Appendix 2—figure 5. Z-profiles of the radiative (emission) and non-radiative (loss) rates in the proximity of the freestanding zero-mode waveguide (ZMW) obtained from finite-difference time-domain (FDTD) simulations for the blue (A, ${\displaystyle {\lambda }_{ex}=}$ 488 nm, ${\displaystyle {\lambda }_{em}=}$ 525 nm) and red (B, ${\displaystyle {\lambda }_{ex}=}$ 640 nm, ${\displaystyle {\lambda }_{em}=}$ 670 nm) channels.

The position of the palladium membrane is indicated as a gray shaded area. The z-axis is defined as in Appendix 2—figure 4A. For the radiative rate (bottom), the rate of emission directed toward the objective lens is displayed in addition as a dashed line. The normalized loss rate ${\displaystyle {\gamma }_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}/{\gamma }_r^0}$ and radiative emission rate ${\displaystyle {\gamma }_r/{\gamma }_r^0}$ are obtained by measuring the total power emitted by the dipole and comparing it to the power that is emitted into the far field, that is, not absorbed by the metal. From these rates, the quantum yield ${\displaystyle \mathrm{\Phi }}$ and fluorescence lifetime ${\displaystyle \tau }$ are computed according to Equations 8 and 10. The ratio of the total emission rate and the rate of the detected emission (solid and dashes lines) is used to compute the detection efficiency ${\displaystyle \eta }$ as given in Equation 11. See ‘Materials and methods’ for details.