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Spatio-temporal shaping of electron beams is a bold frontier in electron microscopy, enabling new routes toward spatial-resolution enhancement, selective probing, low-dose imaging and faster data acquisition. Over the last decade, shaping methods evolved from passive phase plates to low-speed electrostatic and magnetostatic displays. Recently, higher shaping speed and flexibility have become feasible by the advent of ultrafast electron microscopy, embodying a swift change of paradigm that relies on using light to control free electrons. Here, we experimentally demonstrate that arbitrary transverse modulation of electron beams is possible without the need for designing and fabricating complicated electron-optics elements or material nanostructures, but rather resorting to shaping light beams reflected from a planar thin film. We demonstrate arbitrary transverse modulation of electron wavepackets via inelastic interaction with a shaped ultrafast light field controlled by an external spatial light modulator (SLM). We illustrate this method by generating Hermite-Gaussian (HG) electron beams with HG10 and HG01 symmetry and discuss their possible use in enhancing the imaging contrast of microscopic features. Relative to current schemes, our approach adopting an external SLM dramatically widens the range of patterns that can be imprinted on the electron wave function and makes electron shaping a much easier task to perform., Comment: 21 pages, 5 figures

Frequency multiplication of terahertz signals on a solid state platform is highly sought-after for the next generation of high-speed electronics and the creation of frequency combs. Solutions to efficiently generate extreme harmonics (up to the $31^{\rm{st}}$ harmonic and beyond) of a terahertz signal with modest input intensities, however, remain elusive. Using fully nonperturbative simulations and complementary analytical theory, we show that 3D Dirac semimetals (DSMs) have enormous potential as compact sources of extreme terahertz harmonics, achieving energy conversion efficiencies beyond $10^{-5}$ at the $31^{\rm{st}}$ harmonic with input intensities on the order of $10$ MW/cm$^2$, over $10^5$ times lower than in conventional THz high harmonic generation systems. Our theory also reveals a fundamental feature in the nonlinear optics of 3D DSMs: a distinctive regime where higher-order optical nonlinearity vanishes, arising as a direct result of the extra dimensionality in 3D DSMs compared to 2D DSMs. Our findings should pave the way to the development of efficient platforms for high-frequency terahertz light sources and optoelectronics based on 3D DSMs., Comment: 10 pages, 3 figures

Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and phase of that signal. Commonly performed with photons and electrons, it finds numerous applications in imaging, cryptography and arts. With electrons, the extension of holography to the ultrafast time domain remains a challenge, although it would yield the highest possible combined spatio-temporal resolution. Here, we show that holograms of local electromagnetic fields can be obtained with combined attosecond/nanometer resolution in an ultrafast transmission electron microscope (UEM). Unlike conventional holography, where the signal and the reference are spatially separated and then recombined to interfere, in our method we use electromagnetic fields to split an electron wave function in a quantum coherent superposition of different energy states. In the image plane, spatial modulation of the electron-energy distribution reflects the phase relation between reference and signal fields, which we map via energy-filtered UEM. Beyond imaging applications, this approach allows implementing optically-controlled and spatially-resolved quantum measurements in parallel, providing an efficient and versatile tool for the exploration of electron quantum optics., Comment: 10 pages, 5 figures

Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that include electron-hole asymmetry and the detailed electronic bands of basic graphene nanostructures (e.g., nanoribbons with different edge terminations) are beyond the capability of such simple model. Here we show that a similarly simple plane-wave solution for the one-electron states of an atom-based two-dimensional potential landscape, defined by a single fitting parameter (the scattering potential), performs better than the standard tight-binding model, and levels to density-functional theory in correctly reproducing the detailed band structure of a variety of graphene nanostructures. In particular, our approach identifies the three hierarchies of nonmetallic armchair nanoribbons, as well as the doubly-degenerate flat bands of free-standing zigzag nanoribbons with their energy splitting produced by symmetry breaking. The present simple plane-wave approach holds great potential for gaining insight into the electronic states and the electro-optical properties of graphene nanostructures and other two-dimensional materials with intact or gapped Dirac-like dispersions.

