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engines/design23_v1/package/design23_recentered_optimizer/fryett_q_series_phase1/README.md · assembled 2026-07-29 15:57 UTC.

Fryett cavity Q series — phase 1

This is the first rigorous layer of a project to represent the radiative quality factor of the Fryett et al. encapsulated SiN nanobeam cavity as a convergent function of its geometry.

The central result is not a fitted Q formula. It is the pole equation

\[ D_N(\omega,\mathbf p) = \det\!\left[I-K_N(\omega,\mathbf p)\right]=0, \qquad Q_N(\mathbf p) =-\frac{\Re\omega_N}{2\Im\omega_N}, \]

where N indexes a complete basis on the finite collection of holes and the outgoing bare-waveguide Green operator includes guided, evanescent, and radiation channels. The intended exact result is the limit N -> infinity together with convergence of the radiation-continuum quadrature.

Files:

  • DERIVATION.md derives the operator, series, geometry dependence, and pole gradients.
  • fryett_series.py implements the exact Fourier transform of every elliptical hole, its geometry derivatives, the retained legacy geometry reconstruction, and the finite-dimensional pole algebra.
  • tests/test_phase1.py tests the analytical geometry factors and pole identities.

The original paper reports a simulated Q ~ 100,000, resonance near 740 nm, and mode volume near 2.5 (lambda/n)^3. The paper text and the prior project reconstruction do not uniquely specify the same finite geometry. That issue is documented rather than silently resolved in DERIVATION.md.

Run the tests with:

python -m pytest -q

This phase deliberately stops before supplying a numerical bare-waveguide Green tensor. Without that tensor and its converged radiation continuum, a numerical high-Q value would not be trustworthy.