Electron Energy Loss Spectroscopy imaging of surface plasmons at the nanometer scale

Author’s Accepted Manuscript Electron Energy Loss Spectroscopy imaging of surface plasmons at the nanometer scale Christian Colliex, Mathieu Kociak, Odile Stéphan

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To appear in: Ultramicroscopy Received date: 31 July 2015 Revised date: 19 November 2015 Accepted date: 28 November 2015 Cite this article as: Christian Colliex, Mathieu Kociak and Odile Stéphan, Electron Energy Loss Spectroscopy imaging of surface plasmons at the nanometer scale, Ultramicroscopy, http://dx.doi.org/10.1016/j.ultramic.2015.11.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Electron Energy Loss Spectroscopy imaging of surface plasmons at the nanometer scale Christian Colliex, Mathieu Kociak and Odile Stéphan Laboratoire de Physique des Solides (UMR CNRS 8502) Université Paris Sud, Campus Paris Saclay 91405 Orsay, France [email protected]

Abstract Since their first realization, electron microscopes have demonstrated their unique ability to map with highest spatial resolution (sub-atomic in most recent instruments) the position of atoms as a consequence of the strong scattering of the incident high energy electrons by the nuclei of the material under investigation. When interacting with the electron clouds either on atomic orbitals or delocalized over the specimen, the associated energy transfer, measured and analyzed as an energy loss (Electron Energy Loss Spectroscopy) gives access to analytical properties (atom identification, electron states symmetry and localization). In the moderate energy-loss domain (corresponding to an optical spectral domain from the infrared (IR) to the rather far ultra violet (UV), EELS spectra exhibit characteristic collective excitations of the rather-free electron gas, known as plasmons. Boundary conditions, such as surfaces and/or interfaces between metallic and dielectric media, generate localized surface charge oscillations, surface plasmons (SP), which are associated with confined electric fields. This domain of research has been extraordinarily revived over the past few years as a consequence of the burst of interest for structures and devices guiding, enhancing and controlling light at the sub-wavelength scale. The present review focuses on the study of these surface plasmons with an electron microscopy-based approach which associates spectroscopy and mapping at the level of a single and well-defined nano-object, typically at the nanometer scale i.e. much improved with respect to standard, and even near-field, optical techniques. After calling to mind some early studies, we will briefly mention a few basic aspects of the required instrumentation and associated theoretical tools to interpret the very rich data sets recorded with the latest generation of (Scanning)TEM microscopes. The following paragraphs will review in more detail the results obtained on simple planar and spherical surfaces (or interfaces), extending then to more complex geometries isolated and in interaction, thus establishing basic rules from the classical to the quantum domain. A few hints towards application domains and prospective fields rich of interest will finally be indicated, confirming the demonstrated key role of electron-beam nanoplasmonics, the more as an yet-enhanced energy resolution down to the 10 meV comes on the verge of current access.

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I.

Introduction

Surface plasmons are oscillations of charges, in general electrons, at the interfaces between metallic and dielectric media, which create evanescent electromagnetic fields decaying exponentially with the distance to the boundary. They have been over the past recent years a topic of intensive research, both for fundamental challenges and for potential applications in many domains. In particular, their role for manipulating the light, guiding it along metallic stripes or condensing it into holes or gaps, at a scale significantly shorter than its wavelength, has attracted the general interest, so that a “new” field of research has emerged, known as “nanoplasmonics” as a branch of “nanophotonics”. Among the different techniques that have been developed for mapping the distribution in energy and space of these characteristic electronic excitations and their associated fields, the use of the primary electrons in an electron microscope has demonstrated unique and specific possibilities that will be extensively discussed in the present review. Generally speaking, the high-energy electrons in the electron microscope are mostly used for imaging and analyzing with a very high spatial resolution, down to the sub-angström level, the position and nature of atoms, ions and electron clouds in thin objects, using their strong scattering probabilities. The structural information is provided by images or diffraction patterns mostly implying elastic scattering. On its side, the analytical information encompassing a very broad spectral range typically from the infra-red around 1 eV up to the X-ray above 1000 eV, is generated by inelastic processes which transfer energy as well as momentum between the incident electrons and the target. Practically, spectroscopies of the transmitted electrons (EELS for electron energy loss spectroscopy) and of the emitted photons (EDX for the energy dispersive X-ray spectroscopy in the X-ray spectral domain and CL for cathodoluminescence in the near-visible domain) are involved. The impact of the EELS measurements in the low-loss domain, will be specifically addressed in the following, as they associate an unmatched spatial resolution in the nanometer range with a broad spectral range (from 0.5 eV up to 5 eV investigated with a typical 100 meV energy resolution). In this paper, after a short look at historical landmarks that have contributed to the birth and growth of this research field, we will first summarize recent progress in instrumentation and in theory which have brought it to its present blossoming. The richness and diversity of results obtained by EELS, optionally enlightened by CL measurements, will be described with the support of practical situations, involving nanostructures of quite variable nature, shape, size and environment. They will thus emphasize our newly accumulated knowledge on the physical nature and coupling of the plasmonic modes, therefore opening new broad fields for a joint exploration of electronics and optics in nano-sized structures. Let us add that the combination of EELS and CL techniques in TEM techniques for the mapping of the optical response of nanostructures has been extensively discussed in recent reviews [1, 2, 3].

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II. Historical landmarks

In the mid fifties, a burst of activity, as well theoretical as experimental, see for instance [4, 5], has clearly identified bulk plasmons, i.e. collective modes associated to longitudinal oscillations of the electron gas in solids, at the origin of the narrow and intense characteristic lines recorded at multiple values of a quantized energy Ep in an EELS spectrum of fast electrons transmitted through solid foils. Furthermore, the description of the solid in terms of the dielectric formulation (k,) of the many-body problem [6] is particularly useful to relate the data extracted from an EELS measurement to those derived from optical measurements. On his own side, Ritchie [7] has focused on the influence of the boundary conditions set when the specimen is a thin foil of given thickness t, i.e. a loss of intensity at the bulk plasma frequency together with the occurrence of an additional “low-lying” energy loss appearing at energies of typically Ep/√2 to be induced by the presence of surfaces [7] and therefore named “surface plasmon”. If the first experimental demonstration of surface plasmons was recorded by Powell and Swan [8] in a reflection geometry exhibiting a shift in energies set by the presence of thin oxide layers, the real situation of a thin foil was theoretically investigated by Stern and Ferrell [9] and experimentally both with light scattering and emission and with electron energy loss in transmission. In particular, the existence of two coupled modes between the top and bottom surfaces designated as symmetric (+) and antisymmetric (-), was demonstrated and their dispersion properties, i.e. the dispersion relations +(k) and -(k), studied in the reciprocal space k [10]. In the eighties, Raether published two thorough reviews, on plasmons in general [11] and surface plasmons in particular [12]. The second one was focusing on the role of roughness and gratings to couple surface plasmons with light. Later on, the extension to the optical properties of metallic clusters was published in the book by Kreibig and Vollmer [13]. Although these studies and reviews were providing a rather complete knowledge of what a surface plasmon is and what its main features are, in the early eighties no practical image of a surface plasmon had been reported to our knowledge except a few cases. Most studies were concerning spatially homogeneous specimens along the direction perpendicular to the electron beam, so that the spatial localization of the plasmonic excitations had not attracted much attention. However, using an energy filtering microscope, Cundy et al. [14] had recorded a variation in energy of the bulk plasmon in an Al-7wt%Mg alloy across a grain boundary, attributed to a preferential Mg segregation together with a denudation in Mg around it. In these experiments, the spatial resolution was estimated at ≈10 nm and concentration changes of about 1wt% should be detectable. Furthermore, as early as in 1970, using also an energy filtering microscope, Hénoc and Henry visualized “bubbles” of diameter ranging from typically 5 to 20 nm in an irradiated specimen of Al-Li by selecting a narrow slit of energy around 11 eV corresponding to an interface plasmon [15]. They also

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noticed that the range of “bubble” sizes made visible was dependent on the position of the energy window, higher energy loss values being more adapted to see the smaller bubbles. However, this type of “mapping” remained scarce at that time. In the early eighties, with the progress in instrumentation (to be described more extensively in the following paragraph), it became possible to record many EELS spectra at given positions on a specimen, and their changes could be monitored accordingly. In particular, beyond the commercial spread of the energy filters on conventional microscopes and of the associated EFTEM mode, the point analysis mode in the scanning transmission mode (STEM), demonstrated its specific suitability to such working modes, the more as it was later upgraded into the spectrum-image (-line) mode providing access to sequences of spectra over (or across) well defined objects or structures [16]. The direct visualization of localized surface (or interface) plasmon modes has then really emerged with a number of EELS mapping studies on nanostructures and interfaces realized over the period 1982-1992, many of them having been published in the journal Ultramicroscopy. The access to EELS spectra recorded at well-defined positions with respect to the nanostructure under investigation together with filtered images at the energy of the most significant features has been key to the discovery of new effects. Figure 1 illustrates how one can distinguish the spatial distribution of two plasmonic modes, the volume one and the surface one in a given nanostructure, in the present case a tellurium nanowire selfsupported above vacuum, by recording a sequence of EELS spectra when scanning the incident probe of electrons across it. The spectra exhibit three different contributions, the surface plasmon around 12 eV, the volume plasmon at about 17 eV and a characteristic signal of atomic origin the Te N45 edge above 40 eV. Mapping the intensity of this latter signal provides a direct insight into the Te thickness variation. One can then visualize the intensity distribution of the surface plasmon on both edges and that of the volume plasmon slightly compressed within the Te nanowire, because of a redistribution of excitation probabilities from bulk into surface excitations in finite size systems. This “boundary” effect, first predicted by Ritchie [5], has then become known as the “begrenzung” effect by Raether and followers.

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Figure 1 : EELS spectrum-line across a tellurium nanowire emphasizing the localization of the surface plasmon modes. (A) two selected spectra acquired respectively in a non-penetrating (at the surface apex) and in a penetrating (close to the center) positions. (B) Intensity profiles of the relevant spectral features (from D. Taverna, Ph.D. dissertation, Orsay (2007)).