Vortex-carrying matter waves, such as chiral electron beams, are of significant interest in both applied and fundamental science. Continuous wave electron vortex beams are commonly prepared via passive phase masks imprinting a transverse phase modulation on the electron's wave function. Here, we show that femtosecond chiral plasmonic near fields enable the generation and dynamic control on the ultrafast timescale of an electron vortex beam. The vortex structure of the resulting electron wavepacket is probed in both real and reciprocal space using ultrafast transmission electron microscopy. This method offers a high degree of scalability to small length scales and a highly efficient manipulation of the electron vorticity with attosecond precision. Besides the direct implications in the investigation of nanoscale ultrafast processes in which chirality plays a major role, we further discuss the perspectives of using this technique to shape the wave function of charged composite particles, such as protons, and how it can be used to probe their internal structure., Comment: 14 pages, 4 figures

The electronic, optical, and magnetic properties of quantum solids are determined by their low-energy (< 100 meV) many-body excitations. Dynamical characterization and manipulation of such excitations relies on tools that combine nm-spatial, fs-temporal, and meV-spectral resolution. Currently, phonons and collective plasmon resonances can be imaged in nanostructures with sub-nm and 10s meV space/energy resolution using state-of-the-art energy-filtered transmission electron microscopy (TEM), but only under static conditions, while fs-resolved measurements are common but lack spatial or energy resolution. Here, we demonstrate a new method of spectrally resolved photon-induced near-field electron microscopy (SRPINEM) that allows us to obtain nm-fs-resolved maps of nanoparticle plasmons with an energy resolution determined by the laser linewidth (20 meV in this work), and not limited by electron beam and spectrometer energy spreading. This technique can be extended to any optically-accessible low-energy mode, thus pushing TEM to a previously inaccessible spectral domain with an unprecedented combination of space, energy and temporal resolution., Comment: 19 pages, 7 figures

Light absorption in conducting materials produces heating of their conduction electrons, followed by relaxation into phonons within picoseconds, and subsequent diffusion into the surrounding media over longer timescales. This conventional picture of optical heating is supplemented by radiative cooling, which typically takes place at an even lower pace, only becoming relevant for structures held in vacuum or under extreme conditions of thermal isolation. Here we reveal an ultrafast radiative cooling regime between neighboring plasmon-supporting graphene nanostructures in which noncontact heat transfer becomes a dominant channel. We predict that >50% of the electronic heat energy deposited on a graphene disk can be transferred to a neighboring nanoisland within a femtosecond timescale. This phenomenon is facilitated by the combination of low electronic heat capacity and large plasmonic field concentration displayed by doped graphene. Similar effects should take place in other van der Waals materials, thus opening an unexplored avenue toward efficient heat management in ultrathin nanostructures., Comment: 29 figures, 119 references, fully self-contained theory of radiative heat transfer

Saturable absorption is a non-perturbative nonlinear optical phenomenon that plays a pivotal role in the generation of ultrafast light pulses. Here we show that this effect emerges in graphene at unprecedentedly low light intensities, thus opening avenues to new nonlinear physics and applications in optical technology. Specifically, we theoretically investigate saturable absorption in extended graphene by developing a non-perturbative single-particle approach, describing conduction-electron dynamics in the atomically-thin material using the two-dimensional Dirac equation for massless Dirac fermions, which is recast in the form of generalized Bloch equations. By solving the electron dynamics non-perturbatively, we account for both interband and intraband contributions to the intensity-dependent saturated conductivity and conclude that the former dominates regardless of the intrinsic doping state of the material. The results are in excellent agreement with atomistic quantum-mechanical simulations including higher-band effects. Additionally, we find that the modulation depth of saturable absorption in graphene can be electrically manipulated through an externally applied gate voltage. Our results are relevant for the development of graphene-based optoelectronic devices, as well as for applications in mode-locking and random lasers.

Nonlinear optical processes rely on the intrinsically weak interactions between photons enabled by their coupling with matter. Unfortunately, many applications in nonlinear optics are severely hindered by the small response of conventional materials. Metallic nanostructures partially alleviate this situation, as the large light enhancement associated with their localized plasmons amplifies their nonlinear response to record high levels. Graphene hosts long-lived, electrically tunable plasmons that also interact strongly with light. Here we show that the nonlinear polarizabilities of graphene nanoislands can be electrically tuned to surpass by several orders of magnitude those of metal nanoparticles of similar size. This extraordinary behavior extends over the visible and near-infrared for islands consisting of hundreds of carbon atoms doped with moderate carrier densities. Our quantum-mechanical simulations of the plasmon-enhanced optical response of nanographene reveal this material as an ideal platform for the development of electrically tunable nonlinear optical nanodevices., Comment: 16 pages, 12 figures, 54 references

