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engines/design23_v1/package/design23_recentered_optimizer/fryett_q_series_phase2/README.md · assembled 2026-07-29 15:57 UTC.

Fryett cavity Q series — phase 2

This phase constructs the outgoing Green operator of the unperforated Fryett rectangular nanobeam. It is the missing kernel in the phase-1 cavity determinant.

The exact construction is:

  1. Fourier transform along the invariant beam direction x, introducing the longitudinal propagation constant beta.
  2. Represent the homogeneous-cladding Maxwell Green tensor by its exact three-dimensional Fourier symbol.
  3. Solve the compact SiN rectangular cross-section with a vector volume-integral equation.
  4. Invert the beta transform on the outgoing contour. Guided modes are residues of poles; radiation and evanescent fields are the branch continuum.

waveguide_green.py implements the exact Fourier symbol, a complete Legendre-Galerkin cross-section basis, the Dyson-resummed waveguide Green matrix, guided-pole location, pole residues, and an explicit contour quadrature interface.

The current executable sector is beta > k_cladding, where guided poles can be found without crossing the radiation shell. The outgoing branch-contour deformation at complex frequency is derived in DERIVATION_PHASE2.md and is the next implementation target.