Among the first studies reporting surface plasmon maps, one can mention the observation of the plasmon resonance between spheres of aluminum demonstrated by Batson [17, 18], the size dependence of the plasmon surface energy for isolated or supported nanospheres [19-22], the decay of the electric potential generated by a surface plasmon induced by the incident electron beam propagating parallel and at a variable distance from a surface or an interface [23 - 29], a geometry also known as “aloof”. In all cases, the experimental results were compared to simulations performed in a dielectric description for inhomogeneous materials. In the last case, the relativistic contribution has been considered in detail. In this seminal work, due to technical restrictions dealt with later on, the energy loss range in the visible domain could not be accessed. This partly explains why, despite dealing with similar physical effects, optical and EELS studies of nanoparticles were at that time progressing along two different lines. Over the past few years, let us say since the beginning of the century, this field of research has been strongly stimulated. One major reason is to be found in the burst of techniques creating nanostructures for use in different domains of applications, such as in electronics and optics for the transport and storage of information, or in chemistry and mechanics for the development of new devices dedicated to sustainable energy production. As a matter of fact, the methods involved for the elaboration of nano-objects of controlled size and shape have become more and more efficient, whatever they be of top-bottom nature with the progress in lithography and beam sculpting techniques or of bottom-up with the use of chemical processes. It thus appeared in parallel that the relevant sizes for exhibiting new physical or chemical properties may be quite small. Consequently, it rapidly became essential to have access to characterization methods offering the required spatial resolution much below the wavelength of the light for applications in photonics. In this domain, the near-field optical techniques are limited to the range of a few tens of nm, while the electron beam is without contest much more prone to the measurements at the nm level. The present review will illustrate the impact of EELS based techniques to investigate the origin and the spatial distribution of surface and interface plasmons in practical cases involving as well metallic, semiconducting as insulating nanostructures with typical nm sizes (see figure 2).

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Figure 2 : Typical situations exhibiting prominent localized interface or surface plasmons in the EELS spectra recorded when scanning the primary electron beam across them : (a) interface parallel to the beam; (b) nanowire or nanotube with axis perpendicular to the beam; (c) metallic nanoparticle of well-defined shape supported or protruding out of a substrate.

These excitations give rise to specific features in the energy loss range corresponding to the IR to UV spectral domain, typically between 0.1 and 20 eV. They may also overlap individual inter- or intra-band transitions so that it is necessary to develop fully suited theoretical tools for their modeling. Our discussion will start from three reference papers which we have published relatively to the three selected geometries shown above : (a) interfaces in a stack of layers with alternating insulating, semi-conducting and metallic characters, cross sectioned so that the interfaces are oriented parallel to the primary electron beam [30]; (b) carbon (or other 2D layered materials, BN and MoS2) nanotubes with their axis perpendicular to the electron primary beam [31]; (c) metallic nanostructures of different nature (Ag, Au, Al, alloys), of variable shape and size supported on a thin layer or protruding over vacuum [32]. However, beforehand, it is useful to summarize in the following paragraphs, some general considerations about the instrumental and methodological developments of interest, as well as an introduction to the theoretical tools elaborated for modeling and interpreting the recorded sets of data.

lll. Instrumental considerations Measuring the energy loss suffered by the primary electrons of an electron microscope travelling through or close to the object feature under investigation provides simultaneous access to spatial and spectral information. As a matter of fact, the elementary piece (or bit) of information in the relevant 3D mixed position-energy (x,y,E) space [16] is the number of electrons having impacted over the element of area (x,y) at the position (x, y) on the specimen and been detected with an energy loss in an energy window (E) around the energy loss E (E0 is the primary energy of the electrons before beam-specimen interaction). In figure 3, it is named the 0D type of information. From there it is straightforward to introduce extended sets of information, such as the electron energy-loss spectrum I(E,x,y)

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recorded at position (x,y), i.e. the 1D data set, the energy filtered IE(x,y) map for an energy loss E defined within a E window, i.e. the 2D data set, the full 3D data set or spectrumimage consisting of the ensemble of I(E) spectra for all (x,y) positions on the specimen. More recently, with the upgrading in technology and data storage and processing, openings to spaces of higher dimension have been explored and built. It can be, for instance, a 4D set of data consisting either of a succession in time t of EELS spectra I(t,E,x,y) recorded at position (x,y) – such as shown in figure 3 – or a collection of spectrum images recorded under different angles of illumination, from which tomographic data sets of type I(E,x,y,z) can be built. Obviously, this type of concept applies to any type of position-energy data set, such as acquired by photon, tunneling or mass spectrometry, and in particular to cathodoluminescence (CL) spectrum-imaging as it will be shown further.

Figure 3: Definition of the multi-dimensional data sets involved in spatially resolved EELS measurements [16, 33]

Practically, one needs in this SPIM (spectrum-imaging) configuration : (i) an electron source of high brightness, typically a cold field emission gun operated at primary voltages in the 60200 kV range; (ii) a focusing lens on the specimen, optionally coupled with an aberration corrector (see below), without forgetting the scanning coils to move the incident probe over the specimen; (iii) a set of detectors which can collect in parallel several signals, such as the annular dark field one (for topography and structural information) and an EELS spectrometer (a magnetic prism) with its detection chain. It can also be complemented, as shown in figure 4, by a CL collector, spectrometer and detector to record and analyze the photons emitted over an energy range from near IR to near UV.

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At this point, one must add that in the conventional TEM configuration, an alternative is offered: instead of piling together point resolved EELS spectra, one can record filtered 2D images within an energy loss window and store as many of them as windows are required to cover the full range of energy under investigation. This is called the Energy Filtering TEM mode, EFTEM. The comparison with the STEM spectrum-imaging SPIM mode has been developed elsewhere, see for instance [34]. If the STEM SPIM is more efficient in terms of minimum dose required for distinguishing many different spectral contributions, such as signals close in energy, the EFTEM approach is worth considering when a large number of pixels are required. Practical examples recorded with one or the other method will be shown later.

Figure 4 : The global design of a multi-signal STEM microscope providing simultaneous topographical (or structural) images via the HAADF detector together with EELS low loss and optical CL maps – see also [35].

The type of information associated to the mapping of plasmons and associated electromagnetic fields is not very local, it can be explored very fruitfully at the nanometer scale, which means far below the involved photonic wavelengths. Consequently, it does not require the best spatial resolution now offered by probe aberration correctors, which can focus currents of the order of 100 pA within less than 1 Å. On the other hand, the constraints in terms of energy resolution are much more severe, because the signals of interest generally lie in the 1 to 5 eV range and below when the size of the object increases up to the sub- range. Furthermore, they are superimposed onto the high intensity and rapidly

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decreasing tail of the zero-loss peak and correspond to excitations of low probability of generation. A major source of limitation is the natural energy width of the primary electrons imposed by their emission process: typically 0.7 to 1.0 eV for thermal sources, it is reduced to about 0.3 eV for cold field emission. On top of this, one has to consider the instabilities in the high voltage and in the power supplies of the electron optics components. Consequently, several routes have been developed and used to pass over these limitations, thus paving the way for a major breakthrough in the mapping of excitations in the eV spectral domain. The first one is the cheap one and relies on the recording and processing of 4D SPIM, a chrono Spim in which for each pixel, many spectra (typically 50) are acquired with an acquisition time of a few ms and then summed after re-alignment. This step significantly reduces the broadening induced by the mains instabilities on all electrical components. It is followed by the use of a deconvolution procedure, such as the Richardson-Lucy algorithm, which after several iterations improves energy resolution and increases signal-to-noise and signal-tobackground [36] – see figure 5. The zero loss peak in vacuum is used as the point spread function (PSF) for this deconvolution. However, as shown in the figure, deconvolution may generate bias and fake features when one increases too much the number of iterations. Consequently, the optimum (and the rich) solution is the use of a monochromator introduced either in or just at the exit of the electron gun. It constitutes the best solution as demonstrated up to now by Rossouw and Botton [37], who have identified well-resolved peaks down to 0.17 eV – see figure 6.

Figure 5 : Low energy-loss spectra of a star-shaped gold nanoparticle before deconvolution (red) and after 3 (blue), 5 (green) and 15 (orange) iterations. The visibility of the 1.6 eV loss feature significantly increases, but so does the fake peak at – 0.6 eV due to ringing effects. When comparing the full ZLP spectra in inset, their FWHM reduces from 0.3 to 0.21, 0.18 and 0.13 eV when increasing the number of iterations (from S. Mazzucco, Ph.D. dissertation, Orsay 2009).

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Figure 6 : Total EELS spectrum from the green boxed region enclosing a bent silver nanowire (left) and map of the intensity of the lowest energy peak demonstrating capabilities to investigate plasmon modes in the mid-IR domain by use of a monochromated TEM (adapted from [37]).

The two different imaging techniques STEM EELS SI and EFTEM SI have been shown to deliver direct plasmon imaging on metallic nanoparticles in the 1 eV loss domain, when a sufficient energy resolution is achieved [38], as it is the case with a monochromated instrument. The volume of data set accumulated within one chrono-SPIM can be very large (i.e. 200000 spectra for a 64x64 image and 50 spectra per pixel acquired altogether within a total recording time of the order of 10’). It has therefore become critical to develop the suited software for processing them and displaying the key information. At Orsay, through a succession of Ph.D. contributions, custom routines have been written, tested and gathered into a package designed to map the main characteristics of each surface plasmon resonance present within the recorded spectral domain [39]. It includes a fit and then a subtraction of the ZL peak with an experimental vacuum one recorded nearby in the same conditions, followed by an automatic detection and fit of the identified modes with Gaussian or Lorentzian functions. It thus provides maps of the major characteristics of the different modes, such as their energy position, their width and their intensity as displayed in figure 7

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Figure 7 : Results of the numerical analysis of a SPIM recorded on a lithographied aluminum nanoantenna, showing the mapping of Intensity, FWHM and energy of the four principal modes. (Adapted from Z. Mahfoud, Ph.D. Orsay 2014)

The photons resulting from the desexcitation processes following the impact of the (S)TEM primary electrons also convey a very rich information. Although they appear rather marginally in this review dedicated to the mapping of plasmons, it is interesting at this point to provide a few technical details concerning the recording of the CL signals, schematized in fig. 4. In the home-made system in operation at Orsay, now under commercialization, the CL photons are collected by an aluminum parabolic mirror, the focal point of which being coincident with the focused electron probe on the specimen. Through a bundle of optical fibers, light is transmitted to an optical spectrometer and then to a CCD camera. A set of gratings opens three different optical ranges corresponding respectively to near IR, visible and UV, thus covering a full range from about 1.2 eV to 6 eV, although the efficiency drops significantly close to these boundaries. Once a 3D CL data cube has been acquired for these optical signals, the same processing tools can be used as for the EELS ones: consequently, multi-peak fitting techniques deliver maps of the energy (or wavelengths), FWHM and intensity of each identified spectral feature. In [40], it is demonstrated that with this technique EELS and CL maps can nowadays be realized on the same individual metallic nanoparticles (see figure 8) in order to distinguish radiative and non-radiative modes, see further for a more complete discussion of this point.

