Tomographic imaging of the photonic environment of plasmonic nanoparticles

The photonic local density of states (LDOS) governs the enhancement of light–matter interaction at the nanoscale, but despite its importance for nanophotonics and plasmonics experimental local density of states imaging remains extremely challenging. Here we introduce a tomography scheme based on electron microscopy that allows retrieval of the three-dimensional local density of states of plasmonic nanoparticles with nanometre spatial and sub-eV energy resolution. From conventional electron tomography experiments we obtain the three-dimensional morphology of the nanostructure, and use this information to compute an expansion basis for the photonic environment. The expansion coefficients are obtained through solution of an inverse problem using as input electron-energy loss spectroscopy images. We demonstrate the applicability of our scheme for silver nanocuboids and coupled nanodisks, and resolve local density of states enhancements with extreme sub-wavelength dimensions in hot spots located at roughness features or in gaps of coupled nanoparticles.


Supplementary Note 1. Contamination during tilt series acquisition
During acquisition of the tilt series, carbon contamination slowly built up on the samples due to irradiation by the electron beam, causing continuous red-shifts of the resonance energies, in agreement to previous experimental studies [1,2]. Supplementary Fig. 5 shows HAADF STEM images before and after tilt series acquisition highlighting the carbon contamination. Supplementary Fig. 6 shows spectra summed over the full spectrum image (SI) for the nanocuboid sample and for the coupled disks. For each SI the plasmon resonance maps were extracted around the current peak position, i.e. the integration windows were shifted to lower energies for SIs acquired later in the series. While the resonance energies shifted, the modal distribution in the plasmon resonance maps did not change significantly with sample contamination. For each mode resonance maps extracted before, during and after tilt series acquisition are compared in Supplementary Fig. 7. The strongest effect is visible for Mode 1 in the coupled disk sample.
Here the resonance shifts to very low energies, too close to the zero-loss peak to allow extraction of the mode for SIs acquired later in the series. For this reason only the first part of the images was used for reconstruction of this mode.

Supplementary Note 2. Simulation and reprojection of tilted EELS maps
Tilted EELS maps were simulated for the cuboid structure without substrate, see Supplementary

Supplementary Note 3. Estimation of projection quality
The signal to noise ratio (SNR) in the projections can be calculated in analogy to the scheme proposed by Egerton in [3], Eq. (5.23). Assuming Poissonian counting statistics and detector noise the uncertainty associated with the extraction of a weak signal is determined by The detective quantum efficiency (DQE) for the camera used is known from [4] and amounts to 0.3, almost invariant to dose conditions. h is the statistical error describing background subtraction-in our case from the zero-loss peak flanks. For core-loss analysis and the respective cross-sections, h typically lies in the order of 5-10. In the low-loss region we expect a lower h value due to relatively higher signals. I B is the background (zero-loss) intensity and I S is the intensity of the signal after zero-loss removal. For our analysis, both integrals were summed over a range of 0.2 eV, the same value used for the extraction of the EELS maps in the experiment.
We next calculated the SNR for the cuboid sample for the dipolar and quadrupolar modes for projections at 0 • tilt and at −75 • tilt, and conservatively estimated h = 5 ( Supplementary   Fig. 8). For this case the SNR takes on values above 10 and is well beyond the critical threshold of 3 (98% certainty of detection) for all relevant locations. We therefore conclude that the data were of sufficient statistical quality for a reliable reconstruction. An additional observation was that the SNR for electron trajectories outside the particles was even higher, which is explicable with the reduction of the signal due to concurrent scattering events. This effect is present especially at large tilt angles due to the larger effective thicknesses of the sample.
Supplementary Fig. 1: Effect of Richardson-Lucy deconvolution: a,b EELS spectra for cuboid and coupled disks before deconvolution, and c,d after deconvolution. Spectra recorded at same positions as in main text.
Supplementary Fig. 2: Effect of Richardson-Lucy deconvolution on EELS maps for: a nanocuboid and b coupled disks. Sim.
Repr. Supplementary Fig. 3: Comparison between simulated, experimental, and reprojected EELS maps for different tilt angles and for a dipolar mode and b quadrupolar mode of nanocuboide. Data from pixels at black margins around the particles were not used for the reconstruction. Exp.