Toward Optimum Coupling between Free Electrons and Confined Optical Modes.

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

Free Electron-Plasmon Coupling Strength and Near-Field Retrieval through Electron Energy-Dependent Cathodoluminescence Spectroscopy.

Tightly confined optical near fields in plasmonic nanostructures play a pivotal role in important applications ranging from optical sensing to light harvesting. Energetic electrons are ideally suited to probing optical near fields by collecting the resulting cathodoluminescence (CL) light emission. Intriguingly, the CL intensity is determined by the near-field profile along the electron propagation direction, but the retrieval of such field from measurements has remained elusive. Furthermore, the conditions for optimum electron near-field coupling in plasmonic systems are critically dependent on such field and remain experimentally unexplored. In this work, we use electron energy-dependent CL spectroscopy to study the tightly confined dipolar mode in plasmonic gold nanoparticles. By systematically studying gold nanoparticles with diameters in the range of 20-100 nm and electron energies from 4 to 30 keV, we determine how the coupling between swift electrons and the optical near fields depends on the energy of the incoming electron. The strongest coupling is achieved when the electron speed equals the mode phase velocity, meeting the so-called phase-matching condition. In aloof experiments, the measured data are well reproduced by electromagnetic simulations, which explain that larger particles and faster electrons favor a stronger electron near-field coupling. For penetrating electron trajectories, scattering at the particle produces severe corrections of the trajectory that defy existing theories based on the assumption of nonrecoil condition. Therefore, we develop a first-order recoil correction model that allows us to account for inelastic electron scattering, rendering better agreement with measured data. Finally, we consider the albedo of the particles and find that, to approach unity coupling, a highly confined electric field and very slow electrons are needed, both representing experimental challenges. Our findings explain how to reach unity-order coupling between free electrons and confined excitations, helping us understand fundamental aspects of light-matter interaction at the nanoscale.

Roadmap for Optical Metasurfaces.

Metasurfaces have recently risen to prominence in optical research, providing unique functionalities that can be used for imaging, beam forming, holography, polarimetry, and many more, while keeping device dimensions small. Despite the fact that a vast range of basic metasurface designs has already been thoroughly studied in the literature, the number of metasurface-related papers is still growing at a rapid pace, as metasurface research is now spreading to adjacent fields, including computational imaging, augmented and virtual reality, automotive, display, biosensing, nonlinear, quantum and topological optics, optical computing, and more. At the same time, the ability of metasurfaces to perform optical functions in much more compact optical systems has triggered strong and constantly growing interest from various industries that greatly benefit from the availability of miniaturized, highly functional, and efficient optical components that can be integrated in optoelectronic systems at low cost. This creates a truly unique opportunity for the field of metasurfaces to make both a scientific and an industrial impact. The goal of this Roadmap is to mark this "golden age" of metasurface research and define future directions to encourage scientists and engineers to drive research and development in the field of metasurfaces toward both scientific excellence and broad industrial adoption.

Angular Dispersion of Free-Electron-Light Coupling in an Optical Fiber-Integrated Metagrating.

Free electrons can couple to optical material excitations on nanometer-length and attosecond-time scales, opening-up unique opportunities for both the generation of radiation and the manipulation of the electron wave function. Here, we exploit the Smith-Purcell effect to experimentally study the coherent coupling of free electrons and light in a circular metallo-dielectric metagrating that is fabricated onto the input facet of a multimode optical fiber. Using hyperspectral angle-resolved (HSAR) far-field imaging inside a scanning electron microscope, we probe the angular dispersion of Smith-Purcell radiation (SPR) that is simultaneously generated in free space and inside the fiber by an electron beam that grazes the metagrating at a nanoscale distance. Furthermore, we analyze the spectral distribution of SPR that is emitted into guided optical modes and correlate it with the numerical aperture of the fiber. By varying the electron energy between 5 and 30 keV, we observe the emission of SPR from the ultraviolet to the near-infrared spectral range, and up to the third emission order. In addition, we detect incoherent cathodoluminescence that is generated by electrons penetrating the input facet of the fiber and scattering inelastically. As a result, our HSAR measurements reveal a Fano resonance that is coupled to a Rayleigh anomaly of the metagrating, and that overlaps with the angular dispersion of second-order SPR at 20 keV. Our findings demonstrate the potential of optical fiber-integrated metasurfaces as a versatile platform to implement novel ultrafast light sources and to synthesize complex free-electron quantum states with light.