Controlling the energy flow processes and the associated energy relaxation rates of a light emitter is of high fundamental interest, and has many applications in the fields of quantum optics, photovoltaics, photodetection, biosensing and light emission. While advanced dielectric and metallic systems have been developed to tailor the interaction between an emitter and its environment, active control of the energy flow has remained challenging. Here, we demonstrate in-situ electrical control of the relaxation pathways of excited erbium ions, which emit light at the technologically relevant telecommunication wavelength of 1.5 $\mu$m. By placing the erbium at a few nanometres distance from graphene, we modify the relaxation rate by more than a factor of three, and control whether the emitter decays into either electron-hole pairs, emitted photons or graphene near-infrared plasmons, confined to $<$15 nm to the sheet. These capabilities to dictate optical energy transfer processes through electrical control of the local density of optical states constitute a new paradigm for active (quantum) photonics., Comment: 9 pages, 4 figures

The ability to modulate light at high speeds is of paramount importance for telecommunications, information processing, and medical imaging technologies. This has stimulated intense efforts to master optoelectronic switching at visible and near-infrared frequencies, although coping with current computer speeds in integrated architectures still remains a major challenge. As a partial success, midinfrared light modulation has been recently achieved through gating patterned graphene. Here we show that atomically thin noble metal nanoislands can extend optical modulation to the visible and near-infrared spectral range. We find plasmons in thin metal nanodisks to produce similar absorption cross-sections as spherical particles of the same diameter. Using realistic levels of electrical doping, plasmons are shifted by about half their width, thus leading to a factor-of-two change in light absorption. These results, which we substantiate on microscopic quantum theory of the optical response, hold great potential for the development of electrical visible and near-infrared light modulation in integrable, nanoscale devices., Comment: 30 pages, 11 figures

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch., Comment: 4+ pages, 3 Figures, V2: minor changes, added supplemental

The near-field interaction between fluorescent emitters and graphene exhibits rich physics associated with local dipole-induced electromagnetic fields that are strongly enhanced due to the unique properties of graphene. Here, we measure emitter lifetimes as a function of emitter-graphene distance d, and find agreement with a universal scaling law, governed by the fine-structure constant. The observed energy transfer- rate is in agreement with a 1/d^4 dependence that is characteristic of 2D lossy media. The emitter decay rate is enhanced 90 times (transfer efficiency of ~99%) with respect to the decay in vacuum at distances d ~ 5 nm. This high energy-transfer rate is mainly due to the two-dimensionality and gapless character of the monoatomic carbon layer. Graphene is thus shown to be an extraordinary energy sink, holding great potential for photodetection, energy harvesting, and nanophotonics., Comment: 17 pages, 4 figures

We map the complex electric fields associated with the scattering of surface plasmon polaritons by single sub-wavelength holes of different sizes in thick gold films. We identify and quantify the different modes associated with this event, including a radial surface wave with an angularly isotropic amplitude. This wave is shown to arise from the out-of-plane electric dipole induced in the hole, and we quantify the corresponding polarizability, which is in excellent agreement with electromagnetic theory. Time-resolved measurements reveal a time-delay of 38? +/- 18 fs between the surface plasmon polariton and the radial wave, which we attribute to the interaction with a broad hole resonance.

The properties of surface plasmons localized at the interface between graphene and kerr-type nonlinear medium in three dimensions are investigated. Compared with surface plasmons at the surface of metal, with the inevitable nonlinear refractive effect, the confinement of plasmon can be improved to three times than graphene plasmons without nonlinear contribution, but also with almost the same relative propagation length. Moreover, the dispersion relation and propation distance of graphene plasmons can be easily controlled by changing the fermi energy, temperature and relaxation time of graphene. Our results suggest a simple but useful potential application for precise nonlinear material sensor using graphene plasmons., Comment: 4 pages, 5 figures

We study the frictional torque acting on particles rotating in empty space. At zero temperature, vacuum friction transforms mechanical energy into light emission and produces particle heating. However, particle cooling relative to the environment occurs at finite temperatures and low rotation velocities. Radiation emission is boosted and its spectrum significantly departed from a hot-body emission profile as the velocity increases. Stopping times ranging from hours to billions of years are predicted for materials, particle sizes, and temperatures accessible to experiment. Implications for the behavior of cosmic dust are discussed., Comment: 4 figures, 10 pages, includes paper and supplementary information in the appendix

