Electron beams probe quantum coherence.

Scientists have traditionally employed superimposed mutually-coherent electron beams for holography and phase retrieval of electron wavepackets. However, recent theoretical exploration delves into the interaction of superposed electron beams with the matter. This investigation aims to elucidate long-range Coulomb correlations and quantum decoherence phenomena when electrons interact with their environment.

Electron Beam Induced Circularly Polarized Light Emission of Chiral Gold Nanohelices.

Chiral plasmonic nanostructures possess a chiroptical response orders of magnitude stronger than that of natural biomolecular systems, making them highly promising for a wide range of biochemical, medical, and physical applications. Despite extensive efforts to artificially create and tune the chiroptical properties of chiral nanostructures through compositional and geometrical modifications, a fundamental understanding of their underlying mechanisms remains limited. In this study, we present a comprehensive investigation of individual gold nanohelices by using advanced analytical electron microscopy techniques. Our results, as determined by angle-resolved cathodoluminescence polarimetry measurements, reveal a strong correlation between the circular polarization state of the emitted far-field radiation and the handedness of the chiral nanostructure in terms of both its dominant circularity and directional intensity distribution. Further analyses, including electron energy-loss measurements and numerical simulations, demonstrate that this correlation is driven by longitudinal plasmonic modes that oscillate along the helical windings, much like straight nanorods of equal strength and length. However, due to the three-dimensional shape of the structures, these longitudinal modes induce dipolar transverse modes with charge oscillations along the short axis of the helices for certain resonance energies. Their radiative decay leads to observed emission in the visible range. Our findings provide insight into the radiative properties and underlying mechanisms of chiral plasmonic nanostructures and enable their future development and application in a wide range of fields, such as nano-optics, metamaterials, molecular physics, biochemistry, and, most promising, chiral sensing via plasmonically enhanced chiral optical spectroscopy techniques.

Numerical investigation of sequential phase-locked optical gating of free electrons.

Recent progress in coherent quantum interactions between free-electron pulses and laser-induced near-field light have revolutionized electron wavepacket shaping. Building on these advancements, we numerically explore the potential of sequential interactions between slow electrons and localized dipolar plasmons in a sequential phase-locked interaction scheme. Taking advantage of the prolonged interaction time between slow electrons and optical near-fields, we aim to explore the effect of plasmon dynamics on the free-electron wavepacket modulation. Our results demonstrate that the initial optical phase of the localized dipolar plasmon at the starting point of the interaction, along with the phase offset between the interaction zones, can serve as control parameters in manipulating the transverse and longitudinal recoil of the electron wavefunction. Moreover, it is shown that the incident angle of the laser light is an additional control knop for tailoring the longitudinal and transverse recoils. We show that a sequential phase-locking method can be employed to precisely manipulate the longitudinal and transverse recoil of the electron wavepacket, leading to selective acceleration or deceleration of the electron energy along specific diffraction angles. These findings have important implications for developing novel techniques for ultrafast electron-light interferometry, shaping the electron wavepacket, and quantum information processing.

Spin-orbit interactions in plasmonic crystals probed by site-selective cathodoluminescence spectroscopy.

The study of spin-orbit coupling (SOC) of light is crucial to explore the light-matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin-orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin-orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin-orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin-orbit interactions.

Plasmonic vortices for tunable manipulation of target particles, using arrays of elliptical holes in a gold layer.

Here, we numerically prove that light with linear polarization can be coupled to surface plasmon polaritons at an elliptical hole perforated in a gold layer to generate plasmonic vortex (PV). Benefiting from the smooth variation of the minor to major ellipse axes, a gradual variation in the phase profile of the generated PV is achieved. Regarding this, three types of independent arrays of elliptical holes are presented, which can produce uniform and high quality PVs with different topological charges at the center of the arrays. The first array can produce PV with topological charges of + 1 and - 1, depending on the polarization orientation of the incident light. In the second one, the topological charge of the PV can be switched between 0 and + 2, by switching the polarization direction of the incident light. In the third array, a robust PV with topological charge of + 1 is generated independent of possible tolerances in the polarization orientation. In order to use the generated PVs for plasmonic tweezing application, there are side fringes around the central vortex of the arrays that should be eliminated. To produce a single vortex, we propose metal-insulator-metal (MIM) structures, screening excessive fringes and allowing the central PVs to leak out. It is also demonstrated by simulation that target particles, such as gold and polystyrene spheres of subwavelength dimensions, can be efficiently manipulated by our MIM designs, suitable for different applications including local mixing, and applying switchable torque or force to target particles to explore their complete elastic characteristics.