Electrons catch light pulses on the fly.

Energy exchange between electrons and photons enables ultrafast probing of materials.

Nanopatterned Back-Reflector with Engineered Near-Field/Far-Field Light Scattering for Enhanced Light Trapping in Silicon-Based Multijunction Solar Cells.

Multijunction solar cells provide a path to overcome the efficiency limits of standard silicon solar cells by harvesting a broader range of the solar spectrum more efficiently. However, Si-based multijunction architectures are hindered by incomplete harvesting in the near-infrared (near-IR) spectral range as Si subcells have weak absorption close to the band gap. Here, we introduce an integrated near-field/far-field light trapping scheme to enhance the efficiency of silicon-based multijunction solar cells in the near-IR range. To achieve this, we design a nanopatterned diffractive silver back-reflector featuring a scattering matrix that optimizes trapping of multiply scattered light into a range of diffraction angles. We minimize reflection to the zeroth order and parasitic plasmonic absorption in silver by engineering destructive interference in the patterned back-contact. Numerical and experimental assessment of the optimal design on the performance of single-junction Si TOPCon solar cells highlights an improved external quantum efficiency over a planar back-reflector (+1.52 mA/cm2). Nanopatterned metagrating back-reflectors are fabricated on GaInP/GaInAsP//Si two-terminal triple-junction solar cells via substrate conformal imprint lithography and characterized optically and electronically, demonstrating a power conversion efficiency improvement of +0.9%abs over the planar reference. Overall, our work demonstrates the potential of nanophotonic light trapping for enhancing the efficiency of silicon-based multijunction solar cells, paving the way for more efficient and sustainable solar energy technologies.

Optical Characterization of Plasmonic Indium Lattices Fabricated via Electrochemical Deposition.

The optical properties of periodic metallic nanoparticle lattices have found many exciting applications. Indium is an emerging plasmonic material that offers to extend the plasmonic applications given by gold and silver from the visible to the ultraviolet spectral range, with applications in imaging, sensing, and lasing. Due to the high vapor pressure/low melting temperature of indium, nanofabrication of ordered metallic nanoparticles is nontrivial. In this work, we show the potential of selective area electrochemical deposition to generate large-area lattices of In pillars for plasmonic applications. We study the optical response of the In lattices by means of angle-dependent extinction measurements demonstrating strong plasmonic surface lattice resonances and a good agreement with numerical simulations. The results open avenues toward high-quality lattices of plasmonic indium nanoparticles and can be extended to other promising plasmonic materials that can be electrochemically grown.

Solving integral equations in free space with inverse-designed ultrathin optical metagratings.

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analogue optical computing enables the processing of large amounts of data at a negligible energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real time, in particular for edge detection. By incorporating feedback, it has also recently been shown that metamaterials can be tailored to solve complex mathematical problems in the analogue domain, although these efforts have so far been limited to guided-wave systems and bulky set-ups. Here, we present an ultrathin Si metasurface-based platform for analogue computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed kernel corresponding to the mathematical problem of interest. Next, a semitransparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analogue domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free space, implying high processing speeds and the possibility of on-chip integration.

Passive Radiative Cooling of Silicon Solar Modules with Photonic Silica Microcylinders.