The passage of a free-electron beam through a nano-hole in a periodically layered metal/dielectric structure creates a new type of tuneable, nanoscale radiation source - a 'light-well'. With a lateral size of just a few hundred nanometers, and an emission intensity of ~200 W/cm^2 such light-wells may be employed in nanophotonic circuits as chip-scale sources, or in densely packed ensembles for optical memory and display applications., Comment: 4 pages, 3 figures

This colloquium analyzes the interaction of light with two-dimensional periodic arrays of particles and holes. The enhanced optical transmission observed in the latter and the presence of surface modes in patterned metal surfaces are thoroughly discussed. A review of the most significant discoveries in this area is presented first. A simple tutorial model is then formulated to capture the essential physics involved in these phenomena, while allowing analytical derivations that provide deeper insight. Comparison with more elaborated calculations is offered as well. Finally, hole arrays in plasmon-supporting metals are compared to perforated perfect conductors, thus assessing the role of plasmons in these types of structures through analytical considerations., Comment: 19 figures

This review discusses how low-energy, valence excitations created by swift electrons can render information on the optical response of structured materials with unmatched spatial resolution. Electron microscopes are capable of focusing electron beams on sub-nanometer spots and probing the target response either by analyzing electron energy losses or by detecting emitted radiation. Theoretical frameworks suited to calculate the probability of energy loss and light emission (cathodoluminescence) are revisited and compared with experimental results. More precisely, a quantum-mechanical description of the interaction between the electrons and the sample is discussed, followed by a powerful classical dielectric approach that can be in practice applied to more complex systems. We assess the conditions under which classical and quantum-mechanical formulations are equivalent. The excitation of collective modes such as plasmons is studied in bulk materials, planar surfaces, and nanoparticles. Light emission induced by the electrons is shown to constitute an excellent probe of plasmons, combining sub-nanometer resolution in the position of the electron beam with nanometer resolution in the emitted wavelength. Both electron energy-loss and cathodoluminescence spectroscopies performed in a scanning mode of operation yield snap shots of plasmon modes in nanostructures with fine spatial detail as compared to other existing imaging techniques, thus providing an ideal tool for nanophotonics studies., Comment: 67 pages, 36 figures. Reviews of Modern Physics (in press)

Arrays of parallel metallic nanowires are shown to provide a tunable, robust, and versatile platform for plasmon interconnects, including high-curvature turns with minimum signal loss. The proposed guiding mechanism relies on gap plasmons existing in the region between adjacent nanowires of dimers and multi-wire arrays. We focus on square and circular silver nanowires in silica, for which excellent agreement between both boundary element method and multiple multipolar expansion calculations is obtained. Our work provides the tools for designing plasmon-based interconnects and achieving high degree of integration with minimum cross talk between adjacent plasmon guides., Comment: 4 pages, 5 figures

We introduce optically tunable surfaces based upon metallic gold nanoparticles trapped in open, water-filled gold cavities. The optical properties of the surfaces change dramatically with the presence and location of the particles inside the cavities. The precise position of the particles is shown to be controllable through optical forces exerted by external illumination, thus leading to all-optical tunability, whereby the optical response of the surfaces is tuned through externally applied light. We discuss the performance of the cavity-particle complex in detail and provide theoretical support for its application as a novel concept of large-scale optically tunable system., Comment: 4 pages, 5 figures

We study sound transmission in perforated plates as a function of incident angle and conclude that it holds distinctive properties that make it unique and essentially different from optical transmission through perforated metallic plates. More precisely, we conclude the following: (a) similar to its optical counterpart, acoustic transmission minima respond to Wood anomalies in which the periodicity plays a central role; (b) in contrast to both the optical case and the acoustical case with slits, homogeneous-plate modes (Lamb and Scholte-Stoneley modes) are strongly coupled to lattice and Fabry-P\'erot resonances. This gives rise to unique transmission behavior, thus opening new perspectives for exotic wave phenomena., Comment: 4 figures. Submitted to Phys. Rev. Lett

We use focused-ion-beam milling of a single-crystal Au surface to fabricate a 590-nm-long linear ridge that acts as a surface plasmon nanoresonator. Cathodoluminescence imaging spectroscopy is then used to excite and image surface plasmons on the ridge. Principal component analysis reveals distinct plasmonic modes, which proves confinement of surface-plasmon oscillations to the ridge. Boundary-element-method calculations confirm that a linear ridge is able to support highly-localized surface-plasmon modes (mode diameter < 100 nm). The results demonstrate that focused-ion-beam milling can be used in rapid prototyping of nanoscale single-crystal plasmonic components., Comment: 4 pages, 4 figures