Figure 8 : EELS and CL maps of the same individual gold nanoprism recorded with the mode of higher intensity in the respective spectra (marked with the blue energy window), which is shown to be localized at the tips of the triangle (from A. Losquin et al [34])

lV. Theoretical developments

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A vast literature has been published to describe the nature and the physical mechanisms involved in surface plasmons and associated electric fields in general. In the present text, we will restrict ourselves to the presentation and application of theoretical tools and simulation software which have been developed to interpret the EELS results and maps of surface plasmon distribution at the nanoscale in interfaces and nanostructures. The starting point of these modelling tools is the use of classical electrodynamics, relying on Maxwell equations and of a dielectric constant (r,k,), reduced to (r,) in the local approximation, which describes the response of the material, at position r, to an external electric field of pulsation . As a matter of fact, the primary swift electron of charge - e and of velocity v, travelling in the vacuum at a distance of a few nm with respect to a surface, an interface or an isolated particle, generates an incident electric field Einc. This field induces charge oscillations and an associated evanescent induced electric field Eind. In an EELS experiment, one measures the energy lost (or the work produced and therefore of type v.Eind) by the primary electron travelling through the induced field it has itself generated. It is therefore obvious that only its (Eind)z component along the trajectory Oz of the probe electron comes into account. In a CL experiment, the induced electric field is detected and analyzed in the far-field by a photon detector, see figure 9 for a comparison of the two mechanisms.

Figure 9 : Schematics of the generation and detection channels for the EELS and CL signals induced by an impinging swift electron on a metallic nanoparticle

The EELS response for the basic geometries, from bulk to planar surfaces at glancing incidence and spherical nanoparticles is shown in figure 10. The resonance peaks of the energy loss functions in the bulk, close to a planar and to a spherical surface correspond to zero values of their denominator (resp. 0, -1 and -2) and in the Drude model of the free electron gas, to values of p = (ne2/m0)1/2, p/2 and p/3

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

Figure 10 : Definition of the EELS response function P() and of the resonance plasmon frequency of a material of dielectric coefficient () for three basic geometrical configurations

For more complex situations, efforts have been realized over the past years to elaborate numerical approaches for simulating the energy and intensity of the EELS peaks as a function of the shape and environment of the interfaces or nanostructures under consideration. In particular, following the pioneering works of Ouyang and Isaacson [41] and of Garcia de Abajo and Aizpurua [42], a boundary element method (BEM) has been implemented to solve the Maxwell equations with well-suited boundary conditions on the abrupt interfaces between the particles and their dielectric environment. First implemented in the quasi-static situation, it has then been extended to the retarded case, where the size of the particle is no longer smaller than the wavelength of the involved electromagnetic fields. However, the principle of the method being easier to understand in the quasi-static case, we will deal with it in the next paragraph. Relying on a discretization of the interface, the quasi-static BEM methods calculate from an integral equation involving the surface charge densities, the eigenvalues i and the spatial distributions i(r) of each eigenmode for a given geometry. Specifically, in the quasi-static regime, the optical properties of nano-objects do not depend on their absolute size, but on their relative dimension [42].

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Although not straightforward at first sight, the BEM formulas can be understood [2] as an extension for arbitrary geometries of the formulas given in figure 10 for planes and spheres. Indeed, the eigenvalues are related to the eigen-energies through a simple relation [41,42]. For example, in a Drude model with negligible damping, the eigen-energies si are related to the i through the relation [43] si =P((1+i)/2)1/2, with P being the bulk plasmon frequency. For example, for a plane, i=0 and for a the dipolar plasmon of a sphere i=-1/3, leading to the well-known formulas for the interface plasmon and the dipolar plasmon in the Drude Model, see [43,2] for more details. For more complex shapes, the calculated eigenvalues are governed by the dielectric coefficient of the nanostructure and its shape. For instance, for a nanorod of metal in vacuum, the aspect ratio governs the existence of plasmons. The first three modes correspond successively to antisymmetric, then symmetric, then antisymmetric charge distributions with respectively one, two and three nodes along the rod (each of these modes displaying a revolution symmetry along the nanorod axis). From there one can calculate the associated eigen-potentials i(r) and eigen-electric fields Ei(r) at any position, and then the induced EELS maps (and also SNOM [43] or CL [1] maps which remain outside the scope of this review). In figure 11, we show non-retarded BEM calculations for a silver nanorod displaying the calculated charge, potential and EELS maps for the three first surface plasmon geometrical modes, compared to experimental EELS maps.

Figure 11 : Comparison of simulated and experimental maps of the three first order (n=1 to 3 from left to right) longitudinal plasmon modes in nanowires of aspect ratio typically > 10. From top to bottom : calculated map of the eigencharges, calculated map of the electric field parallel to the beam direction, calculated EELS map experimental maps for a nanowire of aspect ratio 30, experimental maps for a nanowire of aspect ratio 30, together with the map of the transversal mode at 3.55 eV and an HADF image (scale bar = 100 nm). Adapted from [2] for the calculations and Rossouw et al [44] for the experiment

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This numerical approach has been largely used over the past few years for the simulation of surface plasmon maps in many systems of variable geometries. A quite convenient progress has been by Hohenester and Trügler who have developed a BEM based software (MNPBEM) that is a Matlab toolbox dedicated to the simulation of plasmonic properties of nanoparticles [45]. An alternative approach consists in the Discrete Dipole Approximation (DDA) that instead of discretizing the surface, deals with the volume of the particle described by a discrete number of polarizable volume elements [46]. It has been applied with great success to interpret the origin of the tip and edge modes observed in the EELS maps of triangular silver nanoprisms, as quasistatic stationary surface plasmons with a symmetric charge distribution between surfaces and a standing wave behavior in the plane direction [47]. It has later been extended to other systems [48], including coupled ones exhibiting marked Fano resonances [49]. Furthermore, it has been noticed that both simulation approaches (BEM and DDA) lead to similar results when used for instance to simulate the modes observed on individual gold nanodecahedrae with different techniques (optical dark-field imaging, EELS and CL) [50]. At that point, it is interesting to pinpoint the close connection put forward by Garcia de Abajo and Kociak [51] between the energy and spatial variations of the SP modes and a generic concept, that of electromagnetic local density of states (EMLDOS), which gives at any given point in space, at a given energy, the probability of finding a given EM mode. It brings EELS closer to photonics, the exact relation having been deepened in a succession of papers [43,52,53], this last one giving access to the modeling of the three-dimensional plasmon fields from a collection of rotated EELS maps. Very recently showed that a major step forward could be performed in reconstructing directly the whole (vectorial and three dimensional) EMLDOS from a series of tilted EELS spectral-image. Practically, EELS and CL are both closely related to the z-EMLDOS [43,ACS 54], i.e. the projection of the EMLDOS along the electron beam direction. However, the understanding of the relation between EELS or CL and optical spectroscopy has been a constant effort of the community. If these earlier works pointed to the fact that EELS/CL resonances energy were very close to that of optical techniques (extinction and scattering, for example), the true fact that the optical spectroscopy may exhibit already obvious differences between themselves (see for example [55]) calls for a refining investigation of the link between specific optical and electronic spectroscopies. In a proof-of-principle study [40] comparing on the same individual objects (gold nanoprisms) EELS and CL, it has been shown that both spectroscopies are delivering a signal which is the sum on all modes of the product of two terms: the first one represents the spectral properties through response terms associated to the dielectric properties of the nanoparticle : Im(fi()) for EELS and |fi()|2 for CL, which exhibit resonance peaks at frequencies defined by the eigenvalue i of the mode i. For example, in the Drude model, both functions are peaked around the energy si, although due to damping the energy position of the maximum might be shifted between the two quantities, see [40] for details.

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As for the second term, it reflects the spatial variation of the square of the eigenpotential of the mode that is similar for both signals. Consequently, the position of the maxima in the simulated EELS and CL intensity maps coincide exactly for one given mode (in this case the dipolar one at smallest energy). But, in the calculated spectra, the square and the imaginary part of the function fi() have the exact same maximum in energies only in the absence of dissipation while a shift appears between them when dissipation is included. These theoretical simulations can be positively compared with the experimental results obtained on the same type of particle deposited on a thin graphene layer shown in figure 8, see [40] for an extended discussion. Getting deeper in the understanding of the difference between EELS and CL [54], Losquin and Kociak refined the above mentioned description for the spectral properties of CL, showing that contrary to EELS, CL spectra may reflect far-field interferences of overlapping modes, a phenomenon sometimes ambiguously coined as Fano interference. Finally, as already discussed, EELS spatial variations are related to eigen potential variations. However, these are in turn related to eigen charges variations [2,41,42,43], see figure 11. Eigen charges variations are conceptually easier to apprehend as a surface plasmon observable. It is thus appealing to try to reconstruct them, which has been successfully performed by Collins et al. using tomographic approaches [56].

V.

Surface (interface) plasmons in simple geometries involving planar or spherical shapes

Surface plasmon resonances can be found at the surface of most materials, at least those exhibiting clear collective response in the bulk. Examples related to different situations involving metals, semiconductors and insulators are shown in this paragraph. However, the family of metals with a wavelength-dependent dispersion of their dielectric function prone to give resonance conditions in the IR and visible spectral domains, has been mostly investigated up-to-now, i.e. the noble metals Ag and Au which furthermore are little reactive. Recently, Al has also been considered because of its potential applications in the UV domain.