Passive radiative cooling is a method to dissipate excess heat from a material by the spontaneous emission of infrared thermal radiation. For a solar cell, the challenge is to enhance PRC while retaining transparency for sunlight above the bandgap. Here, we design a hexagonal array of cylinders etched into the top surface of silica solar module glass to enhance passive radiative cooling. Multipolar Mie-like resonances in the cylinders are shown to cause antireflection effects in the infrared, which results in enhanced infrared emissivity. Using Fourier transform infrared spectrometry we measure the hemispherical reflectance of the fabricated structures and find the emissivity of the silica cylinder array in good correspondence with the simulated results. The microcylinder array increases the average emissivity between λ = 7.5-16 µm from 84.3% to 97.7%, without reducing visible light transmission.

Optically Resonant Bulk Heterojunction PbS Quantum Dot Solar Cell.

We design an optically resonant bulk heterojunction solar cell to study optoelectronic properties of nanostructured p-n junctions. The nanostructures yield strong light-matter interaction as well as distinct charge-carrier extraction behavior, which together improve the overall power conversion efficiency. We demonstrate high-resolution substrate conformal soft-imprint lithography technology in combination with state-of-the art ZnO nanoparticles to create a nanohole template in an electron transport layer. The nanoholes are infiltrated with PbS quantum dots (QDs) to form a nanopatterned depleted heterojunction. Optical simulations show that the absorption per unit volume in the cylindrical QD absorber layer is enhanced by 19.5% compared to a planar reference. This is achieved for a square array of QD nanopillars of 330 nm height and 320 nm diameter, with a pitch of 500 nm on top of a residual QD layer of 70 nm, surrounded by ZnO. Electronic simulations show that the patterning results in a current gain of 3.2 mA/cm2 and a slight gain in voltage, yielding an efficiency gain of 0.4%. Our simulations further show that the fill factor is highly sensitive to the patterned structure. This is explained by the electric field strength varying strongly across the patterned absorber. We outline a path toward further optimized optically resonant nanopattern geometries with enhanced carrier collection properties. We demonstrate a 0.74 mA/cm2 current gain for a patterned cell compared to a planar cell in experiments, owing to a much improved infrared response, as predicted by our simulations.

Nanopatterning of Perovskite Thin Films for Enhanced and Directional Light Emission.

Lead-halide perovskites offer excellent properties for lighting and display applications. Nanopatterning perovskite films could enable perovskite-based devices with designer properties, increasing their performance and adding novel functionalities. We demonstrate the potential of nanopatterning for achieving light emission of a perovskite film into a specific angular range by introducing periodic sol-gel structures between the injection and emissive layer by using substrate conformal imprint lithography (SCIL). Structural and optical characterization reveals that the emission is funnelled into a well-defined angular range by optical resonances, while the emission wavelength and the structural properties of the perovskite film are preserved. The results demonstrate a flexible and scalable approach to the patterning of perovskite layers, paving the way toward perovskite LEDs with designer angular emission patterns.

Cylindrical Metalens for Generation and Focusing of Free-Electron Radiation.

Metasurfaces constitute a powerful approach to generate and control light by engineering optical material properties at the subwavelength scale. Recently, this concept was applied to manipulate free-electron radiation phenomena, rendering versatile light sources with unique functionalities. In this Letter, we experimentally demonstrate spectral and angular control over coherent light emission by metasurfaces that interact with free-electrons under grazing incidence. Specifically, we study metalenses based on chirped metagratings that simultaneously emit and shape Smith-Purcell radiation in the visible and near-infrared spectral regime. In good agreement with theory, we observe the far-field signatures of strongly convergent and divergent cylindrical radiation wavefronts using in situ hyperspectral angle-resolved light detection in a scanning electron microscope. Furthermore, we theoretically explore simultaneous control over the polarization and wavefront of Smith-Purcell radiation via a split-ring-resonator metasurface, enabling tunable operation by spatially selective mode excitation at nanometer resolution. Our work highlights the potential of merging metasurfaces with free-electron excitations for versatile and highly tunable radiation sources in wide-ranging spectral regimes.

Directional quantum dot emission by soft-stamping on silicon Mie resonators.