Coupled and shape-tailored metallic nanoparticles are known to exhibit hybridized plasmon resonances. This Letter discuss the optical properties of a complementary system formed by overlapped nanovoid dimers buried in gold and filled with silica. This is an alternative route for plasmon engineering that benefits from vanishing radiation losses. Our analysis demonstrates the possibility of designing artificial plasmon molecules on the basis of void plasmon hybridization, which allows fine mode tuning by varying the overlap between voids. The proposed structures could find application to both signal processing through buried optical elements and tunable-plasmon biosensing., Comment: 4 pages, 4 figures

Electron energy-loss spectroscopy (EELS) performed in transmission electron microscopes is shown to directly render the photonic local density of states (LDOS) with unprecedented spatial resolution, currently below the nanometer. Two special cases are discussed in detail: (i) 2D photonic structures with the electrons moving along the translational axis of symmetry and (ii) quasi-planar plasmonic structures under normal incidence. Nanophotonics in general and plasmonics in particular should benefit from these results connecting the unmatched spatial resolution of EELS with its ability to probe basic optical properties like the photonic LDOS., Comment: 4 pages, 2 figures

Optical tweezers and optical lattices are making it possible to control small particles by means of electromagnetic forces and torques. In this context, a method is presented in this work to calculate electromagnetic forces and torques for arbitrarily-shaped objects in the presence of other objects illuminated by a plane wave. The method is based upon an expansion of the electromagnetic field in terms of multipoles around each object, which are in turn used to derive forces and torques analytically. The calculation of multipole coefficients are obtained numerically by means of the boundary element method. Results are presented for both spherical and non-spherical objects., Comment: 5 papges, 2 figures

The dielectric properties of metamaterials consisting of periodically arranged metallic nanoparticles of spherical shape are calculated by rigorously solving Maxwell's equations. Effective dielectric functions are obtained by comparing the reflectivity of planar surfaces limiting these materials with Fresnel's formulas for equivalent homogeneous media, showing mixing and splitting of individual-particle modes due to inter-particle interaction. Detailed results for simple cubic and fcc crystals of aluminum spheres in vacuum, silver spheres in vacuum, and silver spheres in a silicon matrix are presented. The filling fraction of the metal f is shown to determine the position of the plasmon modes of these metamaterials. Significant deviations are observed with respect to Maxwell-Garnett effective medium theory for large f, and multiple plasmons are predicted to exist in contrast to Maxwell-Garnett theory., Comment: 6 pages, 4 figures

A mechanism of light transmission through metallic films is proposed, assisted by tunnelling between resonating buried dielectric inclusions. This is illustrated by arrays of Si spheres embedded in Ag. Strong transmission peaks are observed near the Mie resonances of the spheres. The interaction among various planes of spheres and interference effects between these resonances and the surface plasmons of Ag lead to mixing and splitting of the resonances. Transmission is proved to be limited only by absorption. For small spheres, the effective dielectric constant can be tuned to values close to unity and a method is proposed to turn the resulting materials invisible., Comment: 4 papges, 5 figures

Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of non-absorbing scatterers is shown to be complete at some wavelengths regardless how weak the scatterers are. These results are proven analytically and corroborated by rigorous numerical solution of Maxwell's equations. This work supports the central role played by dynamical diffraction during light transmission through subwavelength hole arrays and it provides a systematics to analyze more complex geometries and many of the features observed in connection with transmission through hole arrays., Comment: 5 pages, 4 figures

The response of gold nanoparticle dimers is studied theoretically near and beyond the limit where the particles are touching. As the particles approach each other, a dominant dipole feature is observed that is pushed into the infrared due to interparticle coupling and that is associated with a large pileup of induced charge in the interparticle gap. The redshift becomes singular as the particle separation decreases. The response weakens for very small separation when the coupling across the interparticle gap becomes so strong that dipolar oscillations across the pair are inhibited. Lower-wavelength, higher-order modes show a similar separation dependence in nearly touching dimers. After touching, singular behavior is observed through the emergence of a new infrared absorption peak, also accompanied by huge charge pileup at the interparticle junction, if initial interparticle-contact is made at a single point. This new mode is distinctly different from the lowest mode of the separated dimer. When the junction is made by contact between flat surfaces, charge at the junction is neutralized and mode evolution is continuous through contact. The calculated singular response explains recent experiments on metallic nanoparticle dimers and is relevant in the design of nanoparticle-based sensors and plasmon circuits.

