---
title: Symmetric dipole-waveform MSE optimizer
---

# Symmetric dipole-waveform MSE optimizer

**Status:** `running_symmetric_dipole_waveform_mse_adam` · **Adam steps:** 273 ·
**vector MSE:** 0.0811058 ·
**fidelity:** 0.924979

This is the corrected x/y/z-symmetric two-port experiment. The sole objective
is the normalized squared error between the fixed ideal vector field at the
central y dipole and the simulated 2 ps waveform. Q, V, wavelength, and field
images are telemetry only. Physical beta is not measured in this scene.

| quantity | current | target |
|---|---:|---:|
| pole status | **trusted** | trustworthy fit |
| Q | 605.66 | 10,000 |
| wavelength | 779.972 nm | 780 nm |
| normalized mode volume, fixed target n=1.75512 | 2.29915 (λ/n)³ | 1.1393 (λ/n)³ |
| local-index-corrected normalized volume, current n=1.77697 | 2.32777 (λ/n)³ | — |
| physical mode volume, local-index corrected | 0.196851 µm³ | 0.1 µm³ |
| physical beta | **not measured** | requires guided-port and total-loss flux |
| fixed tape | 2.0 ps | — |
| learning rate | 0.01 | — |
| reduced grid | 194×42×42 | x/y/z symmetry |
| density variables | 3,200 | direct 25 nm pixels |

The Q and wavelength are direct single-pole fits. Mode volume comes from the
symmetry-restored stored energy divided by the central field; its history uses
the explicitly fixed target index, while the table also corrects the latest
point using the dielectric currently occupying the dipole cell.

No beta number is plotted. The artifact retains a legacy amplitude-derived
quantity under `inferred_beta_*`, but values far above one prove that it is not
a probability. The present scene has neither guided-port flux monitors nor a
closed loss-flux measurement, so reporting that quantity as beta would be
physically misleading.

The source mode is normalized to unit flux on the retained y/z quadrant. After
transverse unfolding and x reflection, the configured `1/sqrt(2)` amplitude is
four units of total two-port power in that solver convention, not one. This
common linear field scale cancels from the normalized waveform MSE, so it does
not change the material gradient, but it is another reason not to interpret the
amplitude-derived proxy as an absolute beta measurement.

The fixed temporal waveform has the exact discrete Gaussian carrier and the
specified single-pole lifetime, but its sqrt(Purcell) amplitude relative to the
prompt waveguide field is a design normalization. It is not an independently
calibrated temporal coupled-mode solution because the bare guided-mode LDOS and
port-cavity coupling phase are not specified. The normalized objective remains
well-defined, but the target should be read as a prescribed waveform rather
than a uniquely physical optimum.

## Temporal objective

![Dipole response](../_static/generated/fryett_symmetric_dipole_mse_response.png)

## Physical telemetry

![Q, V, wavelength, and MSE](../_static/generated/fryett_symmetric_dipole_mse_history.png)

## Geometry and fields

![Initial, evaluated, and difference geometry](../_static/generated/fryett_symmetric_dipole_mse_geometry.png)

![Late 780 nm fields](../_static/generated/fryett_symmetric_dipole_mse_fields.png)

{download}`Complete methodology <../_static/downloads/fryett/PORT_DIPOLE_4D_ADAM_METHOD.md>`

{download}`Normalization audit <../_static/downloads/fryett/PORT_DIPOLE_NORMALIZATION_AUDIT.md>`

{download}`Plateau diagnosis <../_static/downloads/fryett/PORT_DIPOLE_PLATEAU_AUDIT.md>`