Coupling Single Giant Nanocrystal Quantum Dots to the Fundamental Mode of Patch Nanoantennas through Fringe Field

Through single dot spectroscopy and numerical simulation studies, we demonstrate that the fundamental mode of gold patch nanoantennas have fringe-field resonance capable of enhancing the nano-emitters coupled around the edge of the patch antenna. This fringe-field coupling is used to enhance the radiative rates of core/thick-shell nanocrystal quantum dots (g-NQDs) that cannot be embedded into the ultra-thin dielectric gap of patch nanoantennas due to their large sizes. We attain 14 and 3 times enhancements in single exciton radiative decay rate and bi-exciton emission efficiencies of g-NQDs respectively, with no detectable metal quenching. Our numerical studies confirmed our experimental results and further reveal that patch nanoantennas can provide strong emission enhancement for dipoles lying not only in radial direction of the circular patches but also in the direction normal to the antennas surface. This provides a distinct advantage over the parallel gap-bar antennas that can provide enhancement only for the dipoles oriented across the gap.

| (a) SEM image of the fabricated single g-NQD-gap bar nanoantenna coupled structure utilizing two-step e-beam lithography; (b) The simulated emission enhancement spectrum for this g-NQD positioned inside a 50 nm antenna gap. The peak wavelength of the enhancement spectrum is 650 nm, which coincides with the emission band of the CdSe/CdS/SiO 2 g-NQD.
The fabricated gap bar nanoantennas have a 140-nm bar width, 900-nm bar length, and 45-nm thickness. The gap between the two bars is approximately 50 nm. The same geometric parameters are used to perform the simulation. The calculated local field enhancement is for light normal incident on the patch nanoantennas. In the simulation, an E-field probe was placed 20 nm away from the patches and 20 nm above the Au ground since the radius of the g-NQDs is about 20 nm.

S3. Simulated local field enhancement around the 405-nm laser excitation wavelength.
Figure S3 | The simulated local field enhancement for patch nanoantennas with 100-nm patches (blue) and 142-nm patches (red) with ~405-nm wavelength (the laser excitation wavelength).

S4. Poissonian distribution model for the pump-power dependent PL intensity.
Figure S4 | (a) and (b) measured (red) and fitted (blue) PL intensity of single g-NQDs as the function of laser pump power. While (a) corresponds to one single g-NQD placed on the 104 nm patch nanoantenna, (b) corresponds to one single g-NQD placed on glass for reference. The fit to the measured saturation was performed for the data points in the top 5% of intensity since those data in all likelihood are the emissions from neutral excitons having near-unity quantum yield.
Upon photoexcitation with a laser pulse, one NQD can absorb N photons and form an N-excitons state with N obeying the Poisson distribution, i.e., Here, 〈N〉 is the average NQD occupancy per excitation pulse, depending on the absorption cross-section of g-NQDs (), laser power w, laser repetition rate R, excitation spot area D and photon energy E ph .
The PL intensity from this NQD can then be modeled as Here, C is a constant mainly representing the photon collection efficiency of the measurement system. Q mX is the quantum yield of m-exciton state and can be calculated from Q 2X : Equations S1, S2, S3, and S4 together allow us to model the PL saturation behavior of single g-NQDs in terms of the bi-exciton quantum yields 4 and the proportionality constant A that provide a direct measure of , absorption cross-section.
The PL intensity (red circles) as the function of laser pump power are shown in Figure S4 (a) and (b), with (a) representing one g-NQD placed on the 104-nm patch nanoantennas and (b) representing a reference g-NQD placed on glass substrate. While the reference g-NQD shows an apparent emission saturation behavior, the emission of g-NQDs on antennas maintains a rapid increase with the increasing pump power due to its large bi-exciton quantum yield. The fitting to the pump dependent PL (blue curves) in Figure S4 (a) and (b) gives exactly the same value of A (i.e., 9.5), which indicates that g-NQDs on glass and on antennas have the same absorption cross sections and thus the same local excitation power. Consequently, the enhanced radiative decay rate and bi-excitation quantum yield observed for g-NQDs-antenna-coupled structures should be attributable to the emission-band coupling instead of the excitation enhancement.

S5. Derivation of the dispersion curve of patch nanoantennas.
Figure S5 | Schematic of the studied air-Au patch-dielectric space-Au ground structure.
The surface plasmons can only be excited by a TM wave so we can set the direction of the magnetic field as the ydirection. Then, only H y , E x , and E z components exist in the studied structure, and they satisfy the following: Here, the phase factor can be ignored in the analysis. Considering the continuation of the tangential component of electric and magnetic fields, we only need to discuss and .

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At z=0, we have the boundary condition: By solving boundary condition equations, i.e. S10, S11 and S12, we can obtain the dispersion relation as mentioned in the main manuscript: