Historical derivation — preserved in full

Source: design23_autonomous_optimizer_v1.0.0/design23_autonomous_optimizer/multilayer_nanobeam_phase18/README.md
Snapshot: design23-v1.0.0. The body below is unabridged.

Multilayer nanobeam — Phase 18

This phase constructs power-consistent left/right feed functionals from the continued multilayer strip beta pole and evaluates the rank-one QNM residue of the guided two-port scattering matrix. Its leading singular value is the two-port external full linewidth in dimensionless frequency units. Combined with the total pole linewidth it yields Q_external, the remaining-loss Q, and the fraction of cavity decay entering the feed waveguide.

The reported FDTD transmission proxy is retained only as a benchmark hint; it is not assumed to equal the decay fraction.