# No-slot atom-hole waveguide inverse design

<div class="status-banner"><strong>RUNNING BINARY BETA</strong> · campaign <code>hole_square_v1</code> · updated 2026-08-23T12:03:04+00:00</div>

This is the live checkpoint for a z-oriented atom in a hard 1 µm-diameter central air hole. A 7.5 × 7.5 µm free-form silicon mask is extruded through a 500 nm slab and attaches only to one 400 nm right-hand waveguide. There is no atom-access slot and no left waveguide. The y and z mirror planes reduce the solve by four; x is simulated explicitly.

| Quantity | Current value |
|---|---:|
| Ordinary beta adjoint updates | 550 / ∞ |
| Guided branching ratio βwg | 81.47% into the single right-hand guide |
| Rejected nonphysical beta samples | 44 |
| Latest raw modal-power excess | 0.00% |
| Total normalized LDOS | 0.3775 |
| Guided normalized LDOS | 0.3075 |
| Atom-frequency coherent retention | pending |
| Late-window atom-frequency coherence | pending |
| Gray material fraction | 0.00% |
| Projection stage | 7 / 7 |
| Campaign phase | binary beta and pole search |
| Latest audited/ringdown Q | 21.31 |
| Latest pole detuning | 4.125% |
| Latest pole-fit residual | 13.946% |
| Purcell factor | pending |
| Guided Purcell βwg FP | pending |

![Literal geometry and routing objective](../_static/generated/atom_hole_waveguide_geometry.png)

![Optimization history](../_static/generated/atom_hole_waveguide_progress.png)

![Current electric field](../_static/generated/atom_hole_waveguide_field.png)


## What is being optimized now

The objective is the passive, energy-bounded right-waveguide branching ratio; there is no LDOS guard rail. A separate penalty rejects any modal/closed-surface power mismatch that would imply beta above 100%. Projection sharpness first follows a finite 90-update schedule; the optimizer then remains exactly binary and continues beta updates in 20-step blocks. A fresh 4 ps broadband audit after every block controls the handoff—neither iteration count nor a noisy instantaneous Q can activate shifting.

The state machine is deliberately simple: beta optimization and binarization → perpetual exact-binary beta with independent pole audits → unbounded shifted-LDOS optimization. A clean Q≈100 pole is required before shifting, and no stage may reintroduce gray material after binarization.