The force exerted on nanoparticles and atomic clusters by fast passing electrons like those employed in transmission electron microscopes are calculated and integrated over time to yield the momentum transferred from the electrons to the particles. Numerical results are offered for metallic and dielectric particles of different sizes (0-500 nm in diameter) as well as for carbon nanoclusters. Results for both linear and angular momentum transfers are presented. For the electron beam currents commonly employed in electron microscopes, the time-averaged forces are shown to be comparable in magnitude to laser-induced forces in optical tweezers. This opens up the possibility to study optically-trapped particles inside transmission electron microscopes., Comment: 6 pages, 5 figures

Atom and nanoparticle arrays trapped in optical lattices are shown to be capable of sustaining collective oscillations of frequency proportional to the strength of the external light field. The spectrum of these oscillations determines the mechanical stability of the arrays. This phenomenon is studied for dimers, strings, and two-dimensional planar arrays. Laterally confined particles free to move along an optical channel are also considered as an example of collective motion in partially-confined systems. The fundamental concepts of dynamical response in optical matter introduced here constitute the basis for potential applications to quantum information technology and signal processing. Experimental realizations of these systems are proposed., Comment: 4 figures. Optics Express (in press)

We report on the observation of enhanced microwave transmission through quasi-periodic hole arrays in metal films. The fraction of transmitted light reaches 50% in a self-standing metal film and approaches 90% when the film is sandwiched between thin dielectric slabs, while the holes occupy only 10% of the sample area. The maximum transmission is accompanied by zero phase change, rendering the film almost 'invisible' over a wide frequency range. The extraordinary transmission phenomenon is interpreted in terms of resonances in the self-consistent interaction between holes, which are represented by effective electric and magnetic dipoles., Comment: 4 pages, 2 figures

We present experimental and theoretical results for the variation of the O 1s intensity from a NiO(001) surface as the excitation energy is varied through the Ni 2p1/2,3/2 absorption resonances, and as the incidence angle of the radiation is varied from grazing to larger values. For grazing incidence, a strong multi-atom resonant photoemission (MARPE) effect is seen on the O 1s intensity as the Ni 2p resonances are crossed, but its magnitude decreases rapidly as the incidence angle is increased. Resonant x-ray optical (RXRO) calculations are found to predict these effects very well, although the experimental effects are found to decrease at higher incidence angles faster than those in theory. The potential influence of photoelectron diffraction effects on such measurements are also considered, including experimental data with azimuthal-angle variation and corresponding multiple-scattering-diffraction calculations, but we conclude that they do not vary beyond what is expected on the basis of the change in photoelectron kinetic energy. Varying from linear polarization to circular polarization is found to enhance these effects in NiO considerably, although the reasons are not clear. We also discuss the relationship of these measurements to other related interatomic resonance experiments and theoretical developments, and make some suggestions for future studies in this area., Comment: Phys. Rev. B, in press

X-ray photoelectron diffraction is used to directly probe the intra-cell polar atomic distortion and tetragonality associated with ferroelectricity in ultrathin epitaxial PbTiO3 films. Our measurements, combined with ab-initio calculations, unambiguously demonstrate non-centro-symmetry in films a few unit cells thick, imply that films as thin as 3 unit cells still preserve a ferroelectric polar distortion, and also show that there is no thick paraelectric dead layer at the surface.

A powerful analytical approach is followed to study light transmission through subwavelength holes drilled in thick perfect-conductor films, showing that full transmission (100%) is attainable in arrays of arbitrarily narrow holes as compared to the film thickness. The interplay between resonances localized in individual holes and lattice resonances originating in the array periodicity reveals new mechanisms of transmission enhancement and suppression. In particular, localized resonances obtained by filling the holes with high-index-of-refraction material are examined and experimentally observed through large enhancement in the transmission of individual holes., Comment: 5 figures

Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that these metamaterials cannot be described in general by local, frequency-dependent permittivities and permeabilities for small periods compared to the wavelength, except in certain limiting cases that are discussed in detail. New related metamaterials are shown to exhibit exciting optical properties that are elucidated in the light of our simple analytical approach., Comment: 5 figures

