Source

engines/quan_loncar_v1/package/quan_loncar_optimizer/engine/quan_loncar_series_phase42/README.md · assembled 2026-07-29 15:57 UTC.

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Phase 42: guided two-port scattering residue

This phase turns the exact guided beta-pole residues into incident-drive and outgoing-amplitude functionals for the left/right fundamental feed waveguide ports. Direct driven solves return a dimensionless 2x2 scattering matrix. At the cavity pole, the same functionals sandwich the rank-one hole resolvent residue to give Res_s S.

Amplitude ratios are independent of the arbitrary electric-field scaling of the guided eigenvectors because each incident mode and its outgoing dual are scaled together. The resulting S matrix must still pass reciprocity and real-frequency guided-power checks before its residue singular value is interpreted as an external decay rate.

test_phase42.py checks the left/right parity matching and reciprocal direct scattering matrix in a compact cavity.

run_phase42_guided_scattering.py validates the QNM scattering residue by complex-frequency direct inversion, checks the real-frequency even scattering eigenchannel and its smooth background, and only then interprets the residue's nonzero singular value as the total external guided decay rate.

Because offset * S(pole + offset) contains the desired residue plus a smooth term linear in the offset, run_phase42_richardson_gate.py combines successive halved offsets as 2 F(h) - F(2h). This cancels the background without any additional Maxwell solve and supplies the final residue-validation gate.