Feedthrough coupling¶
Decay into a guided channel¶
For a cavity eigenmode, define the outward power in the continued fundamental feedthrough mode on both sides as (P_\mathrm{TE0}). Then
For a mirror-symmetric cavity, one port can be doubled only after confirming the field parity and identical normalization.
Analytical channel extraction¶
The outgoing background Green function contains guided poles and a radiation continuum. The analytical model continues the intended guided pole to the cavity's complex frequency, projects the QNM residue onto its power-normalized left/right port functionals, and sums outward amplitudes. Feed-pole subtraction must be consistent with the contour used in the complete cavity determinant; otherwise the same channel can be omitted or counted twice.
FDTD mode decomposition¶
A mode monitor in a straight, uniform port expands the cavity field into local waveguide modes. Select the fundamental outgoing Ey-like branch using effective index, polarization, direction, and continuation—not a fixed array index. Record incoming contamination and mode-power closure.
The port decomposition and total closed-surface flux must use the same fitted cavity pole and the same source-free apodization window. For an exactly mirror-symmetric cavity, a measured one-port TE0 fraction may be applied to both independently measured x-face powers. Asymmetric cavities require explicit mode decomposition at both ports.
Trust requires the direct power ratio to agree with the independent \(Q_\mathrm{total}/Q_\mathrm{TE0}\) construction. It also requires signed six-face loss closure, inner/outer flux-box agreement, low incoming modal power, modal closure against the x-face flux, and mesh/time-window convergence. The quantitative gates and current Design23 evidence are documented in FDTD verification.
What beta is not¶
Eigenmode decay fraction is not transmission, reflection, extinction, or the fraction of an incident field captured by the cavity. Those require a driven port source, reference normalization, and an S-parameter/coupled-mode recipe. Keeping these experiment types separate prevents a common but serious metric substitution.
It is also not automatically an emitter's total spontaneous-emission beta. That interpretation requires a single-pole emitter model and separate accounting for direct/background emission.