V.1 Single and multiple planar surfaces and interfaces : The simplest case is the planar interface between two materials probed by an electron beam travelling parallel to it as in the geometry shown in figure 2 (left). In the classical static description the response function in this situation is proportional to Im(1/(A() + B())) so that there can be an interface plasmon peak only when one can find an energy S for which A(S) + B(S) = 0 (corresponding to poles in the response function). When the interface is a free surface with A being a Drude metal and B vacuum with  = 1, the equation becomes (s) = -1 and its solution is S = p/2.

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The largely investigated Si-SiO2 interface can be considered as a representative example for a refined analysis of the mapping of an interface plasmon IP, or more simply of its profiling because the characteristic variation of the signal is along the direction perpendicular to the interface. Very early, see for example [27,28], a bright line at 8 eV had been identified when the probe was located at the apex of the interface. A more refined investigation [29] with improved spatial and energy resolution has demonstrated a shift of this peak from typically 7.8 to 6.8 eV when moving the probe from the interface to about 5 nm from it. This shift can only be interpreted when considering relativistic terms in the used dielectric theory. Furthermore, the introduction in the model of a thin (1.0 nm thick) layer of SiO x still improves the agreement between experiments and simulations. This result emphasizes the sensitivity of the interface plasmon mode with respect to the detailed structure of the interface, however keeping in mind that this information is mediated through a dielectric response typically averaged over thickness of the order of 1 nm. More recently, pushed by the development of ultra-thin gate stacks in field-effect transistors of latest generations, more complex systems consisting of multilayered slabs have been grown and EELS studies have been performed on them. Experimental EELS profiles [30,57] have been recorded and interpreted when scanning the incident electron probe on cross sections of Si structures incorporating either a stack of three different components (SiO2, HfO2 and TiN) or one component (SiO2) with different thicknesses of 2 and 10 nm. These studies confirm the dominant role of interface modes when aiming at the determination of local dielectric constant of the different materials involved. These modes can significantly couple up to distances of the order of v/, typically 10 nm, inducing multiple-interface contributions, which can be detected in the different components of the multilayered structure. Simulations performed within a dielectric formalism including relativistic effects (based on the methods elaborated by Bolton and Chen [58]) are shown to predict accurately the delocalized contributions of the coupled interface plasmons together with those due to Čerenkov radiation and interband transitions in the neighboring Si material.

V.2 Single and multiple spherical surfaces and interfaces : The second seminal example is the metallic spherical object, the optical properties of which have been studied and explained more than one century ago by Mie [59] for particles of size significantly below the illumination optical wavelength. In this geometry, the excited surface modes are categorized as a function of their angular momentum quantum number l in spherical coordinates, l = 1 corresponding to the dipolar mode. Practically, it was established [60, 61] that within the Drude model approximation:

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(i) For a metal sphere in vacuum : (s)l = p/[(2l+1)/l ]1/2 which increases from p/√3 for

l = 1 up to p/√2 for l → ∞ (ii) For an empty sphere in a metal (void, bubble) : (s)l = p/[(2l+1)/(l+1) ]1/2 which

decreases from p/√3/2 for l = 1 down to p/√2 for l → ∞ In the quasi-static approximation, the energy of the different modes does not change with the radius of the particle. However, the probability of exciting the different modes changes with the position of the electron trajectory with respect to the external surface of the sphere, all modes being excited at glancing incidence with a weighting probability varying as 1/l, while the dipolar mode only is excited far from the outer surface [19, 62]. The extension to the case of concentric spheres of different nature, such as a metallic core and a surrounding oxide shell, has been studied both experimentally and theoretically within the frame of the standard dielectric description [63 - 65]]. In particular, the case of an empty sphere can therefore be straightforwardly deduced from the previous two cases (sphere and void) as shown in figure 12. When the thickness of the shell decreases, the surface plasmons of both surfaces couple inducing an energy shift and therefore an enhanced splitting of both families of modes. This approach has been further extended to the case of three spheres with a Si core, a SiO2 coverage exhibiting a clear interface mode at their boundary and an extra mode on the outer surface which could only be explained by introducing an extra very thin layer of reduced SiOx as the outermost component [21]. This behavior has also been recently verified in a study of the dispersion of surface plasmon modes in gold nanorings [66].

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Figure 12 : Eigenfrequencies of surface plasmon modes of a thin Al spherical shell as function of the ratio of external R and internal radius r1 calculated with the dielectric model in the quasi-static approximation (from [21]). When the shell becomes thinner, the surface plasmon of both surfaces interact inducing a shift and an enhanced splitting of the resonant frequencies. These coupled modes involve collective oscillations of the electrons of the whole system. For comparison, the curves corresponding to the surface plasmon modes with different quantum numbers l for the isolated sphere and the isolated void are also shown. They do not shift with size and they correspond to the asymptotic behaviour of the curves calculated for a spherical shell when the inner void becomes infinitely small.

Let us point out that such results are valid for the radial distribution of charges in an infinite cylinder, in which case the used quantum number to define the different modes is m (the azimuthal quantum number in the cylindrical coordinates). Consequently, a similar approach has been developed to interpret the origin of the different modes detected on nanotubes of lamellar 2D materials such as carbon, boron nitride, dichalcogenides (WS2). However, there is a significant difference because the material is made of a stacking of 2D atomic layers exhibiting strongly anisotropic properties, and in particular a local dielectric coefficient (r) which is no longer a scalar but a tensor with two main components andrespectively parallel and perpendicular to the c axis at this position. In the case of thin walled nanotubes, the two collective modes resulting from the coupling between the outer and inner surfaces of the hollow cylinder can be indexed as a tangential (symmetric in terms of charge distribution between both surfaces) mode and a radial (antisymmetric) one [62]. Furthermore, each mode can be separately associated with a specific component of the dielectric tensor of the corresponding bulk material (graphite for carbon nanotubes), see figure 13 left. In the case of the single wall carbon nanotube, the only observed mode centered at 15 eV (see figure 13 right) results from the disappearance of the radial (antisymmetric) mode while the tangential (symmetric) mode remains [67]. Similar results have been obtained in the case of h-BN nanotubes in which case the in plane component terms  dominate [68].

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Figure 13 : Left : Geometry of the charges and the electric field lines in an hollow cylinder for the dipolar mode [Right : (a) EELS spectra recorded on several carbon nanotubes (CNT) at glancing incidence : NT1 and NT2 are single walled with only one peak at 15 eV corresponding to a tangential mode, NT3 has two walls, a small contribution of a radial mode at 18 eV (of increased visibility in the second derivative spectra (b)) survives.

Vl. How the shape, size and nature of individual nanoparticles govern their surface plasmon maps

Beyond the simple geometries (plane, sphere) described there above, the newly developed techniques of fabrication, either bottom-up or top-down, have generated the creation of metallic nanostructures exhibiting many different types of shapes. Because of their ability for locally exalting EM fields in particular, the collective excitation modes in these nanoobjects have been extensively investigated experimentally as well as theoretically over the past few years. In this effort, electron beam induced spectroscopies, such as EELS and CL, have gained a highly visible recognition because of their intrinsic high spatial resolution giving access to a mapping at the nanometer scale, much below the wavelength of the photons in the concerned visible range from IR to near UV domains. Altogether, this joined effort in fabrication, characterization and theoretical modeling has largely been involved in the recent fast development of nanoplasmonics and associated nanophotonics. In the present paragraph, we will report the major results gathered on different families of nanoparticle shapes (rods and slits, prisms, cubes and a few more complex) to extract some of the general rules governing their specific individual response. The seminal example of a triangular silver nanoprism of rather constant thickness deposited on a thin sheet of mica is shown in figure 14 [32]. When analysing the EELS spectrum-image recorded while scanning the incident probe of electrons over it, three distinct modes clearly appear with the lowest energy one (at 1.75 eV) localized at the tips, the medium energy one (at 2.70 eV) along the sides and the high energy one (around 3.2 eV) roughly in the centre. These modes, in

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particular the tip and the edge ones, have been interpreted with the support of BEM simulations as eigenmodes of the associated electromagnetic fields respectively of dipolar and quadrupolar types.

Figure 14 : Localized surface plasmons (LSP) modes on a single silver triangular nanoplatelet with the HADF image and profile, a selection of different spectra recorded at three positions (A, B and C) on the nanoparticle and the corresponding maps (from [32])

Generally speaking, two broad families of surface plasmons can be distinguished, those propagating along unbounded metallic surfaces, also known as surface plasmon polaritons, (SPP), in contrast with those localized on metallic nanoparticles (LSP) of size in the nanometer range, typically up to a few hundreds of nm. They will be discussed on specific cases in the following paragraphs. Beforehand, it is interesting to consider an important factor for applications, i.e. the sharpness of the SP resonance, or more precisely its quality factor Q defined as the ratio of the energy value of a given resonance (Ep) divided by its width (). The Q factor depends on two contributions: the dissipation in the material, encoded in the imaginary part of the dielectric function, and the dissipation through radiation. Following Wang and Chen [69], the former only depends on the dielectric function of the metal at the given plasmon frequency but not on the shape of the nanostructure and the dielectric environment. Practically, Q corresponds to the number of oscillations, which a surface plasmon can make before decaying. VI.1 Nanorods, nanoantennas and nanoslits : These shapes can either be derived from an elongated sphere along one direction or from a cylinder of finite length. In the first approach corresponding basically to an ellipsoid, the dipolar mode is split into two modes a transverse and a longitudinal one, the transverse

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corresponding to oscillations of the electrons perpendicular to the long axis of the rod and the longitudinal along this axis. Typically when the aspect ratio i.e. the ratio AR = L/D (where L is the length and D is the diameter of the nanorod) remains limited, typically below 3, one clearly distinguishes two main peaks corresponding to these transverse (T) and longitudinal (L) modes. As shown in the early studies on this type of specimen made either of gold or silver [70-72], the resonance energy of the transverse mode is close to that of the equivalent sphere (2.4 eV for Au and 3.5 eV for Ag) and that of the longitudinal mode is significantly shifted towards lower energies, this shift being as more important as the AR increases. A nice demonstration is provided by Chu et al. [73], as shown in figure 15.