We present a soft-stamping method to selectively print a homogenous layer of CdSeTe/ZnS core-shell quantum dots (QDs) on top of an array of Si nanocylinders with Mie-type resonant modes. Using this new method, we gain accurate control of the quantum dot's angular emission through engineered coupling of the QDs to these resonant modes. Using numerical simulations we show that the emission into or away from the Si substrate can be precisely controlled by the QD position on the nanocylinder. QDs centered on a 400 nm diameter nanocylinder surface show 98% emission directionality into the Si substrate. Alternatively, for homogenous ensembles placed over the nanocylinder top-surface, the upward emission is enhanced 10-fold for 150 nm diameter cylinders. Experimental PL intensity measurements corroborate the simulated trends with cylinder diameter. PL lifetime measurements reflect well the variations of the local density of states at the QD position due to coupling to the resonant cylinders. These results demonstrate that the soft imprint technique provides a unique manner to directly integrate optical emitters with a wide range of nanophotonic geometries, with potential applications in LEDs, luminescent solar concentrators, and up- and down-conversion schemes for improved photovoltaics.

Unlocking Higher Power Efficiencies in Luminescent Solar Concentrators through Anisotropic Luminophore Emission.

The luminescent solar concentrator (LSC) offers a potential pathway for achieving low-cost, fixed-tilt light concentration. Despite decades of research, conversion efficiency for LSC modules has fallen far short of that achievable by geometric concentrators. However, recent advances in anisotropically emitting nanophotonic structures could enable a significant step forward in efficiency. Here, we employ Monte Carlo ray-trace modeling to evaluate the conversion efficiency for anisotropic luminophore emission as a function of photoluminescence quantum yield, waveguide concentration, and geometric gain. By spanning the full LSC parameter space, we define a roadmap toward high conversion efficiency. An analytical function is derived for the dark radiative current of an LSC to calculate the conversion efficiency from the ray-tracing results. We show that luminescent concentrator conversion efficiency can be increased from the current record value of 7.1-9.6% by incorporating anisotropy. We provide design parameters for optimized luminescent solar concentrators with practical geometrical gains of 10. Using luminophores with strongly anisotropic emission and high (99%) quantum yield, we conclude that conversion efficiencies beyond 28% are achievable. This analysis reveals that for high LSC performance, waveguide losses are as important as the luminophore quantum yield.

Employing Cathodoluminescence for Nanothermometry and Thermal Transport Measurements in Semiconductor Nanowires.

Thermal properties have an outsized impact on efficiency and sensitivity of devices with nanoscale structures, such as in integrated electronic circuits. A number of thermal conductivity measurements for semiconductor nanostructures exist, but are hindered by the diffraction limit of light, the need for transducer layers, the slow scan rate of probes, ultrathin sample requirements, or extensive fabrication. Here, we overcome these limitations by extracting nanoscale temperature maps from measurements of bandgap cathodoluminescence in GaN nanowires of <300 nm diameter with spatial resolution limited by the electron cascade. We use this thermometry method in three ways to determine the thermal conductivities of the nanowires in the range of 19-68 W/m·K, well below that of bulk GaN. The electron beam acts simultaneously as a temperature probe and as a controlled delta-function-like heat source to measure thermal conductivities using steady-state methods, and we introduce a frequency-domain method using pulsed electron beam excitation. The different thermal conductivity measurements we explore agree within error in uniformly doped wires. We show feasible methods for rapid, in situ, high-resolution thermal property measurements of integrated circuits and semiconductor nanodevices and enable electron-beam-based nanoscale phonon transport studies.

Spontaneous and stimulated electron-photon interactions in nanoscale plasmonic near fields.