Inelastic electron scattering at a single-beam structured light wave.

In free space, electrons undergo inelastic scattering in the presence of ponderomotive potentials generated by light pulses and standing light waves. The resulting modulated electron energy spectrum can exhibit the formation of discrete energy sidebands when multiple light beams are employed. Here, we demonstrate the inelastic scattering of slow-electron wavepackets at a propagating Hermite-Gaussian light beam. The pulsed Hermite-Gaussian beam thus forms a ponderomotive potential for the electron with sufficient momentum components, leading to the inelastic scattering and subsequent formation of discrete energy sidebands. We show that the resulting energy-gain spectra after the interaction are strongly influenced by the self-interference of the electrons in this ponderomotive potential. This effect is observable across various wavelengths, and the energy modulation can be controlled by varying the electron velocity and light intensity. By utilizing the vast landscape of structured electromagnetic fields, this effect introduces an additional platform for manipulating electron wavepackets.

Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals.

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Mapping optical Bloch modes of a plasmonic square lattice in real and reciprocal spaces using cathodoluminescence spectroscopy.

Strong electron-light interactions supported by the surface plasmon polaritons excited in metallic thin films can lead to faster optoelectronic devices. Merging surface polaritons with photonic crystals leads to the formation of Bloch plasmons, allowing for the molding of the flow of polaritons and the controlling of the optical density of states for even stronger electron-light interactions. Here, we use a two-dimensional square lattice of holes incorporated inside a plasmonic gold layer to investigate the interaction of surface plasmon polaritons with the square lattice and the formation of plasmonic Bloch modes. Cathodoluminescence spectroscopy and hyperspectral imaging are used for imaging the spatio-spectral near-field distribution of the optical Bloch modes in the visible to near infrared spectral ranges. In addition, the higher-order Brillouin zones of the plasmonic lattice are demonstrated by using angle-resolved cathodoluminescence mapping. We further complement our experimental results with numerical simulations of the optical modes supported by the plasmonic lattice that helps to better resolve the superposition of the various modes excited by the electron beam. Next to previous works in this context, our results thus place cathodoluminescence scanning spectroscopy and angle-resolved mapping as complementary techniques to uncover the spatio-spectral distribution of optical Bloch modes in real and reciprocal spaces.

Quantum optics with swift electrons.

Stimulated and spontaneous interactions of electron wavepackets with optical near fields were explored with complementary techniques. In striking agreement with theory, scientists have demonstrated the dependence of spontaneous and stimulated quantum mechanical processes on the spatial distribution of optical modes.

Probing plasmonic excitation mechanisms and far-field radiation of single-crystalline gold tapers with electrons.

Conical metallic tapers represent an intriguing subclass of metallic nanostructures, as their plasmonic properties show interesting characteristics in strong correlation to their geometrical properties. This is important for possible applications such as in the field of scanning optical microscopy, as favourable plasmonic resonance behaviour can be tailored by optimizing structural parameters like surface roughness or opening angle. Here, we review our recent studies, where single-crystalline gold tapers were investigated experimentally by means of electron energy-loss and cathodoluminescence spectroscopy techniques inside electron microscopes, supported by theoretical finite-difference time-domain calculations. Through the study of tapers with various opening angles, the underlying resonance mechanisms are discussed. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'.

Strong Interaction of Slow Electrons with Near-Field Light Visited from First Principles.

Strong interaction between light and matter waves, such as electron beams in electron microscopes, has recently emerged as a new tool for manipulating the electron wave packets. Here, we systematically investigate electron-light interactions from first principles. We show that enhanced coupling can be achieved for systems involving slow electron wave packets interacting with plasmonic nanoparticles, due to simultaneous classical recoil and quantum mechanical photon absorption and emission processes. For slow electrons with longitudinal broadenings longer than the dimensions of nanoparticles, phase matching between slow electrons and plasmonic oscillations is manifested as an additional degree of freedom to control the strength of coupling. Our findings pave the way toward a systematic and realistic understanding of electron-light interactions beyond adiabatic approximations, and lay the ground for the realization of matter-wave interferometry and boson-sampling devices involving light and matter waves.