Figure 15: (Top): calculated STEM-EELS loss probability for locations I (red curve) and II (blue curve) of the electron beam in the vicinity of an Au nanorod (with l/D = 85nm/27nm). Inset represents calculated excitation intensity maps and associated charge distributions. (Bottom): corresponding experimental maps of the modes A and B and their associated spectra recorded at positions indicated on the image (courtesy Chu et al. [73]).

With increased energy resolution and on longer nanowires, two groups of excitations well separated in energy (at least more visible for Ag than for Au nanostructures) can clearly be distinguished, as it can be seen on figure 6 (left). The first group, typically between 0.3 and 1.5 eV in this case, is made of a series of well-resolved peaks, while the second one around 3.4 eV consists of a single peak of large width. These two groups can be deduced from the longitudinal and transversal modes introduced there above. The second one, as a matter of fact, is very similar to the well-known (transverse) surface plasmon, as the maps indicate that it is pretty well homogeneous in intensity all along the cylindrical surfaces of the nanostructure. In the case of gold, it largely coincides with the onset of interband transitions around 2.4 eV.

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As for the longitudinal modes, which have been thoroughly studied in several papers [44, 74 - 77], they are due to the combination of surface plasmons propagating in the two opposite directions (SPP) to give rise to stationary waves with a succession of quantized nodes and antinodes, as it has been confirmed by different numerical simulations. Figure 11 above compares MNPBEM calculations of the eigencharges, the electric field distribution parallel to the incident electron beam, theoretical and experimental EELS maps for the first three longitudinal modes (n= 1, 2 and 3 and m=0) observed in an Ag nanorod of aspect ratio about 30. With high energy resolution, modes with m up to 10 have been visualized in nanowires of length > 1m [37].

As a matter of fact, these spectra and maps are very informative when considering them in more detail. One specific output is the extraction of dispersion curves (i.e. maps of energy  versus wave vector q) for all observed modes, depending mostly on AR values. It relies on the fact that the EELS intensity maxima are observed at the position of the antinodes of the charge distribution where the field component parallel to the beam is maximum (see figure 11). For each mode, a line profile through the observed peaks along and slightly outside one of the external surfaces exhibits quasi-equidistant peaks, the number of which being directly associated with the mode number. The distance between these peaks (L/n) is equal to half the SP wavelength (sp), so that the mode wavevectors are quantified as qn = n/L. Such a curve is shown in figure 16. At low q values, the curve exhibits a high dispersion and is close to the light line, at high q it disperses much less and tends towards the asymptotic value sp. All high order modes appear at energies close to this value. For long wires on the opposite, all modes are at low energies and well separated, close to the light dispersion curve  = ck. In this case, they behave rather as surface plasmon polaritons (SPP) than as localized surface plasmons (LSP) and can be more easily coupled with light.

a

b

Figure 16 : (a) Schematic representation of the dispersion curve (q) for the longitudinal modes (labelled n = 1, n = 2, n = 3..) in nanowires of length L. (b) Multipolar plasmonic resonance dispersion relations for several Al nanoantennas (from J. Martin et al. in [78])

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Several of the above mentioned studies [2, 37, 76] have compared experimentally determined dispersion curves on Ag and Au nanowires of varying aspect ratios to this simple model and to more refined ones, which can account for retardation effects for longer wires, for substrate influence and for bunching behavior of the modes close to their end. This bunching is observed close to the extremity of the nanowires where the imperfect reflection may induce a slight phase change, which has also been investigated in particular in [44, 76, 77]. It is responsible for a moderate variation of the internode distances measured close to the ending with respect to those measured in the middle of the particles. Practically, the experimental data sets display some distribution around the simple theoretical line because of their different AR. In figure 16 b, we show such an experimental analysis of the dispersion curve extracted from measurements on aluminum nanowires with different aspect ratio and compared to BEM calculations [78]. Aluminum nanoparticles have recently emerged as a potential alternative to Ag and Au ones, as they offer a very broad optical band of response in the UV in particular and obviously are much less expensive. However, they suffer from a slightly reduced quality factor (Q = energy/linewidth) and exhibit some interband radiative damping around 1.8 eV. It is also interesting to point out a recent study [79] which has combined a direct angular-resolved E(q) measurement in a diffraction mode with that issued from intensity maps in the real space described there above, which offers the possibility to explore the behavior for longer wires (typically 2 to 3 m in length). A useful parameter has been investigated in several studies [37, 76], the decay length of the SP associated evanescent electric field in vacuum, i.e. perpendicular to the surface of the nanoparticle. This parameter is essential, when one is interested by the possible coupling of neighbouring metallic nanostructures leading to hybridization effect and collective response of an assembly of well-organized nanostructures (see later). The published results agree that this decay is exponential with a characteristic length varying with the energy, and/or the specific mode. But values which can be as high as 100 nm in the sub-1 eV range and lie in the 40 to 50 m in the 1.5 to 2.5 eV range for silver, constitute quite reasonable estimates. An interesting situation has been put forward when comparing rods of a metal on a layer and slits in the same metal [80]. In these complementary nanostructures, following the wellknown Babinet principle, the role of the electrical and magnetic fields is interchanged. Furthermore because of the change of sign of the dielectric constant in the material (<0) and in vacuum (>0) at the considered frequencies, the distribution of electric charges is symmetric for nanorods with respect to the axis of the structure while it is antisymmetric in the nanoslits (positive charges facing negative charges) with respect to the center line of the structure. Figure 17 demonstrates experimentally and theoretically the exchange between the spatial distribution of the E and B components for a single metallic Au U-shaped split ring resonator and for its complementary U-shaped nanoslit drilled in an Au thin film.

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Figure 17: Complementarity between U-shaped Au nanorod (top) and nanoslit (bottom) – scale bar is 200 nm : (a) HADF images, (b) EELS map of the 1st antisymmetric mode, (c) schematic design for simulations, (d) calculated |Ez| and (e) calculated |Bz| for the same mode, with the polarization of the incident light field shown with an arrow (courtesy F. von Cube et al [81])

Cathodoluminescence (CL), as introduced in the sections respectively devoted to the instrumental considerations (see figure 8) and to the theoretical developments, has been shown to constitute an alternative to EELS for measuring the spectral distribution of the emitted radiation under the impact of the electron beam and for mapping its spatial origin. Following the pioneering study by Yamamoto et al [82] on submicron silver nanoparticles, several works have been devoted to CL mapping of surface plasmon modes in Ag [83] and in Al [84] nanorods of variable aspect ratios. They confirm, although with lower spatial resolution, the interest of this route for exploring the plasmonic properties of individual nanoantennas. However, it has generally been stated that EELS detects all modes while optical techniques cannot reveal some of them, which are therefore called “dark” modes. Strictly speaking, these “dark” modes cannot be optically excited or detected in the far field and consequently should not be visible or at least of much reduced intensity in the CL maps, see [51] for a simulation of the EELS and CL signals generated by a thin silver disk. This strictly holds in the quasi-static regime. It is therefore not surprising that a priori “dark” modes, such as the longitudinal quadrupolar ones in long Al nanorods, can be CL mapped because their length becomes of the order of half the photonic wavelength and consequently involves retardation effects

VI.2 Flat nanoprisms : The silver triangular nanoprisms (generally of equilateral shape) such as the one shown in figure 14 have constituted a reference specimen for demonstrating the capability of the STEM-EELS to discriminate and to map 2D stationary surface plasmon modes at the tips, on the edges and in the center of such an individual nanostructure. Indeed these platelet systems of triangular shapes, but also of hexagonal or circular shapes, have been found to be

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ideal to investigate the relationship between the structure and the optical properties at the nanoscale. As a matter of fact, this simple morphology can be considered as a 2D extension of the simple 1D nanorod shape extensively discussed in the previous paragraph. Consequently, most of the physics investigated and revealed on nanowires can be transferred to the nanoprism geometry : (i) Smaller nanoprisms, with typical lateral sizes in the 100 nm range and thickness of

about 10 nm, exhibit stationary, quasi-static short range surface plasmons, with a symmetric charge distribution between top and bottom surfaces and a standing wave in the in-plane direction [32]. The most intense modes at the tip and in the middle of the edges correspond to the dipolar and quadrupolar modes. They globally shift downwards in energy (toward IR in wavelengths) when the lateral dimension increases and it has been demonstrated that the aspect ratio is a key factor to govern this energy shift [47]. With increased energy resolution [85], a supplementary peak has been detected along the edges suggesting the existence of a higher index mode (i.e. with an increased n value as introduced for the longitudinal modes along a rod).

(ii) For bigger nanoprisms, in particular when the thickness is significantly larger than the

skin depth for penetration of electric fields in the material at the relevant thickness, the coupling between the two horizontal surfaces is much reduced. In this case, surface plasmon polaritons can be observed propagating along the wedges of the platelet with increased numbers of nodes and antinodes along the edges [86]. At platelet corners, these plasmon polaritons are partially reflected or transmitted to neighboring edges. Experimentally, these modes have been shown to exhibit 0, 1, 2, 3 and 4 resonances between 0.6 and 1.6 eV along a single edge in triangles. They have also been identified in hexagonal and truncated gold nanoprisms.

(iii) As demonstrated in figure 8, triangular nanoplatelets of small dimensions (with edges

of 60 nm in length) also constitute excellent test specimens for an extensive and accurate comparison of their surface plasmon modes with EELS and CL on exactly the same particle [40]. This study has clearly confirmed that CL probes only the radiative dipolar modes, while EELS additionally reveals dark modes such as the quadrupolar ones. Furthermore, slight shifts between the resonance energies of the tip dipolar modes, as measured by EELS and CL, have been interpreted in terms of different energy dissipation via the substrate. It must however be emphasized that the CL technique is less adapted to the study of the plasmon modes in nanosized particles because the window of recorded wavelengths is reduced with respect to that of EELS and its signal is much less intense. An

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interesting further conclusion of this study is to demonstrate that CL and EELS are respectively connected to optical scattering and extinction as explored by farfield optical techniques, which further are far from achieving the same level of nanometer spatial resolution.

