Modelling the long-term fairness dynamics of data-driven targeted help on job seekers.

The use of data-driven decision support by public agencies is becoming more widespread and already influences the allocation of public resources. This raises ethical concerns, as it has adversely affected minorities and historically discriminated groups. In this paper, we use an approach that combines statistics and data-driven approaches with dynamical modeling to assess long-term fairness effects of labor market interventions. Specifically, we develop and use a model to investigate the impact of decisions caused by a public employment authority that selectively supports job-seekers through targeted help. The selection of who receives what help is based on a data-driven intervention model that estimates an individual's chances of finding a job in a timely manner and rests upon data that describes a population in which skills relevant to the labor market are unevenly distributed between two groups (e.g., males and females). The intervention model has incomplete access to the individual's actual skills and can augment this with knowledge of the individual's group affiliation, thus using a protected attribute to increase predictive accuracy. We assess this intervention model's dynamics-especially fairness-related issues and trade-offs between different fairness goals- over time and compare it to an intervention model that does not use group affiliation as a predictive feature. We conclude that in order to quantify the trade-off correctly and to assess the long-term fairness effects of such a system in the real-world, careful modeling of the surrounding labor market is indispensable.

Excitation of long-wavelength surface optical vibrational modes in films, cubes and film/cube composite system using an atom-sized electron beam.

Using spatially resolved Electron Energy-Loss Spectroscopy, we investigate the excitation of long-wavelength surface optical vibrational modes in elementary types of nanostructures: an amorphous SiO2 slab, an MgO cube, and in the composite cube/slab system. We find rich sets of optical vibrational modes strongly constrained by the nanoscale size and geometry. For slabs, we find two surface resonances resulting from the excitation of surface phonon polariton modes. For cubes, we obtain three main highly localized corner, edge, and face resonances. The response of those surface phonon resonances can be described in terms of eigenmodes of the cube and we show that the corresponding mode pattern is recovered in the spatially resolved EELS maps. For the composite cube/substrate system we find that interactions between the two basic structures are weak, producing minor spectral shifts and intensity variations (transparency behaviour), particularly for the MgO-derived modes.

Novel Modal Approximation Scheme for Plasmonic Transmission Problems.

The concept of resonances and modes for the description of particle plasmons has recently received great interest, both in the context of efficient simulations as well as for an intuitive interpretation in physical terms. While resonance modes have been successfully employed for geometries whose optical response is governed by a few modes only, the resonance mode description exhibits considerable difficulties for larger nanoparticles with their richer mode spectra. We analyze the problem using a boundary element method approach together with a Mie solution for spherical particles, and identify the fixed link between the electric and magnetic components of the resonance modes as the main source for this shortcoming. We suggest a novel modal approximation scheme that allows us in principle to overcome this problem.

3D Imaging of Gap Plasmons in Vertically Coupled Nanoparticles by EELS Tomography.

Plasmonic gap modes provide the ultimate confinement of optical fields. Demanding high spatial resolution, the direct imaging of these modes was only recently achieved by electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). However, conventional 2D STEM-EELS is only sensitive to components of the photonic local density of states (LDOS) parallel to the electron trajectory. It is thus insensitive to specific gap modes, a restriction that was lifted with the introduction of tomographic 3D EELS imaging. Here, we show that by 3D EELS tomography the gap mode LDOS of a vertically stacked nanotriangle dimer can be fully imaged. Besides probing the complete mode spectrum, we demonstrate that the tomographic approach allows disentangling the signal contributions from the two nanotriangles that superimpose in a single measurement with a fixed electron trajectory. Generally, vertically coupled nanoparticles enable the tailoring of 3D plasmonic fields, and their full characterization will thus aid the development of complex nanophotonic devices.

Tomographic imaging of the photonic environment of plasmonic nanoparticles.

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

Mapping vibrational surface and bulk modes in a single nanocube.

Imaging of vibrational excitations in and near nanostructures is essential for developing low-loss infrared nanophotonics, controlling heat transport in thermal nanodevices, inventing new thermoelectric materials and understanding nanoscale energy transport. Spatially resolved electron energy loss spectroscopy has previously been used to image plasmonic behaviour in nanostructures in an electron microscope, but hitherto it has not been possible to map vibrational modes directly in a single nanostructure, limiting our understanding of phonon coupling with photons and plasmons. Here we present spatial mapping of optical and acoustic, bulk and surface vibrational modes in magnesium oxide nanocubes using an atom-wide electron beam. We find that the energy and the symmetry of the surface polariton phonon modes depend on the size of the nanocubes, and that they are localized to the surfaces of the nanocube. We also observe a limiting of bulk phonon scattering in the presence of surface phonon modes. Most phonon spectroscopies are selectively sensitive to either surface or bulk excitations; therefore, by demonstrating the excitation of both bulk and surface vibrational modes using a single probe, our work represents advances in the detection and visualization of spatially confined surface and bulk phonons in nanostructures.

