Observable conventions

This short site page prevents the derivation archive from relying on implicit definitions. The complete retained source discussions live in derivations/quality-factor.md, mode-volume.md, and coupling.md.

Quality factor

With time dependence \(e^{-i\omega t}\), a passive outgoing pole has \(\tilde\omega=\omega_0-i\gamma\), \(\gamma>0\), and \(Q=\omega_0/(2\gamma)\). Analytical pole Q and independently fitted FDTD Q are distinct observables even when they refer to the same intended mode.

Mode volume

Mode volume must name the energy/QNM normalization, evaluation position and orientation, dispersive convention, and refractive index used to express \(V/(\lambda/n)^3\). It is not inferred from field-image brightness.

Feedthrough coupling

Coupling metrics must identify the driven port or guided mode, spectral normalization, direction, and whether the quantity is amplitude, power, or a rate. In the layered operator the desired guided feed pole is subtracted from the radiation continuum before the finite cavity is assembled.