(iv) The nanodisk geometry is an interesting situation as it exhibits rich EELS spectra

corresponding to several families of plasmon modes, depending on the impact position of the electron beam [87]. Close to the edge, the low energy modes between 1.2 and 2.0 eV for a disk of 200 nm in diameter correspond to the dipolar, quadrupolar and hexapolar modes with azimuthally different charge distributions. However, this azimuthally governed symmetry is averaged in a filtered map because all beam positions along the edge produce similar responses. A very strong peak is observed at about 2.6 eV when the beam is positioned at the center of the disk. This mode couples strongest with the electron beam and not with light, it has radial symmetry and no net dipole mode. It is a breathing mode corresponding to an extended 2D surface plasmon confined over the circular disk.

(v) The major trends observed on specific 2D flat metallic nanostructures mostly

generated by electron-beam lithography have recently been revisited and classified as the result of two major components: surface and edge modes of a semi-infinite metallic thin film – Ag - deposited on the thin dielectric substrate Si3N4 – [88].

VI.3 From 2D to 3D : nanocubes Silver nanocubes with a flat face deposited on a thin supporting layer (Si 3N4 or mica) practically constitute ideal test specimens to investigate the 3D distribution of the surface plasmon modes and the potentially disturbing role of the substrate. In most cases, they are deposited with a (100) surface lying on the supporting film. In the continuation of the results gathered for 1D and 2D nanostructures, they are supposed to exhibit corners, edges and faces modes. When explored with a primary electron beam, superposition effects between these modes are expected and one has to solve a 3D complex case to disentangle them. Furthermore, preliminary studies associating optical measurements on sets of nanocubes and simulations have shown that the presence of the support is responsible of a splitting of the peaks into a pair named “proximal” and “distal” with reference to the structure features in direct contact with the support or on the opposite face [89, 90]. An EELS study on an Ag cube of 60 nm side length deposited on Si3N4 and of one of 90 nm on mica has allowed to identify three main features (two peaked at the corners and one on the

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edges) and to highlight the role of the size of the particle, of the substrate and of the local environment such as the presence of contamination induced by the primary beam, to modify the energy, the intensity and the position of these peaks [91]. Later, a more refined analysis has been performed by Nicoletti et al. [92] with a real 3D reconstruction of the plasmon modes by a combination of EELS spectrum-imaging, of tilting series and of dedicated data processing for electron tomography. In each one of the EELS spectra acquired over an energy-loss window from 1 to 4 eV for all scanned pixels over an area encompassing a 100 nm cube and for all tilted images (5 angles from 0° to 60° at 15° intervals), several components labeled as  to  have been identified with a blind source separation method, fitted and measured. A compressed sensing tomographic algorithm has then been used to provide the 3D views shown in figure 18, which confirms that the  component is a bottomcorner localized surface plasmon resonance (LSPR),  a mixture of top-corner and bottomedge LSPR,  a mixture of top-corner and bottom-face LSPR,  a top- and side-edge LSPR and  a top- and side-face one. A small sketch is added which summarizes how the substrateinduced hybridization can split the corner, edge and face modes valid for an isolated cube into proximal (close to the surface) and distal (away from the substrate) components. One of the issues left by this approach was the physical origin of the 3D reconstructed signal, although almost at the same time a theoretical paper showed the possibility to recover, for objects small enough to be interpreted in the quasistatic approximation, either the eigen potentials or the eigen charges distributions [53]. Following a conceptually similar approach,Collins et al. [56] showed experimentally the possibility to measure in three dimension a physical observable, namely the eigen charges distributions. On their own side, Hohenester et al. [53] had theoretically demonstrated the possibility to measure, again through tomographic approaches, the full, vectorial and three dimensional Electro Magnetic Local Density of States.

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Figure 18 : 3D visualization of the LSPR components of a silver nanocube, displayed as voxel projections of the reconstructed 3D volumes. The colour bar indicates the LSPR intensity. The sketch (bottom right) illustrates how the coupling between the lower (100) face of the Ag nanocube and its 30nm thick Si3N4 substrate induces a splitting of the modes in the isolated cube (corner, edge, face) into proximal and distal components (from Nicoletti et al. [92])

Let us briefly mention the interesting case of star-shaped nanoparticles which constitute another interesting type of 3D nano-objects but without obvious symmetry. Very different morphologies ranging from spheroids to well-developed gold nanostars with clearly protruding individual arms, have been grown in gold and their SP resonances investigated using the STEM-EELS method [93]. It has been shown that essentially two groups of SP modes are detected: a first one is localized around the core of the stars and has an energy slightly below the quasi-static dipolar mode of a gold nanosphere (about 2.0 eV). As for the second group, the modes are localized at the extremity of the nanostar arms, with varying energies depending on the arm length and on the local curvature at the tip. These modes are weakly coupled between them and represent local answers associated with field enhancements.

VI.4 The quantum limit The previous case raises an obvious question: what is the smallest object size for which the classical description in terms of fields, of dielectric constants and of Maxwell equations breaks down. As a matter of fact, most of the early works addressing this topic have been performed on ensemble of nanoparticles using optical techniques. It is therefore not surprising that owing to the difficulty of analyzing weaker and weaker signals as the size of the particles is reduced from the 10 nm level down to 1 or 2 nm, that “redshifts” as well as “blueshifts” of the LSRP have been reported. In particular, optical absorption resonances measured on mass filtered free ionized clusters of alkali metals (Kn+, Lin+) have exhibited a redshift of the resonance attributed to the Mie absorption on small spheres, typically of 0.3 eV between Li1500+ and Li150+ [94, 95]. These measurements of the optical response of lithium clusters have confirmed the macroscopic dielectric function as a pertinent parameter to interpret the results. The redshift of the Mie resonance energy, as the cluster size decreases, is then attributed to the “spill out” of the electron density outside of the particle. Furthermore, this type of study is the only one really dealing with free clusters or nanoparticles without any interaction with a support or an embedding material. When considering supported individual nanoparticles, very few detailed EELS studies have been realized on well-defined nano-objects deposited on very thin supporting layers. Early experiments have investigated the evolution of the energy of the surface plasmon mode measured at glancing incidence on metallic spheres (Ga in [19], Ag in [22]) of decreasing size down to a diameter of 2 nm. The first ones for Ga report a “redshift” of about 1 eV (between 9 and 8 eV) below 10 nm, the second ones for Ag report a decrease of a few tenths of eV to 3.1 eV at about 8 to 10 nm, followed by a rise to values (3.6 eV) higher than that of the

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larger particles (3.5 eV). Let us remind that classically in this range of sizes, the energy and line shape of each mode (see V.2 above) are independent of the size of the object, but the weight of the various modes can depend on the size and also of the trajectory of the incident electron (impact parameter, velocity). As for microscopic theories, an accurate knowledge of the surface layer, the importance of which is increasing when the particle becomes smaller, is required and was missing at the time of these early studies, so that no quantitative agreement was established between experiments and theory. This subject has been addressed again with much more comprehensive and refined data acquired on a selection of ligand-free silver nanoparticles characterized by high resolution TEM together with quantum mechanical calculations [96], suggesting a comment entitled “Plasmons go quantum” [97]. In their paper, Scholl et al. [96] have recorded the EELS spectra at two positions (center and surface) of individual nanospheres with diameters ranging from 20 nm to less than 2 nm. They demonstrate that the LSPR mode excited at the surface, shifts towards higher energy values by typically 0.5 eV when the diameter is reduced from 10 to below 2 nm. The bulk Ag plasmon clearly visible when the beam is focused at the center also shifts but marginally and cannot be made visible by itself for smallest sizes (below 5nm in diameter), in which case it seems to merge with the LSPR mode. The observed shift is explained with a quantum based calculation (either analytical or based on the DFT theory) of the size dependent permittivity, in which the quantum nature of the conduction electrons emerges. The quantum limit will also be more extensively discussed in the following chapter when quantum electron tunneling may take place between two protruding and closely spaced spherical tips.

Vll. Resonant surface plasmons on nanoparticles in interaction In real systems designed for applications in photonics, it is important to build and couple many (or at least two) individual nano-objects, thus opening the way to manipulate light at the nanometer scale with metal nanostructures as nano-optical components. VII.1 Hybridization of plasmon modes In a seminal paper, Prodan et al. [98] have introduced an elegant description of the electromagnetic interaction between “free” LSPRs on neighboring nanostructures, exhibiting a strong analogy with molecular orbitals which leads to the mixing (or hybridization), splitting and shifts of the plasmon energies of the individual and independent components, see figure 19a. The distance between the interacting nanoparticles must be smaller than the critical decay length of the electric field perpendicularly to their outer surfaces in order to ensure sufficient field interaction between them.

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Figure 19 : (a) Definition and (b) characteristics (charges and fields) of the hybridization of the two basic dipolar surface plasmon modes (m=1) between adjacent nanorods

A simple case consists of a dimer of two closely spaced spheres where the hybridization of plasmonic modes can be investigated as a function of their separation [99]. It is predicted and demonstrated that the LSPRs of the two particles couple to give rise to two energy split modes: the one with lowest energy (“bonding” mode) corresponds to an asymmetric distribution of charges on the spheres with respect to their midpoint and consequently a strong finite dipole moment along the direction between their centers. It is commonly referred as a “bright” mode because it can easily be excited by incident light. The electric field in the gap is directed from one sphere to the other and therefore is largely invisible in an EELS experiment. In the second mode (“antibonding” mode), at higher energy, the distribution of charges is symmetric with respect to the midpoint, and the electric field there is perpendicular to the line between the centers of the two spheres. There is no net dipole moment and it is thus referred as an optically “dark” mode, but it is the mode which is most intense in the EELS images because then the electric field in the gap is mostly parallel to the trajectory of the incident high energy electron, see figure 19b. These coupling and hybridization effects have been practically investigated in a number of geometries for the individual structures: nanorod dimers [73], split nanowires [77], sphere dimers [99], triangular platelets facing tip to tip in a bowtie configuration [100}, families of holes [101, 102]. Figure 20 below, extracted from [77], illustrates the general remarks there above on a practical situation with two long Au wires of 800 nm separated by a gap of only ≈ 8 nm. Using the STEM-EELS technique, it displays a 2D spectrum image in which one axis is a line along the dimer and the other one the energy loss encompassing a window from 0.3 to 2.8 eV. The dipolar longitudinal mode n = 1 (indexed as l =1 in this specific figure) is clearly split into two components with that at higher energy (0.5 eV) showing a very intense peak in the gap between the wires. The same behavior is observed for higher order modes (2 and 3). Note that the transverse mode (around 2.2 eV) is visible all along the wires but absent in the gap.