Mapping the local particle plasmon sensitivity with a scanning probe.

We probe the local sensitivity of an optically excited plasmonic nanoparticle by changing the local dielectric environment through a scanning glass fiber tip. Recording the particle plasmon scattering spectrum for each tip position allows us to observe spectral resonance shifts concurrent with changes in scattering intensity and plasmon damping. For the tip-induced spectral shifts we find the strongest sensitivity at the particle edges, in accordance with the spatial plasmonic field profile. In contrast, the strongest sensitivity occurs at the center of the particle if the scattering intensity is probed at the short wavelength slope of the plasmon resonance instead of the resonance position. This bears important implications for plasmonic sensing, in particular when done at a single light wavelength.

Plasmon modes of a silver thin film taper probed with STEM-EELS.

By focusing propagating surface plasmons, electromagnetic energy can be delivered to nanoscale volumes. In this context, we employ electron energy loss spectroscopy in a scanning transmission electron microscope to characterize the full plasmonic mode spectrum of a silver thin film tapered to a sharp tip. We show that the plasmon modes can be ordered in film and edge modes and corroborate our assignment through supplementary numerical simulations. In particular, we find that the focused plasmon field at the taper tip is fueled by edge modes.

Full Three-Dimensonal Reconstruction of the Dyadic Green Tensor from Electron Energy Loss Spectroscopy of Plasmonic Nanoparticles.

Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in terms of optical quantities, such as the photonic local density of states, remains challenging. Recent work has demonstrated that, under restrictive assumptions, including the applicability of the quasistatic approximation and a plasmonic response governed by a single mode, one can rephrase EELS as a tomography scheme for the reconstruction of plasmonic eigenmodes. In this paper we lift these restrictions by formulating EELS as an inverse problem and show that the complete dyadic Green tensor can be reconstructed for plasmonic particles of arbitrary shape. The key steps underlying our approach are a generic singular value decomposition of the dyadic Green tensor and a compressed sensing optimization for the determination of the expansion coefficients. We demonstrate the applicability of our scheme for prototypical nanorod, bowtie, and cube geometries.

Correlated 3D Nanoscale Mapping and Simulation of Coupled Plasmonic Nanoparticles.

Electron tomography in combination with electron energy-loss spectroscopy (EELS) experiments and simulations was used to unravel the interplay between structure and plasmonic properties of a silver nanocuboid dimer. The precise 3D geometry of the particles fabricated by means of electron beam lithography was reconstructed through electron tomography, and the full three-dimensional information was used as an input for simulations of energy-loss spectra and plasmon resonance maps. Excellent agreement between experiment and theory was found throughout, bringing the comparison between EELS imaging and simulations to a quantitative and correlative level. In addition, interface mode patterns, normally masked by the projection nature of a transmission microscopy investigation, could be unambiguously identified through tomographic reconstruction. This work overcomes the need for geometrical assumptions or symmetry restrictions of the sample in simulations and paves the way for detailed investigations of realistic and complex plasmonic nanostructures.

Local refractive index sensitivity of gold nanodisks.

We experimentally investigate the local refractive index sensitivity of plasmonic gold nanodisks by applying small polymer dots to selected disk sites by means of two-step lithography. Measured sensitivity profiles obtained from tracking the polymer-induced spectral shift of the plasmon modes are in excellent agreement with numerical simulation of both spectral sensitivity and the electric near field of the nanodisks. Based on the nanodisk sensitivity profile we tailor a sensitive and spatially uniform plasmonic sensor by capping the disk with a dielectric layer, thus restricting analyte access to the disk rim.

Plasmon Mapping in Au@Ag Nanocube Assemblies.

Surface plasmon modes in metallic nanostructures largely determine their optoelectronic properties. Such plasmon modes can be manipulated by changing the morphology of the nanoparticles or by bringing plasmonic nanoparticle building blocks close to each other within organized assemblies. We report the EELS mapping of such plasmon modes in pure Ag nanocubes, Au@Ag core-shell nanocubes, and arrays of Au@Ag nanocubes. We show that these arrays enable the creation of interesting plasmonic structures starting from elementary building blocks. Special attention will be dedicated to the plasmon modes in a triangular array formed by three nanocubes. Because of hybridization, a combination of such nanotriangles is shown to provide an antenna effect, resulting in strong electrical field enhancement at the narrow gap between the nanotriangles.

