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

\[ Q_\mathrm{TE0}=\frac{\omega U}{P_\mathrm{TE0}},\qquad \beta_\mathrm{TE0}=\frac{P_\mathrm{TE0}}{P_\mathrm{all}} =\frac{Q_\mathrm{total}}{Q_\mathrm{TE0}}. \]

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.

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.