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Figure 20 : (a) Plasmonic intensity map along the Au dimer shown in the HADF image. Schematics on top represent the indexation of the identified split modes (n=1, 2, 3). (b) EELS spectra recorded at the two ends of the split nanowire (blue and green) and in the gap (red). Courtesy I. Alber et al. from [77]

The coupling effects between holes drilled in homogeneous silver thin foils has been shown to exhibit similar hybridization behaviors, in particular between aligned holes or holes assembled in triangular configurations [101]. In the case of an heptamer distribution of parallel holes (six equally spaced around a central one), quite new modes have been identified [102]. In particular, a “toroidal” mode corresponds to a distribution of electric field lines circling between the central cylindrical hole and its parallel neighbors, while the associated magnetic field lines circle perpendicularly to the holes in the sample volume between the holes thus behaving as a ring. This is a nanosized equivalent of a solenoid shaped as a ring.

VII.2 From classical to quantum plasmonics across subnanometer gaps In order to further understand the potential transition from classical to quantum behavior, the influence of reducing the gap between the nanostructures down to the subnanometer regime and to the contact has been investigated in different geometries: (a) dimer of spheres; (b) bowtie made of facing triangular platelets; (c) facing nanocubes with connecting molecules. Similarly to the extension from the 1D nanorod to the 2D triangular nanoplatelet in the single isolated nanoparticle case (see VI.1 and VI.2 above), dimers of triangles have first been built either with a non negligible gap (≈25 nm) or with overlapping tips [100]. In the first case, EELS maps exhibit intensity peaks at tips, edges and in the gap of the bowtie.

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Simulations directly confirm the interpretation of the observed patterns in terms of dipolar bright mode at lowest energy but of weak intensity in the 1.3 -1.4 eV window, while the strongest EELS peak at 1.5 eV corresponds to the dipolar dark mode and points out in the gap, thus confirming the general splitting of resonance modes induced by hybridization. The situation is then made more complex for quadrupolar modes because of partial overlaps in space and in energy. In the connected dimer case, electrons are free to flow from one triangle to another, leading to charge-transfer plasmons (CTP). Three main excitations are visible but the corresponding charge density distributions are obviously very different when the triangles are connected. The lowest energy mode predicted by simulations is then a single dipole spanning the whole doublet of triangles with one of them positively charged and the other negatively, which has not been observed because of its position in energy lying too low for the used experimental set-up. The transition between nanoparticles from closely separated with sub-nm gaps to contact (joined with a bridge of increased width) has been further studied for the spherical case [103, 104] and for the bowtie one [105]. For silver spheres, they are in situ displaced by the primary electron beam, so that the inter-distance between them can be controlled externally. As for the gold bowties, a set of different specimens is a priori elaborated by electron beam lithography (with different values of the gap d or of the width of the connecting bridge). As the case of spheres is better suited to easily grasp the important features of the transition, figure 21 (issued from [104]) shows a selection of spectra recorded when the beam is positioned at the extremity of the dimer, for couples of spheres coming into contact. In these spectra, peaks (i) and (iii) are clearly visible when the spheres are well separated and they respectively correspond to the antibonding dark and to the bonding bright mode with the charge configuration shown on the right. Peak (ii) only appears when the gap becomes quite small at interatomic distances (≈ 0.3 nm) and gradually reduces when the overlap increases. It is attributed to the tunneling current before particles are in contact. As for peak (iv), it only appears at contact and gradually increases and shifts. It is a charge transfer plasmon (CTP) mode with its related current between the two spheres, as a precursor of the standard dipolar longitudinal mode for a dimer shown to be consistent with the dipolar mode on the right.

Figure 21 : EELS spectra recorded with the beam position marked on the HADF image, from an Ag dimer during the transition from tunneling regime ( curve A and top right scheme) to nanocontact (curves B, C, D and bottom right scheme) showing the appearance of the CTP (peak iv), from [104]

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The conclusion of these studies is that tunneling charge transfer plasmons and classical dark and bright plasmon modes can be monitored simultaneously, pleading for the coexistence of classical and quantum behaviors. In order to predict and interpret the bridging of classical and quantum plasmonics in such conditions, theoretical developments have proposed a quantum-corrected model [106]. It points out a tunneling regime for 0.1nm ≤ d ≤ 0.5 nm in which the electron transfer neutralizes the high charge densities on the opposite faces of the junction, thus reducing the strong field accumulation in the gap and therefore responsible for the observed continuous and progressive transition between the contact and noncontact regimes. A development of this theoretical description has recently been proposed [107] to explain the origin at larger gaps of the tunneling between the facing particles leading to a CTP for non contact geometries. It involves a Fowler-Nordheim tunnel mechanism across a barrier of potential triangularly shaped by the presence of a strong electric field (typically of the order of 1010 V/m in the gap) instead of the classical tunnel effect across a barrier of constant height. In order to investigate the dependence of the tunneling charge transfer plasmon (tCTP) at larger length scales, Tan et al have fabricated specific plasmonic nanoresonators made of silver nanocubes face to face bridged by self-assembled arrays of molecules of different structure and length [108]. The non-damaging approach of measuring the response of these nanodevices when exciting them with the incident electron-probe aloof one of the external faces has permitted to identify and to measure the CTP tunneling through the molecular bonds as compared to those opened through vacuum. Changing the nature of the molecules has modified the plasmon-induced transfer of frequency from typically 0.6 to 1.2 eV working at interparticle distances up to 1,3 nm and thus introducing some new perspectives of combining molecular electronics with nanoplasmonics and photonics.

VII.3 Towards complex morphologies of practical interest It is now well demonstrated that EELS mapping constitutes a highly efficient tool for investigating and controlling the many different plasmonic modes that can be generated on nano-sized structures of variable shape, size and interactive environment. There is therefore no surprise that the technique can and will play a fruitful role in the broad field of nanoplasmonics, which has therefore become an important component in nanophotonics. It is our pleasure, when approaching the end of the present review, to introduce a couple of such applications.

(i) Photonic metamaterials

The U-shaped nanorod or split-ring resonator (SRR) shown in figure 17 above is also known as a “meta-atom” or a photonic atom, i.e. the building block of a metamaterial. Metamaterials are artificial structures exhibiting extraordinary properties not existing in nature, such as negative optical indexes over a given range of frequencies, and in the

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present case in the visible domain. The EELS spectra and maps recorded on individual isolated “meta-atom” nanostructures made of Au or Ag have demonstrated the existence of several SPR modes typically between 1 and 4 eV and shown their size-dependence [81, 109]. When building a device made of many similar such SRR units, the interactions between neighboring meta-atoms become dominant. In the case of two of them sitting side by side, the hybridization again splits the single mode into a low energy bright mode with opposite charges facing together on closely spaced arms and a high energy dark one with similar charges and strong Ez on closely spaced arms, this latter one being much more intense in EELS maps. As demonstrated in [110], the situation is slightly different between dimers in an on-top configuration with respect to the side-by-side one and generally speaking the hybridization is reduced. Finally for a large array of meta-atoms, it is not surprising that, similarly to the transition between electron states from a two (or 4) atoms system into a large N one, the discrete levels merge into a quasi-continuum band. EELS spectra then reveal a major broadened single peak corresponding to the most intense one in the dimer side by side situation. It is spatially concentrated between neighboring SRRs and homogeneously distributed over the whole array, but at the corners and along the sides of the array, the number of neighboring SRR is reduced and it induces different EELS intensity distributions corresponding to different electro-magnetic field distributions (see figure 22).

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Figure 22: EELS mapping of the SPR resonance at 0.55 eV, respectively in the center (bottom) and in the top left corner (top) of a SRR array made of 100x100 units, scale bar= 200nm (extracted from [110]) (ii) Disordered materials

Instead of the very regularly ordered array of nanostructures, and typically of “meta-atoms” described above, let us now consider random distributions of separated metallic nanoparticles on a supporting thin foil. When their coverage increases, one observes that their density and size also increase, until they coalesce into disordered arrangements and morphologies which at the percolation threshold merge into rather continuous films with arms and holes of quite variable shape. An universal behaviour for disordered materials is to exhibit localization effects, and one of them is the appearance of specific optical properties, such as “hot spots” associated to localized surface plasmons and strongly condensed EM fields. They were first visualized with sub-wavelength resolution, by near-field scanning optical microscopy and interpreted in terms of giant fluctuations of the local electric field in a fractal geometry [111, 112]. In order to investigate with a high level of spatial resolution

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and over a broad spectral range the occurrence of these “hot spots”, surface plasmon EELS mapping has been realized on nanoporous films of gold and silver [113] and on semicontinuous films of silver embedded in silicon nitride [114]. In this latter study, EELS maps connect without ambiguity the appearance of spectral features to their detailed spatial localization. When the morphology of the specimen approaches the percolation regime, localized surface plasmon modes appear at low energies between 0.8 and 1.5 eV, their number increases together with their field strength and confinement. As shown in figure 23, the tools developed for extracting the characteristics of wellidentified modes, i.e. central energy, spectral FWHM, position over the specimen and substrate and spatial extension, are quite useful. The present STEM-EELS technique therefore confirms the existence of the predicted “hot spots” in the infra-red spectral range for fractal geometries, it also suggests that they can result from the mixture of different eigenmodes but does not provide any clear proof of an obvious correlation between the local morphology of the film and the recorded plasmonic pattern.

Figure 23 : EELS mapping of a couple of SP modes identified over a local area of a silver foil embedded in a silicon nitride layer, exhibiting a morphology close to that of the percolation regime. General and local views in HADF, spectra recorded at two positions marked in red and blue on the HADF image. Characteristics (energy, FWHM, amplitude) of the two modes corresponding to the peaks shown by arrows in the EELS spectra (from [114]).

