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The remarkable optical properties of metal nanoparticles are governed by the excitation of localized surface plasmon resonances (LSPRs). The sensitivity of each LSPR mode, whose spatial

distribution and resonant energy depend on the nanoparticle structure, composition and environment, has given rise to many potential photonic, optoelectronic, catalytic, photovoltaic, and

gas- and bio-sensing applications1,2,3. However, the precise interplay between the three-dimensional (3D) nanoparticle structure and the LSPRs is not always fully understood and a spectrally

sensitive 3D imaging technique is needed to visualize the excitation on the nanometre scale. Here we show that 3D images related to LSPRs of an individual silver nanocube can be

reconstructed through the application of electron energy-loss spectrum imaging4, mapping the excitation across a range of orientations, with a novel combination of non-negative matrix

factorization5,6, compressed sensing7,8 and electron tomography9. Our results extend the idea of substrate-mediated hybridization of dipolar and quadrupolar modes predicted by theory,

simulations, and electron and optical spectroscopy10,11,12, and provide experimental evidence of higher-energy mode hybridization. This work represents an advance both in the understanding

of the optical response of noble-metal nanoparticles and in the probing, analysis and visualization of LSPRs.

We acknowledge the Nano Research Facility (NRF), School of Engineering and Applied Science, Washington University, St Louis, USA for the nanoparticle synthesis. The NRF is a member of the US

National Nanotechnology Infrastructure Network, supported by the US National Science Foundation under NSF award no. ECS-0335765. F.d.l.P. and C.D. acknowledge funding from the ERC under

grant no. 259619 PHOTO EM. C.D. acknowledges the Royal Society for funding. P.A.M. and O.N. acknowledge financial support from the European Union’s Seventh Framework Programme (FP/2007-2013)

under the European Research Council ERC Grant Agreement 291522-3DIMAGE and under Grant Agreement 312483-ESTEEM2 (Integrated Infrastructure Initiative – I3). D.J.H. acknowledges Microsoft

Research Connections and the EPSRC (grants nos EP/K008218/1 and EP/K039318/1) for financial support. We thank A. Howie, M. Kociak, E. Ringe and S. M. Collins for discussions and FEI (in

particular E. Yucelen and S. Lazar) for access to an FEI Titan Microscope at the FEI Nanoport in Eindhoven.

Olivia Nicoletti and Francisco de la Peña: These authors contributed equally to this work.

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK,

Olivia Nicoletti, Francisco de la Peña, Rowan K. Leary, Caterina Ducati & Paul A. Midgley

Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK,

P.A.M. and O.N. designed the experiment. O.N. performed the electron microscopy. F.d.l.P. performed simulations and data analysis. R.K.L. and D.J.H. performed compressed sensing electron

tomography. All authors interpreted and discussed the experimental results and wrote and edited the manuscript.

Re-projections of the reconstructed 3D volumes of the five LSPR components, at the same tilt angles as the experimental data acquisition. Letters α–ε correspond to those of Figs 1–3. The

orientation is as in Fig. 1, with the substrate–cube interface towards the top of the image at negative tilts. To exclude false regions of localized intensity that arose at the periphery of

some of the reconstruction volumes (owing to the imperfections involved in seeking a tomographic reconstruction from so few tilt-series images), the re-projected volume was restricted to

that immediately surrounding the nanocube and LSPRs.

Energy filtered series for the 0° tilt (a) and the −60° (b) STEM EELS spectrum images. The images are limited to the range of interest between 1 and 4 eV for LSPRs of the silver nanocube.

The EELS signal in the images is integrated over an energy window 0.2 eV wide.

a, b, DDA EELS simulated as functions of position (as shown by the blue dotted line) for a 100-nm silver cube with rounded corners in vacuum with dielectric function tabulated in ref. 33

(a), and for a 100-nm silver cube with rounded corners in vacuum with dielectric function tabulated in ref. 42 (b). c, 2D tomographic reconstructions of the five spectral features identified

in a and b (C1, C2, C3, E and F), made from a tilt series of simulated spectra in which the cube is rotated about a cube axis perpendicular to the beam. The five spectral features

correspond to lowest-energy (dipole) corner (C1), higher-energy corner (C2 and C3), edge (E) and face (F) components. We note that the individual components C2 and C3 are not separated if

the dielectric tabulation in ref. 42 is used, as in b. Each reconstruction is scaled independently. There are significant negative values only in the reconstruction of the C3 component,

which corresponds to a singly degenerate octupole mode. Tomographic reconstructions made from this tilt series were obtained using SIRT41, implemented using the TOMO3D software package43.

This video shows a combined 3D rendering of the LSPR components, as displayed in Fig. 3 of the manuscript. (MPG 16698 kb)

This video shows a 3D perspective view of each LSPR component, in respective energy order, leading to a combined 3D rendering, as displayed in Fig. 3 of the manuscript. (MPG 28893 kb)

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Metal nanoparticles exhibit a range of striking and useful optical properties thanks to the excitation of localized surface plasmon resonances (LSPRs). But the precise relationship between

the three-dimensional structure of the nanoparticles and the resulting LSPRs can be hard to determine. Paul Midgley and colleagues have developed a spectrally sensitive imaging technique,

based on electron energy-loss spectroscopy, that permits three-dimensional visualization of many of the key features associated with these LSPRs. With this technique, the interplay between

the LSPRs, nanoparticle structure and substrate–nanoparticle interactions can be directly probed. This study focuses on silver nanocubes, but the method demonstrated is applicable to similar

plasmonic phenomena across all metal nanoparticles.