Electrons Generate Self-Complementary Broadband Vortex Light Beams Using Chiral Photon Sieves.

Planar electron-driven photon sources have been recently proposed as miniaturized light sources, with prospects for ultrafast conjugate electron-photon microscopy and spectral interferometry. Such sources usually follow the symmetry of the electron-induced polarization: transition-radiation-based sources, for example, only generate p-polarized light. Here we demonstrate that the polarization, the bandwidth, and the directionality of photons can be tailored by utilizing photon-sieve-based structures. We design, fabricate, and characterize self-complementary chiral structures made of holes in an Au film and generate light vortex beams with specified angular momentum orders. The incoming electron interacting with the structure generates chiral surface plasmon polaritons on the structured Au surface that scatter into the far field. The outcoupled radiation interferes with transition radiation creating TE- and TM-polarized Laguerre-Gauss light beams with a chiral intensity distribution. The generated vortex light and its unique spatiotemporal features can form the basis for the generation of structured-light electron-driven photon sources.

Far-Field Radiation of Three-Dimensional Plasmonic Gold Tapers near Apexes.

Three-dimensional plasmonic gold tapers are widely used structures in nano-optics for achieving imaging at the nanometer scale, enhanced spectroscopy, confined light sources, and ultrafast photoelectron emission. To understand their radiation properties further, especially in the proximity of the apex at the nanoscale, we employ cathodoluminescence spectroscopy with high spatial and energy resolution. The plasmon-induced radiation in the visible spectral range from three-dimensional gold tapers with opening angles of 13° and 47° is investigated under local electron excitation. We observe a much weaker radiation from the apex of the 13° taper than from that of the 47° taper. By means of finite-difference time-domain simulations we show that for small opening angles plasmon modes that are created at the apex are efficiently guided along the taper shaft. In contrast for tapers with larger opening angles, generated plasmon polaritons experience larger radiation damping. Interestingly, we find for both tapers that the most intense radiation comes from locations a few hundreds of nanometers behind the apexes, instead of exactly at the apexes. Our findings provide useful details for the design of plasmonic gold tapers as confined light sources or light absorbers.

Radiation of Dynamic Toroidal Moments.

Dynamic toroidal dipoles, a distinguished class of fundamental electromagnetic sources, receive increasing interest and participate in fascinating electrodynamic phenomena and sensing applications. As described in the literature, the radiative nature of dynamic toroidal dipoles is sometimes confounded, intermixing with static toroidal dipoles and plasmonic dark modes. Here, we elucidate this issue and provide proof-of-principle experiments exclusively on the radiation behavior of dynamic toroidal moments. Optical toroidal modes in plasmonic heptamer nanocavities are analyzed by electron energy loss spectroscopy and energy-filtered transmission electron microscopy supported by finite-difference time-domain numerical calculations. Additionally, their corresponding radiation behaviors are experimentally investigated by means of cathodoluminescence. The observed contrasting behaviors of a single dynamic toroidal dipole mode and an antiparallel toroidal dipole pair mode are discussed and elucidated. Our findings further clarify the electromagnetic properties of dynamic toroidal dipoles and serve as important guidance for the use of toroidal dipole moments in future applications.

Merging transformation optics with electron-driven photon sources.

Relativistic electron beams create optical radiation when interacting with tailored nanostructures. This phenomenon has been so far used to design grating-based and holographic electron-driven photon sources. It has been proposed recently that such sources can be used for hybrid electron- and light-based spectroscopy techniques. However, this demands the design of a thin-film source suitable for electron-microscopy applications. Here, we present a mesoscopic structure composed of an array of nanoscale holes in a gold film which is designed using transformation optics and delivers ultrashort chirped electromagnetic wave packets upon 30-200 keV electron irradiation. The femtosecond photon bunches result from coherent scattering of surface plasmon polaritons with hyperbolic dispersion. They decay by radiation in a broad spectral band which is focused into a 1.5 micrometer beam waist. The focusing ability and broadband nature of this photon source will initiate applications in ultrafast spectral interferometry techniques.