Optical near-field excitation at commercial scanning probe microscopy tips: a theoretical and experimental investigation.

A systematic study of the influence of the excitation angle, the light polarization and the coating thickness of commercial SPM tips on the field enhancement in an apertureless scanning near-field optical microscope is presented. A new method to optimize the alignment of the electric field vector along the major tip axis by measuring the resonance frequency was developed. The simulations were performed with a MNPBEM toolbox based on the Boundary Element Method (BEM). The influence of the coating thickness was investigated for the first time. Coatings below 40 nm showed a drastic influence both on the resonance wavelength and the enhancement. A shift to higher angles of incidence for the maximum enhancement could be observed for greater tip radii.

Tomography of particle plasmon fields from electron energy loss spectroscopy.

We theoretically investigate electron energy loss spectroscopy (EELS) of metallic nanoparticles in the optical frequency domain. Using a quasistatic approximation scheme together with a plasmon eigenmode expansion, we show that EELS can be rephrased in terms of a tomography problem. For selected single and coupled nanoparticles we extract the three-dimensional plasmon fields from a collection of rotated EELS maps. Our results pave the way for a fully three-dimensional plasmon-field tomography and establish EELS as a quantitative measurement device for plasmonics.

Spectral modifications and polarization dependent coupling in tailored assemblies of quantum dots and plasmonic nanowires.

The coupling of optical emitters with a nanostructured environment is at the heart of nano- and quantum optics. We control this coupling by the lithographic positioning of a few (1-3) quantum dots (QDs) along plasmonic silver nanowires with nanoscale resolution. The fluorescence emission from the QD-nanowire systems is probed spectroscopically, by microscopic imaging and decay time measurements. We find that the plasmonic modes can strongly modulate the fluorescence emission. For a given QD position, the local plasmon field dictates the coupling efficiency, and thus the relative weight of free space radiation and emission into plasmon modes. Simulations performed with a generic few-level model give very good agreement with experiment. Our data imply that the 2D degenerate emission dipole orientation of the QD can be forced to predominantly emit to one polarization component dictated by the nanowire modes.

Ultrafast strong-field photoemission from plasmonic nanoparticles.

We demonstrate the ultrafast generation of electrons from tailored metallic nanoparticles and unravel the role of plasmonic field enhancement in this process by comparing resonant and off-resonant particles, as well as different particle geometries. We find that electrons become strongly accelerated within the evanescent fields of the plasmonic nanoparticles and escape along straight trajectories with orientations governed by the particle geometry. These results establish plasmonic nanoparticles as versatile ultrafast, nanoscopic sources of electrons.

Tailoring spatiotemporal light confinement in single plasmonic nanoantennas.

Plasmonic nanoantennas are efficient devices to concentrate light in spatial regions much smaller than the wavelength. Only recently, their ability to manipulate photons also on a femtosecond time scale has been harnessed. Nevertheless, designing the dynamical properties of optical antennas has been difficult since the relevant microscopic processes governing their ultrafast response have remained unclear. Here, we exploit frequency-resolved optical gating to directly investigate plasmon response times of different antenna geometries resonant in the near-infrared. Third-harmonic imaging is used in parallel to spatially monitor the plasmonic mode patterns. We find that the few-femtosecond dynamics of these nanodevices is dominated by radiative damping. A high efficiency for nonlinear frequency conversion is directly linked to long plasmon damping times. This single parameter explains the counterintuitive result that rod-type nanoantennas with minimum volume generate by far the strongest third-harmonic emission as compared to the more bulky geometries of bow-tie-, elliptical-, or disk-shaped specimens.

Highly sensitive plasmonic silver nanorods.

We compare the single-particle plasmonic sensitivity of silver and gold nanorods with similar resonance wavelengths by monitoring the plasmon resonance shift upon changing the environment from water to 12.5% sucrose solution. We find that silver nanoparticles have 1.2 to 2 times higher sensitivity than gold, in good agreement with simulations based on the boundary-elements-method (BEM). To exclude the effect of particle volume on sensitivity, we test gold rods with increasing particle width at a given resonance wavelength. Using the Drude-model of optical properties of metals together with the quasi-static approximation (QSA) for localized surface plasmons, we show that the dominant contribution to higher sensitivity of silver is the lower background polarizability of the d-band electrons and provide a simple formula for the sensitivity. We improve the reversibility of the silver nanorod sensors upon repeated cycles of environmental changes by blocking the high energy parts of the illumination light.