We assert that the physics underlying the extraordinary light transmission (reflection) in nanostructured materials can be understood from rather general principles based on the formal scattering theory developed in quantum mechanics. The Maxwell equations in passive (dispersive and absorptive) linear media are written in the form of the Schr\"{o}dinger equation to which the quantum mechanical resonant scattering theory (the Lippmann-Schwinger formalism) is applied. It is demonstrated that the existence of long-lived quasistationary eigenstates of the effective Hamiltonian for the Maxwell theory naturally explains the extraordinary transmission properties observed in various nanostructured materials. Such states correspond to quasistationary electromagnetic modes trapped in the scattering structure. Our general approach is also illustrated with an example of the zero-order transmission of the TE-polarized light through a metal-dielectric grating structure. Here a direct on-the-grid solution of the time-dependent Maxwell equations demonstrates the significance of resonances (or trapped modes) for extraordinary light transmissio, Comment: 14 pages, 6 figures; Discussion in Section 4 expanded; typos corrected; a reference added; Figure 4 revised

The force exerted on nanoparticles and atomic clusters by fast passing electrons like those employed in transmission electron microscopes are calculated and integrated over time to yield the momentum transferred from the electrons to the particles. Numerical results are offered for metallic and dielectric particles of different sizes (0-500 nm in diameter) as well as for carbon nanoclusters. Results for both linear and angular momentum transfers are presented. For the electron beam currents commonly employed in electron microscopes, the time-averaged forces are shown to be comparable in magnitude to laser-induced forces in optical tweezers. This opens up the possibility to study optically-trapped particles inside transmission electron microscopes.

The interaction of a fast electron with a photonic crystal is investigated by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The energy loss is obtained from the retarding force exerted on the electron by the induced electric field. The features of the energy loss spectra are shown to be related to the photonic band structure of the crystal. Two different regimes are discussed: for small lattice constants $a$ relative to the wavelength of the associated electron excitations $\lambda$, an effective medium theory can be used to describe the material; however, for $a\sim\lambda$ the photonic band structure plays an important role. Special attention is paid to the frequency gap regions in the latter case., Comment: 12 pages, 7 figures

The interaction of a fast electron with a photonic crystal is studied by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The polarization currents and charges produced by the passage of the electron give rise to the emission of the so-called Smith-Purcell radiation. The emitted light probability is obtained by integrating the Poynting vector over planes parallel to the crystal at a large distance from the latter. Both reflected and transmitted light components are analyzed and related to the photonic band structure of the crystal. Emission spectra are compared with the energy loss probability and also with the reflectance and transmittance of the crystal., Comment: 9 pages, 3 figures, nano-7/ecoss-21 proceedings, submitted to Surface Science

The response of fullerenes and carbon nanotubes is investigated by representing each carbon atom by its atomic polarizability. The polarization of each carbon atom produces an induced dipole that is the result of the interaction with a given external field plus the mutual interaction among carbon atoms. The polarizability is obtained from the dielectric function of graphite after invoking the Clausius-Mossotti relation. This formalism is applied to the simulation of electron energy loss spectra both in fullerenes and in carbon nanotubes. The case of broad electron beams is considered and the loss probability is analyzed in detail as a function of the electron deflection angle within a fully quantum-mechanical description of the electrons. A general good agreement with available experiments is obtained in a wide range of probe energies between 1 keV and 60 keV., Comment: 8 pages, 6 figures, submitted to PRB

Wave functions and electron potentials of laterally-confined surface states are determined experimentally by means of photoemission from stepped Au(111) surfaces. Using an iterative formalism borrowed from x-ray diffraction, we retrieve the real-space wave functions from the Fourier transform of their momentum representations, whose absolute values in turn are directly measured by angle-resolved photoemission. The effective confining potential is then obtained by introducing the wave functions into Schroedinger's equation., Comment: 5 pages, 3 figures

X-ray fluorescence holography (XFH) is a method for obtaining diffraction-limited images of the local atomic structure around a given type of emitter. The reconstructed wave-field represents a distorted image of the scatterer electron density distribution; {\it i.e.} it is a convolution of the charge density distribution with a point spread function characteristic of the measurement. We here consider several methods for the iterative deconvolution of such XFH holograms, and via theoretical simulations evaluate them from the point of view of going beyond the diffraction limit so as to image the electron charge density. Promising results for future applications are found for certain methods, and other possible image-enhancement techniques are also discussed., Comment: 8 pages, 5 figures, submitted