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Free electrons are unique 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. 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 ($\sim100$\%) coupling demanding the use of $<100$~eV electrons interacting with $<1$~eV polaritons confined down to tens of nm. 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 an efficient 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., Comment: 30 pages, 11 figures, 97 references

Multi-junction solar cells provide a path to overcome the efficiency limits of standard silicon solar cells by harvesting more efficiently a broader range of the solar spectrum. However, Si-based multi-junction architectures are hindered by incomplete harvesting in the near-infrared (near-IR) spectral range, as Si sub-cells 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 multi-junction 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 0th-order and parasitic plasmonic absorption in the 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 (EQE) 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 (SCIL) 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 multi-junction solar cells, paving the way for more efficient and sustainable solar energy technologies.

Nonreciprocal devices - in which light is transmitted with different efficiencies along opposite directions - are key technologies for modern photonic applications, yet their compact and miniaturized implementation remains an open challenge. Among different avenues, nonlinearity-induced nonreciprocity has attracted significant attention due to the absence of external bias and integrability within conventional material platforms. So far, nonlinearity-induced nonreciprocity has been demonstrated only in guided platforms using high-Q resonators. Here, we demonstrate ultrathin optical metasurfaces with large nonreciprocal response for free-space radiation based on silicon third-order nonlinearities. Our metasurfaces combine an out-of-plane asymmetry - necessary to obtain nonreciprocity - with in-plane broken symmetry, which finely tunes the radiative linewidth of quasi-bound states in the continuum (q-BICs). Third-order nonlinearities naturally occurring in silicon, engaged by q-BICs, are shown to enable over 10 dB of nonreciprocal transmission while maintaining less than 3 dB in insertion loss. The demonstrated devices merge the field of nonreciprocity with ultrathin metasurface technologies, offering an exciting functionality for signal processing and routing, communications, and protection of high-power laser cavities., Comment: 17 pages, 5 figures in main text. 9 pages, 3 figures in supplemental material

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analog optical computing enables processing 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 been recently shown that metamaterials can be tailored to solve complex mathematical problems in the analog domain, although these efforts have so far been limited to guided-wave systems and bulky setups. Here, we present an ultrathin Si metasurface-based platform for analog 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 semi-transparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analog 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.

In this paper we describe the technical implementation of pump-probe cathodoluminescence microscopy (PP-CL), a novel technique for studying ultrafast dynamics in materials using combined excitation of electron and laser pulses. The PP-CL setup is based on a commercial scanning electron microscope combined with a femtosecond laser. Here we discuss the design, technical details, and characterization of the PP-CL setup. The luminescence emitted by the sample (either photoluminescence, cathodoluminescence or a combination of both) can be analyzed in terms of spectrum, temporal statistics, and frequency-modulated intensity (lock-in detection). The laser spot on the sample is characterized by analyzing the changes in the secondary electron signal on a GaN substrate, from which we extract a laser spot size in the $\mu m$ range. While this method ensures spatial overlap of laser and electron pulses on the sample, temporal alignment is achieved using time-correlated measurements of photoluminescence and cathodoluminescence. We also discuss some considerations to take into account when designing a PP-CL experiment, regarding temporal and spatial resolution. This paper provides a detailed reference for the development of any PP-CL microscope.

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, ultra-thin sample requirements, or extensive fabrication. Here, we overcome these limitations by extracting temperature from measurements of bandgap cathodoluminescence in GaN nanowires with spatial resolution limited by the electron cascade, and use this to determine thermal conductivities in the range of 19-68 W/m*K in three new ways. 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 where comparable. Our results provide novel methods of measuring thermal properties that allow for rapid, in-situ, high-resolution measurements of integrated circuits and semiconductor nanodevices, and open the door for electron-beam based nanoscale phonon transport studies.

A spectral splitting, light trapping dielectric metasurface is designed, fabricated and integrated into a four-terminal perovskite/silicon hybrid tandem solar cell to increase the absorption of light close to the bandgap of the perovskite top cell, and enhance transmission of the near-infrared spectral band towards the bottom cell. The metagrating is composed of a hexagonal array of unit cells of 150-nm-tall hydrogenated amorphous silicon trimer nanostructures with dielectric Mie resonances in the 600-800 nm perovskite near-gap region, made using substrate-conformal imprint lithography. By tailoring the metasurface resonant scattering modes and their interference with the direct reflection paths we minimize specular reflection and obtain high diffraction efficiency that leads to improved light trapping in the perovskite top cell. The measured short-circuit current increase in the perovskite top cell is 0.5 mA/cm2 corresponding to an estimated efficiency gain of 0.26% (absolute) for the metasurface-integrated 4T perovskite/silicon tandem cell. Simulations for a further optimized metasurface spectrum splitter geometry predict a short-circuit current gain in the perovskite top cell of 1.4 mA/cm2 and an efficiency gain for the 4T tandem cell of 0.4% (absolute). The metagrating approach for simultaneous spectral splitting, light trapping and reflectance reduction provides a flexible platform that can be applied to many tandem cell geometries., Comment: Main text: 11 pages (with references), 4 figures Supplementary (in same document): 4 pages, 4 figures, 1 table

