Conventions

All derivations and records use SI internally unless a variable explicitly carries nm, um, or another unit in its name. Geometry vectors store a unit beside every coordinate.

Time and pole convention

Fields vary as

\[ \mathbf E(\mathbf r,t)=\Re\{\mathbf E(\mathbf r,\omega)e^{-i\omega t}\}. \]

An outgoing passive quasinormal mode has

\[ \tilde\omega=\omega_r-i\gamma,\qquad \omega_r>0,\;\gamma>0. \]

Thus (Q=-\operatorname{Re}\tilde\omega / (2\operatorname{Im}\tilde\omega)). Any solver returning an upper-half-plane pole must be rejected or explicitly identified as using the opposite time convention.

Coordinates and polarization

For current nanobeams, x is the beam/feedthrough axis, y is the in-plane transverse direction, and z is vertical. The target branch is predominantly Ey-like. This convention is device metadata, not a global assumption for future rings, bullseyes, metasurfaces, or three-dimensional cavities.

Open-system quantities

Quasinormal-mode fields are not square-integrable under the ordinary Hermitian inner product. Analytical normalization therefore uses the residue/left-right eigenvector convention documented by the device engine. FDTD mode volume uses finite-domain dispersive energy and radiated-power diagnostics. The two are comparable observables only after their emitter point, orientation, material index, wavelength normalization, and field convention are matched.

Branch identity

A wavelength window is necessary but not sufficient. A branch record includes parity or symmetry label, polarization, continuation seed, eigenvector overlap, passivity, nonlinear residual, and—where useful—spatial field fingerprints.