)`. The same three source-off
windows define

\[
 V_{\rm eff}=\frac{8\langle U_{\rm reduced}\rangle}
                   {\epsilon_{\rm air}\langle|E_y(\mathbf r_a)|^2\rangle},
 \qquad
 \widetilde V=V_{\rm eff}/\lambda_{\rm pole}^3.
\]

The local permittivity is exactly one because the aperture is immutable.
Outgoing overlap at the retained port is telemetry, not a physical beta
measurement. The x-y field monitor covers the design plane. The x-z field
monitor covers the complete simulation volume, including the vertical air and
PML, and is rendered with equal physical x/z scale so radiation leakage and
boundary proximity are not visually compressed.

## Failed direct-Q/V ablation

The first Stage-B controller directly maximized
`log(Q_harmonic/V_atom)`. It was stopped after 60 accepted updates because it
selected a weakly excited dark mode: Q reached 21,675 while normalized V rose
from 6.60 to 31.77 and the absolute atom response collapsed. Pure eigenmode
Q/V cancels the excitation amplitude and therefore does not contain the
waveguide/cavity coupling required by this device. That branch is preserved as
a negative ablation and is never a restart seed.

## Stage B: reciprocal guided Purcell

At handoff, the exact density is retained, coordinate-specific curvature is
reset, and the source is recentered on the measured pole. Let the fitted
single-pole atom field after the pulse be

\[
 E_y(\mathbf r_a,t)=\Re\{A_a e^{(i\omega_p-\gamma)t}\}.
\]

The three translated Hann-window amplitudes are envelope-corrected and
translated back to the same source-off time before averaging. The known
sampled source spectrum at the fitted pole, `S_in(omega_p)`, is divided out.
With a fixed reference decay rate used only to make the value dimensionless,
the single differentiated scalar is

\[
 J_{\rm guided}=\log\left[
 \frac{|A_a|^2}{|S_{\rm in}(\omega_p)|^2}
 \left(\frac{\gamma_{\rm ref}}{\gamma}\right)^2
 \right].
\]

Temporal coupled-mode theory gives

\[
 |A_a|^2\propto |S_{\rm in}|^2\,\kappa_{\rm wg}/V_a,
 \qquad \gamma=\kappa/2,
\]

so this objective is proportional to
`log(beta_wg Q/V_atom)`: the useful Purcell enhancement into the symmetric
bright waveguide channel. It retains atom position, y polarization, absolute
waveguide/cavity coupling, and cavity lifetime in one scalar. There is no
fitted target amplitude, Q/V weight, frozen V ceiling, or volume-gradient
projection. One forward/reverse pair differentiates the complete reciprocal
transfer. The three-window mode-volume spread must remain below 25%, and the
field/energy Q estimates must agree within 25%; these are fail-closed
measurement-consistency gates rather than objective weights.

Ten-pair L-BFGS-B proposes a raw-density direction. A replay is accepted only
for a trustworthy pole, strict reciprocal guided-Purcell gain, and
actual/predicted trust agreement. Rejected radii reuse the cached gradient and
require only a forward replay. Frequency is tracked rather than constrained.
Stage B runs
indefinitely, including after Q=100,000, until explicitly paused. In short,
the controller runs indefinitely.

## Deliberate omissions

There is no Q-dependent cap, temporal minibatching, fitted target amplitude,
source optimization, binarization, or boundary stage. Q/V remains telemetry;
the optimized scalar is the source-normalized reciprocal guided-Purcell proxy,
with no tunable tradeoff coefficient. Binarization and smooth-boundary work
are separate audited continuations.