Appendix 2—figure 4. Finite-difference time-domain simulations of the dipole emission in the proximity of the freestanding zero-mode waveguide (ZMW).

(A) A scheme of the simulation setup. The dipole is placed in the center of the pore in the xy plane at varying z-positions. The detected signal is monitored on the detection (i.e., lower) side. (B, C) From top to bottom: the z-profiles of the excitation probability, the detection efficiency ${\displaystyle \eta }$, the emitter quantum yield ${\displaystyle \mathrm{\Phi }}$, and the total detected signal along the center of the nanopore are shown for the blue (B, ${\displaystyle {\lambda }_{ex}=}$ 488 nm, ${\displaystyle {\lambda }_{em}=}$ 525 nm) and red (C, ${\displaystyle {\lambda }_{ex}=}$ 640 nm, ${\displaystyle {\lambda }_{em}=}$ 670 nm) channels. The total detected signal ${\displaystyle S(z)}$ is defined as the product of the excitation intensity, detection efficiency, and quantum yield. (D, E) Predicted fluorescence lifetimes ${\displaystyle \tau }$ of BSA–Alexa488 and Kap95–Alexa647. The position of the palladium membrane is indicated as a gray shaded area. The weighted averages of the fluorescence lifetime based on the detected signal ${\displaystyle S(z)}$, ${\displaystyle {⟨\tau ⟩}_S}$ are shown as colored horizontal dashed lines. The gray dashed line indicates the measured fluorescence lifetime ${\displaystyle {\tau }_0}$ in the absence of the ZMW. The predicted signal-averaged lifetimes ${\displaystyle {⟨\tau ⟩}_S}$ are 1.98 ns, 1.88 ns, and 1.88 ns for BSA–Alexa488, and 1.22 ns, 1.95 ns, and 1.15 ns for Kap95–Alexa647, for pore diameters of 50 nm, 100 nm, and 150 nm, respectively (see Equation 13). The quantum yields and fluorescence lifetimes were estimated based on a literature values of ${\displaystyle {\mathrm{\Phi }}_{\mathrm{l}\mathrm{i}\mathrm{t}}}$ = 0.8 and ${\displaystyle {\tau }_{\mathrm{l}\mathrm{i}\mathrm{t}}}$ = 4.0 ns for Alexa488 (Sanabria et al., 2020), and ${\displaystyle {\mathrm{\Phi }}_{\mathrm{l}\mathrm{i}\mathrm{t}}}$ = 0.33 and ${\displaystyle {\tau }_{\mathrm{l}\mathrm{i}\mathrm{t}}}$ = 1.17 ns for Alexa647 (Hellenkamp et al., 2018), and measured lifetimes in the absence of the ZMW of ${\displaystyle {\tau }_0}$ =2.3 ns for BSA–Alexa488 and ${\displaystyle {\tau }_0}$ = 1.37 ns for Kap95–Alexa647 (compare Appendix 7—figure 1).