(iii) Enhancing the plasmon quality factor :

For many practical reasons, photonics applications of metallic structures as localized resonators or light guides require systems of high quality factors (Q) and therefore plasmon peaks as sharp as possible with weak damping. As introduced earlier in this review (see § VI),

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there exist intrinsic upper limits associated with the dielectric properties, so that in silver plasmonic nanostructures Q culminates at 70 around 1.5 eVand at 20 around 1.7 eV in gold ones [69]. However, many other factors can contribute to reduce it, such as radiation damping for large size objects and crystal defects or contact with the support even for smaller objects. Before addressing practically the challenge of remedying these detrimental contributions, it is necessary to measure the quality factor on individual nanostructures and therefore to correlate Q with the local topography at the nm scale. Using a monochromatized beam typically of 60 meV FWHM together with a well-suited bin gain averaging, Bosman et al. [115] have recorded plasmon peaks with sufficiently high SNR so that their width can be accurately measured when investigating complex nanostructures at different positions. Consequently, their results incorporating many individual nanoparticles of different shapes, sections, lengths exhibit a Q curve culminating at 20 for gold nanoparticles very close to the intrinsic dielectric coefficient maximum. This method has then been used to monitor how the Q factor of lithographically defined nanostructures can be enhanced after some specific encapsulated annealing [116].

VIII.

Summary and perspectives

In this review we have demonstrated how much the techniques derived from EELS spectroscopy in an electron microscope (both STEM-EELS and EFTEM) nowadays constitute a most efficient tool to investigate the characteristic electron excitations and accompanying electromagnetic fields at surfaces and interfaces. This has been supported with examples involving quite diversified situations in 1, 2 and 3 dimensions, probing interactions at the ultimate sub-nm scale and covering a spectral domain significantly broader than that accessible with a single optical technique. We have also at some points introduced hints of the enlarged potential brought by the combination of pure EELS techniques with CL ones. Furthermore, the close resemblance and minor differences between both techniques have been worked out very recently on a theoretical basis comparing the full electromagnetic local density of states (EMLDOS) and the radiative one [54]. There is no surprise that these techniques have established themselves, within a relatively short period of time, as key routes for the collection of useful information in the rapidly expanding domain of nanoplasmonics and of nanophotonics. Their impact will therefore accompany the development of new objects involving nanoscale sizes of practical interest in many domains from energy to communication and therapy. For instance, the association of spectroscopies and maps involving electrons and/or photons will be of great assistance when coupling electronics and optics in a single device, such as associating quantum dots as local light sources and metallic wires as photonic guides. In all these cases, further developments in instrumentation, data processing and theoretical modeling will largely be guided by the progress in the realization of new structures and the access to new physical properties. As a first example, what will be the most beneficial materials in the near future? A very recent review [117] focuses on alternative materials, such as transition metal nitrides, for localized surface plasmon applications. The techniques described above will undoubtedly

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be of great assistance as they associate structural and analytical characterization over wide ranges of scales both in dimensions and in energy (or wavelengths). As a conclusion in the context of the present review essentially dedicated to the EELS imaging techniques, it seems to us important to point out a few perspectives which will be, for sure, thoroughly explored within the next few years. An obvious one lies in the immediate continuation of the present efforts for improving the quality of the recorded data. In particular, the newly developed monochromated STEM with a 30 meV-wide, atom-sized electron probe designed and built by Krivanek et al [118] constitutes a generation of instruments particularly well suited to investigate SP lifetimes over a broad range of energies and on reduced size devices. It has already demonstrated its ability in recording phonon losses in the 100 meV range with a zero-loss peak as narrow as 10 meV [119], see figure 24. Furthermore, in this paper, the authors also report a measurement of the vibrational signal in the aloof geometry at distances up to 100 nm from the surface. We have thus access to phonon-polariton modes coupling vibrations of the ions at the surface with the associated electromagnetic field, similarly to the plasmon-polaritons concerning electron vibrations. This is surely a gateway to the yet largely unexplored nanophononics domain, at least with electron beams and their associated high spatial resolution. One step further, the coupling between optical phonons and surface plasmons is becoming, in the infra-red domain, a broad field for future investigation. For example, graphene nanoribbons of defined width, exhibit tunable plasmon resonances which can be coupled with surface phonons of the underlying silicon oxide support [120, 121 ], thus offering access to potentially sensitive and frequency-selective photodetectors.

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Figure 24 : EELS spectrum displaying a 18 meV wide optical phonon peak in h-BN at 173 meV recorded with a 14 meV wide zero loss peak (courtesy O. Krivanek et al [ 119])

Let us finally mention the newly opened access to time-resolved studies pioneered by Ahmed Zewail and coworkers at Caltech [122 – 125]] and its potential outputs. The basic idea of their technique is to realize in time and space the overlap of the wave packet associated to a single-electron of high energy with the evanescent electromagnetic field generated by an intense femtosecond (fs) pulse of light around a nanostructure, such as a carbon nanotube or silver nanowire. A typical delay time between both pulses is of a few ps maximum. Within this configuration schematically shown in figure 25, the external pulse of light with a given wavelength (or energy) generates resonant charge oscillations and associated evanescent EM fields, which the incoming electron may detect. Consequently an energy analysis of the transmitted beam having intersected this field exhibits a poissonian distribution of peaks incremented with the characteristic energy of the laser photons, which may appear as well as losses as gains. This was named PINEM (for photon-induced near-field electron microscopy) by the authors and it has been fruitfully used for direct space-time imaging of localized fields at surfaces and interfaces. The theory describing the interaction of swift electrons with strong evanescent light fields has been developed in [126, 127] to explain the experimental results shown in the experiments at Caltech. But it has also introduced the possibility of quantum coherent manipulation of electron energy distributions deviating from the Poissonian distribution and exhibiting a behaviour of Rabi oscillation type, which has just been reported [128, 129]

Figure 25 : Generation of EEGS (electron energy gain spectroscopy) when firing the STEM electron beam in the close vicinity of a metallic nanoparticle illuminated by a pulse of light. The time delay between both light pulses on the tip in the EM gun and on the specimen must be shorter than typically a few ps. (Top) : schematics of the experiment (to be compared with figure 9 above).

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(Bottom) : spectra of the energy distribution of the transmitted electrons showing as well energy gains and losses with steps of energy equal to that of the impinging laser pulses when the two light pulses coincide in time (from [122])

As a matter of fact, these experiments only involve the nanostructure as the necessary ingredient to transfer energy and momentum between free electrons and photons. One step further has been cleared when the wavelength of the laser pulse is in accordance with that of a resonant SP mode on the metallic nanostructure. This was achieved by Piazza et al [130]. The wavelength of the IR laser pulse corresponds to the resonant energy of a SP on the illuminated nanoparticle, as shown in figure 26. An electron energy gain map at this energy clearly displays the spatial interference pattern along the silver nanorod. This experiment will be without any doubt extended with the use of a scalable laser wavelength over the energy window of interest. This novel approach has the advantage of generating and controlling the SP modes created by the laser beam over an extended range of wavelengths and polarizations while mapping them with the electron beam, thus giving access to a much richer collection of SP patterns and confined electromagnetic fields.

Figure 26: Generation and mapping of a surface plasmon polariton (SPP) pattern (in the present case, the m = 11 longitudinal mode) on an isolated silver nanowire deposited on a very thin graphene layer. Left: schematic representation of the experimental configuration. Right: (a) an illustrative spectrum showing that the sum of energy gain peaks is used for realizing the energy filtered PINEM image; (b) Experimental PINEM image of a Ag nanowire (800 nm of length, 45 nm of radius) illuminated with a s-polarized laser pulse of wavelength 800 nm and polarization parallel to the long axis, time delay between electron and photon pulses t = 0 ; (c) Corresponding finite element simulation of the SPP field IEzI in the plane 10 nm above the wire. Scale bar = 1 m (from [130]).

In the above depicted experiments, the pump-probe approach offers optimum conditions to investigate with superior time resolution the electron-photon interactions in an evanescent

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field generated around a nanostructure. As pointed out by Howie [131], substantial attractive possibilities should also be offered to the combination of the very high spatial resolution of EELS with the spectral resolution of optical techniques, when using a tuned continuous laser illumination. It would indeed boost the probabilities of detecting excitation modes in the low energy loss domain at the price of the loss in time resolution. As a conclusion, when ”photons and electrons team up” as mentioned by Garcia de Abajo [132], there is for sure a rich field of experimental and theoretical science to be explored.

Acknowledgements This review basically relies on studies realized in the STEM group at the Laboratoire de Physique,des Solides in Orsay, over typically three decades. Consequently many students, post-docs and collaborators have been involved and have realized successive developments which have all contributed to this new plasmonic “euphoria” (as it has been designed by Archie Howie in one recent publication) : let us first mention, thank and congratulate the involved Ph.D. students starting from 1985 Mustapha Achèche, Daniel Ugarte, Dario Taverna, Jaysen Nelayah, Stefano Mazzucco, Guillaume Boudarham, Arthur Losquin, Romain Bourrelier and Zaccharia Mahfoud. The contribution to CL developments of Luiz F Zagonel, when he was a post doc in the team, iis worth emphazing as well. The whole team of researchers and engineers has been permanently creating new technical developments and innovative software. Let us thank in particular Paul Ballongue, Marcel Tencé, Mike Walls, Nathalie Brun and Katia March. Many collaborators have brought decisive contributions to the development of theoretical tools for the modeling of the experimental data, it is our great pleasure to mention there Javier Garcia de Abajo at ICFO (Spain) and Luc Henrard at Namur University (Belgium). The access to well suited specimens has been made possible thanks of many colleagues, special thanks are due to Luiz Liz-Marzan and collaborators at San Sebastian (Spain). Financial support has been permanently brought by CNRS and Université Paris Sud XI. The authors acknowledge financial support from the European Union under the Framework 7 program under a contract for an Integrated Infrastructure Initiative. The research leading to these results has received funding from the European Union Seventh Framework Programme [FP7/2007-2013] under Grant Agreement No. 312483 (ESTEEM2)

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highlight -Up to date review on plasmon mapping with EELS -Gives an historitical view on the subject, as well as reviewing very last developments

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