Nanoscopy through a plasmonic nanolens

Significance Imaging of single to a few molecules has received much recent interest. While superresolution microscopies access subdiffraction resolution, they do not work for plasmonic hot spots due to the loss of positional information that results from plasmonic coupling. Here, we show how to reconstruct the spatial locations of molecules within a plasmonic hot spot with 1-nm precision. We use a plasmonic nanoball lens to demonstrate that plasmonic nanocavities can be used simultaneously as a nanoscopic and spectroscopic tool. This work opens up possibilities for studying the behavior of a few to single molecules in plasmonic nanoresonators, while simultaneously tracking their movements and spectral features. Our plasmonic nanolens is useful for nanosensing, nanochemistry, and biofunctional imaging.

obtain the spatial frequency domain image of the field in the focal plane of the objective. In order to account for the numerical aperture of the objective, this result is multiplied by a k-plane mask 1 − tanh + − , where = (2 ⁄ ) sin(50°) and = 0.1 , before taking the inverse Fourier transform to recover the fields at the detection plane (in the spatial domain). The squared norm of these fields then yields the images shown in Fig.1b and supplementary Fig.S3.

1B) FDTD
To confirm the COMSOL results, the CB:MB in NPoM system is also simulated using a finite-difference time-domain Maxwell solver (Lumerical FDTD). The simulation is set up assuming an 80 nm spherical nanoparticle with a 20 nm diameter circular bottom facet. Material data used for the gold is taken from Johnson and Christy, and the CB:MB layer is assumed to have a refractive index of 1.4 and a thickness of 0.9 nm.
Simulations of an 80 nm spherical NPoM with a flat bottom facet of a range of sizes between 0 nm and 34 nm are designed to replicate as closely as possible the system used in the experiments. Dimensions of the particle, particle facet, and gap size are set correspondingly, and complex wavelength-dependent refractive indices are selected to match each material used. To simulate a molecule emitting in the NPoM gap, we use a broad-spectrum vertically-oriented dipole source placed in the plasmonic hot-spot. The same filtering applied to the results of the COMSOL simulations is then applied here in order to obtain the images shown in supplementary Fig.S1.
Fig.S1 | Far-field real-space images (normalized) simulated using FDTD after collection through an 0.9NA objective. The images confirm those obtained using the FEM method (Fig.1b).

Recovering emitter position from dark field and photoluminescence images
The method used to localize a single emitter within the cavity of each NPoM is derived from the results of modelling the NPoM structure numerically. This is done using either the FDTD model produced in Lumerical, or using the FEM model produced in COMSOL. The emitter positions obtained from either model agree to within <1 nm for emitter positions within a radial coordinate <10 nm of the cavity centre. For emitter positions beyond 9 nm of the cavity centre, the emission intensity drops off rapidly for most NPoM geometries (supplementary Fig.S3). The spatial distribution of the emission here begins to resemble that observed at smaller values of (supplementary Fig.S3 =15 nm vs 3 nm) and hence it becomes less possible to unambiguously determine the position of the emitter. However since such highly displaced emitters give very weak light intensities, this has little effect on our results.
The procedure for extracting the position of a single emitter under each NPoM is outlined in supplementary Fig.S2. First, the centre of mass of both the DF and the emission images is computed. The azimuthal coordinate of the emission centre of mass relative to the dark field centre of mass is then compared against an interpolated lookup table of the azimuthal coordinates for different emitter positions, generated from the simulation results. This yields the azimuthal coordinate of the emitter. Then, utilizing the fact that the DF spatial distribution of a NPoM is always ring-like, the overlap integral of the DF and emission is computed, and used as a measure of the degree to which the NPoM emission is ring-like (vs. spot-like). As before, this value is compared against an interpolated lookup table generated from the simulation results. This yields the radial coordinate of the emitter, completing the localization process.

COMSOL simulation of emission profile for various facet sizes
FEM simulations using COMSOL for a large range of facet sizes and emitter positions reveal a consistent drop-off in integrated emission intensity for emitter positions greater than 10 nm away from the centre of the NPoM cavity. Furthermore, the emission profile of a centred emitter is always a ring, and always evolves into a spot at a distance within 3 to 9 nm from centre. For facet sizes greater than 20 nm, there exists a limiting radius to the emitter position beyond which the emission profile reverts from spot to ring (around 12 nm for all facet sizes >20 nm). In all cases this reversion occurs for an emitter position with an integrated intensity <30% of that at the maximally out-coupled position.
The emitter position recovery procedure outlined in Fig.S2 depends on the facet size being known a priori, which can be extracted by suitably fitting the peak positions of the dark field scattering (eg Fig.4e with Fig.2a). From the 3 < < 9 nm region of Fig.S3, we see that, around = 20 nm, changes in facet size of 10 nm result in far-field pattern shifts equivalent to dipole position shifts of at most 2 nm. We can therefore conclude that achieving an accuracy in the recovered emitter position of ±1 nm requires knowledge of the facet size to within ±5 nm, which gives easily measurable peak shifts in the dark field. If a substrate of template stripped gold prepared initially with CB[7] but omitting the MB is used to build NPoMs from 80 nm gold nanoparticles using the usual drop-casting method, no emission is observed in most nanoparticles (supplementary Fig.S7a,c). The few particles in the sample that exhibit some form of weak emission have spot-like spatial distributions (supplementary Fig.S7b). This weak emission is most likely from electronic Raman scattering from the Au nanoparticle and it is 10-20 times weaker than the peak PL emission with dyes in the gap.