The interplay between free electrons, light, and matter offers unique prospects for space, time, and energy resolved optical material characterization, structured light generation, and quantum information processing. Here, we study the nanoscale features of spontaneous and stimulated electron-photon interactions mediated by localized surface plasmon resonances at the tips of a gold nanostar using electron energy-loss spectroscopy (EELS), cathodoluminescence spectroscopy (CL), and photon-induced near-field electron microscopy (PINEM). Supported by numerical electromagnetic boundary-element method (BEM) calculations, we show that the different coupling mechanisms probed by EELS, CL, and PINEM feature the same spatial dependence on the electric field distribution of the tip modes. However, the electron-photon interaction strength is found to vary with the incident electron velocity, as determined by the spatial Fourier transform of the electric near-field component parallel to the electron trajectory. For the tightly confined plasmonic tip resonances, our calculations suggest an optimum coupling velocity at electron energies as low as a few keV. Our results are discussed in the context of more complex geometries supporting multiple modes with spatial and spectral overlap. We provide fundamental insights into spontaneous and stimulated electron-light-matter interactions with key implications for research on (quantum) coherent optical phenomena at the nanoscale.

Photon Statistics of Incoherent Cathodoluminescence with Continuous and Pulsed Electron Beams.

Photon bunching in incoherent cathodoluminescence (CL) spectroscopy originates from the fact that a single high-energy electron can generate multiple photons when interacting with a material, thus, revealing key properties of electron-matter excitation. Contrary to previous works based on Monte Carlo modeling, here we present a fully analytical model describing the amplitude and shape of the second order autocorrelation function (g (2)(τ)) for continuous and pulsed electron beams. Moreover, we extend the analysis of photon bunching to ultrashort electron pulses, in which up to 500 electrons per pulse excite the sample within a few picoseconds. We obtain a simple equation relating the bunching strength (g (2)(0)) to the electron beam current, emitter decay lifetime, pulse duration, in the case of pulsed electron beams, and electron excitation efficiency (γ), defined as the probability that an electron creates at least one interaction with the emitter. The analytical model shows good agreement with the experimental data obtained on InGaN/GaN quantum wells using continuous, ns-pulsed (using beam blanker) and ultrashort ps-pulsed (using photoemission) electron beams. We extract excitation efficiencies of 0.13 and 0.05 for 10 and 8 keV electron beams, respectively, and we observe that nonlinear effects play no compelling role, even after excitation with ultrashort and dense electron cascades in the quantum wells.

Photonics for Photovoltaics: Advances and Opportunities.

Photovoltaic systems have reached impressive efficiencies, with records in the range of 20-30% for single-junction cells based on many different materials, yet the fundamental Shockley-Queisser efficiency limit of 34% is still out of reach. Improved photonic design can help approach the efficiency limit by eliminating losses from incomplete absorption or nonradiative recombination. This Perspective reviews nanopatterning methods and metasurfaces for increased light incoupling and light trapping in light absorbers and describes nanophotonics opportunities to reduce carrier recombination and utilize spectral conversion. Beyond the state-of-the-art single junction cells, photonic design plays a crucial role in the next generation of photovoltaics, including tandem and self-adaptive solar cells, and to extend the applicability of solar cells in many different ways. We address the exciting research opportunities and challenges in photonic design principles and fabrication that will accelerate the massive upscaling and (invisible) integration of photovoltaics into every available surface.

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.

Phase-Resolved Surface Plasmon Scattering Probed by Cathodoluminescence Holography.

High-energy (1-100 keV) electrons can coherently couple to plasmonic and dielectric nanostructures, creating cathodoluminescence (CL) of which the spectral features reveal details of the material's resonant modes at a deep-subwavelength spatial resolution. While CL provides fundamental insight in optical modes, detecting its phase has remained elusive. Here, we use Fourier-transform CL holography to determine the far-field phase distribution of fields scattered from plasmonic nanoholes, nanocubes, and helical nanoapertures and reconstruct the angle-resolved phase distributions. From the derived fields, we derive the relative strength and phase of induced scattering dipoles. Fourier-transform CL holography opens up a new world of coherent light scattering and surface wave studies with nanoscale spatial resolution.