Impact of a Soccer Game on Cardiac Biomarkers in Adolescent Players.

PURPOSE: Biochemical markers such as cardiac troponin I (cTnI) and N-terminal pro B-type natriuretic peptide (NT-proBNP) have become indispensable tools for the diagnosis of myocardial injury, providing highly sensitive and specific information about cardiac cell damage and wall stress. The purpose of the present research was to examine the response of cardiac biomarkers to a soccer game in adolescent male soccer players. METHODS: Twenty-two trained adolescent male soccer players (14-16 y) were selected in a purposive manner. Blood samples were taken before, immediately after, and 2 and 24 hours after the game for the determination of cTnI and NT-proBNP. RESULTS: Serum concentration of cTnI and NT-proBNP increased immediately and 2 hours after the soccer game (P < .001). After 24 hours, the levels of cTnI dropped but remained above baseline (P = .002), whereas serum NT-proBNP levels returned to baseline. At no time point did any of the values exceed the upper reference value. CONCLUSIONS: This is the first study to investigate the acute responses of cardiac biomarkers to a soccer game in adolescent male players. The postgame elevation of cardiac biomarkers and their rapid recovery are indicative of a physiological rather than a pathological response.

Spectral Interferometry with Electron Microscopes.

Interference patterns are not only a defining characteristic of waves, but also have several applications; characterization of coherent processes and holography. Spatial holography with electron waves, has paved the way towards space-resolved characterization of magnetic domains and electrostatic potentials with angstrom spatial resolution. Another impetus in electron microscopy has been introduced by ultrafast electron microscopy which uses pulses of sub-picosecond durations for probing a laser induced excitation of the sample. However, attosecond temporal resolution has not yet been reported, merely due to the statistical distribution of arrival times of electrons at the sample, with respect to the laser time reference. This is however, the very time resolution which will be needed for performing time-frequency analysis. These difficulties are addressed here by proposing a new methodology to improve the synchronization between electron and optical excitations through introducing an efficient electron-driven photon source. We use focused transition radiation of the electron as a pump for the sample. Due to the nature of transition radiation, the process is coherent. This technique allows us to perform spectral interferometry with electron microscopes, with applications in retrieving the phase of electron-induced polarizations and reconstructing dynamics of the induced vector potential.

Reflection and Phase Matching in Plasmonic Gold Tapers.

We investigate different dynamic mechanisms, reflection and phase matching, of surface plasmons in a three-dimensional single-crystalline gold taper excited by relativistic electrons. Plasmonic modes of gold tapers with various opening angles from 5° to 47° are studied both experimentally and theoretically, by means of electron energy-loss spectroscopy and finite-difference time-domain numerical calculations, respectively. Distinct resonances along the taper shaft are observed in tapers independent of opening angles. We show that, despite their similarity, the origin of these resonances is different at different opening angles and results from a competition between two coexisting mechanisms. For gold tapers with large opening angles (above ∼20°), phase matching between the electron field and that of higher-order angular momentum modes of the taper is the dominant contribution to the electron energy-loss because of the increasing interaction length between electron and the taper near-field. In contrast, reflection from the taper apex dominates the EELS contrast in gold tapers with small opening angles (below ∼10°). For intermediate opening angles, a gradual transition of these two mechanisms was observed.

Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulator Bi2Se3 Probed by Electron Beams.

Bi2Se3 has recently attracted a lot of attention because it has been reported to be a platform for the realization of three-dimensional topological insulators. Due to this exotic characteristic, it supports excitations of a two-dimensional electron gas at the surface and, hence, formation of Dirac-plasmons. In addition, at higher energies above its bandgap, Bi2Se3 is characterized by a naturally hyperbolic electromagnetic response, with an interesting interplay between type-I and type-II hyperbolic behaviors. However, still not all the optical modes of Bi2Se3 have been explored. Here, using mainly electron energy-loss spectroscopy and corresponding theoretical modeling we investigate the full photonic density of states that Bi2Se3 sustains, in the energy range of 0.8 eV-5 eV. We show that at energies below 1 eV, this material can also support wedge Dyakonov waves. Furthermore, at higher energies a huge photonic density of states is excited in structures such as waveguides and resonators made of Bi2Se3 due to the hyperbolic dispersion.