Time evolution of NPoM emission profile
An example of the time evolution of the intensity and angular distribution of NPoM emission was given in Fig.4. This evolution is subtly different for different NPoMs, with some exhibiting a greater or lesser number of revivals in emission intensity over time. This can be seen in the following additional examples (supplementary Fig.S8-10):

Simulations of multiple dipoles in a NPoM
Generating the far-field scattering profile for a NPoM hosting two or more molecular emitters within its plasmonic hot spot can be achieved by suitably combining the optical fields in the far-field from different emitters at different locations.

Fig.S12 | Resulting emission from 1,2,3 dipole places at =3 or =9 nm, when coherently summed with phases as marked, or incoherently summed.
Results of a few such combinations (Fig.S12) show how the asymmetric patterns are rapidly wiped out in both coherent and incoherent sums. As a result, it is not possible to uniquely quantify if the emitting multiple dipoles are coherently locked (as in a nanocavity polaritonic state) or independently incoherent.

Preservation of samples under nitrogen
Experiments studying the number of each type of far-field scattering distribution are repeated using two different samples, to explore aging. The second sample gave the same result as the first, revealing no change in the numbers of each type (supplementary Fig.S14, compare with first sample in Fig.3g). The average integrated emission intensity of nanoparticles in this sample are also observed to be stable for the full duration of the experiments. Emission and dark field spectra are likewise observed to be stable in samples stored for more than 12 days (supplementary Fig.S15). The experimental setup can be subdivided into three distinct parts. The first consists of an imaging microscope (Olympus BX51) equipped with a motorized stage (Prior Scientific H101) upon which the NPoM samples are placed. The samples are illuminated and imaged through a 100x bright field/dark field objective (Olympus, numerical aperture of 0.9), with either laser illumination or white light from a halogen lamp. A dark field (DF) cube and circular beam block are used in conjunction with the halogen lamp to illuminate the sample only at high angles for DF imaging. A reflective neutral density filter (Thorlabs ND503A, optical density of 0.3) is used in transmission as a broadband non-polarizing 50:50 beamsplitter. The ND filter directs part of the transmitted light to an imaging charge-coupled camera (Lumenera Infinity3-1) to view the sample, and to a fibre-coupled spectrometer (Ocean Optics QEPRO) for dark field spectroscopy. A cube beamsplitter (60:40 R:T) distributes light between these the imaging camera and the dark field spectrometer. The same reflective ND filter is used in reflection to both guide laser illumination towards the sample, and for directing emission towards the spatio-spectral detection system.

Experimental setup
The second part of the setup is the Raman laser system used to excite the NPoM samples. It consists of an automatically shuttered HeNe laser (Thorlabs HNL210L, emission wavelength at 633 nm) directed through a radial polarization converter (Altechna RPC-632-04 S-waveplate). A computer controlled ND filter wheel is used for power control, a beam expander with a magnification of 10x, and a dichroic beamsplitter used to direct the radially polarized laser towards the main experimental setup, and to direct collected emission towards the final part of the setup.
The spatio-spectral detection system consists of a telescope (magnification 10) formed with two planoconvex lenses. This is followed by a sequence of filters chosen to block the excitation wavelength and limit detection to the desired wavelength range by using a long pass filter (Thorlabs FEL0650, cut-off wavelength at 650 nm) and a short pass filter (Thorlabs FES0750, cut-off wavelength at 750 nm). After magnification and filtering, the remaining light is focused onto the slit of a monochromator (Andor Shamrock SR-303i), where it is directed to an electron-multiplying CCD camera (Andor Newton 970 EMCCD) using either the zero order of the grating monochromator if images are desired, or using the first diffraction order when spectra are desired.
Note: Effect of gap size on emission The CB[7] spacer layer used in the experimental portion of this paper precisely fixes the gap separation to 0.9±0.05 nm.(4) However, similar far field emission images are found theoretically for larger gap sizes. In such a case, the mode energy positions shift (see maps in (5), and Fig.S17), and thus so does the mode mixing. This is very similar to the use of different NP sizes (Fig.3e,f). Despite these changes, the evolution of the emission spatial image as the emitter is moved away from centre remains very similar (a ring is observed for a centred emitter, and emission becomes more spot-like as the emitter is shifted away from centre, as shown in Fig.S18). As a result, dye position reconstruction remains feasible for larger gap sizes.

Note: Mode nomenclature
In this article, the QNMs of the NPoM are labelled in order of increasing energy as = 10, 11, 20, 21, 22, 30, 31, 32, 33… where and are indices analogous to those of the spherical harmonics ( , ) (see for example (6)). This nomenclature was chosen as it closely reflects the distribution of charge on the surface of a NPoM for each mode. Note the = 00 mode is intentionally left out as it represents the case of the NPoM accumulating or dissipating charge, which is not possible to excite for a NPoM on an electrically insulating spacer layer such as the CB:MB layers used here. Modes with even radiate into a ring-shaped far-field spatial distribution, whereas modes with odd radiate into spot-shaped far-field spatial distributions.