We derive the photovoltaic conversion efficiency limit for two-terminal tandem solar cells with a perovskite top cell and silicon bottom cell with an embedded spectrum splitter. For large-bandgap top-cells a spectrum splitter strongly enhances the efficiency because of enhanced light absorption and trapping. A Lambertian spectral splitter shows a significantly improved effect compared to a planar splitter: we find an ideal efficiency enhancement in the thermodynamic limit for a 500 nm thick top cell of 6% absolute for bandgaps above 1.75 eV. Vice versa, the use of a spectral splitter geometry enables the use of a thinner top cell. Using experimental parameters for perovskite cells we show that for a top-cell bandgap of 1.77 eV a 2.8% absolute efficiency can be gained. The calculations in this work show that integration of a spectral splitter into perovskite/silicon tandem cells with a top bandgap above 1.7 eV can lead to a large increase in efficiency, even with realistic experimental losses and non-unity reflection of the spectral splitter., Comment: 11 pages, 4 figures

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 modelling, here we present a fully analytical model describing the amplitude and shape of the second order autocorrelation function ($g^{(2)}(\tau)$) 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 excitation efficiency ($\gamma$), electron beam current, emitter decay lifetime and pulse duration, in the case of pulsed electron beams. The analytical model shows good agreement with 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 non-linear effects play no compelling role even after excitation with ultrashort and dense electron cascades in the quantum wells., Comment: 29 pages (including supplementary information), 14 figures (including supplementary figures)

We demonstrate spatially-resolved measurements of spontaneous and stimulated electron-photon interactions in nanoscale optical near fields using electron energy-loss spectroscopy (EELS), cathodoluminescence spectroscopy (CL), and photon-induced near-field electron microscopy (PINEM). Specifically, we study resonant surface plasmon modes that are tightly confined to the tip apexes of an Au nanostar, enabling a direct correlation of EELS, CL, and PINEM on the same physical structure at the nanometer length scale. Complemented by numerical electromagnetic boundary-element method calculations, we discuss the spontaneous and stimulated electron-photon interaction strength and spatial dependence of our EELS, CL and PINEM distributions. We demonstrate that in the limit of an isolated tip mode, spatial variations in the electron-near field coupling are fully determined by the modal electric field profile, irrespective of the spontaneous (in EELS and CL) or stimulated nature (in PINEM) of the process. Yet we show that coupling to the tip modes crucially depends on the incident electron energy with a maximum at a few keV, depending on the proximity of the interaction to the tip apex. Our results provide elementary insights into spontaneous and stimulated electron-light-matter interactions at the nanoscale that have key implications for research on (quantum) coherent optical phenomena in electron microscopy., Comment: 20 pages, 6 figures, 1 table

Progress in electron-beam spectroscopies has recently enabled the study of optical excitations with combined space, energy and time resolution in the nanometer, millielectronvolt and femtosecond domain, thus providing unique access into nanophotonic structures and their detailed optical responses. These techniques rely on $\approx$ 1-300 keV electron beams focused at the sample down to sub-nanometer spots, temporally compressed in wavepackets a few femtoseconds long, and in some cases controlled by ultrafast light pulses. The electrons undergo energy losses and gains, also giving rise to cathodoluminescence light emission, which are recorded to reveal the optical landscape along the beam path. This review portraits these advances, with a focus on coherent excitations, emphasizing the increasing level of control over the electron wave functions and ensuing applications in the study and technological use of optically resonant modes and polaritons in nanoparticles, 2D materials and engineered nanostructures.

Nitrogen-vacancy (NV) centers in diamond are reliable single-photon emitters, with applications in quantum technologies and metrology. Two charge states are known for NV centers: NV$^0$ and NV$^-$, with the latter being mostly studied due to its long electron spin coherence time. Therefore, control over the charge state of the NV centers is essential. However, an understanding of the dynamics between the different states still remains challenging. Here, conversion from NV$^-$ to NV$^0$ due to electron-induced carrier generation is shown. Ultrafast pump-probe cathodoluminescence spectroscopy is presented for the first time, with electron pulses as pump, and laser pulses as probe, to prepare and read out the NV states. The experimental data is explained with a model considering carrier dynamics (0.8 ns), NV$^0$ spontaneous emission (20 ns) and NV$^0$ $\rightarrow$NV$^-$ back transfer (500 ms). The results provide new insights into the NV$^-$$\leftrightarrow$NV$^0$ conversion dynamics, and into the use of pump-probe cathodoluminescence as a nanoscale NV characterization tool.

Image processing and edge detection are at the core of several newly emerging technologies, such as augmented reality, autonomous driving and more generally object recognition. Image processing is typically performed digitally using integrated electronic circuits and algorithms, implying fundamental size and speed limitations, as well as significant power needs. On the other hand, it can also be performed in a low-power analog fashion using Fourier optics, requiring however bulky optical components. Here, we introduce dielectric metasurfaces that perform optical image edge detection in the analog domain using a subwavelength geometry that can be readily integrated with detectors. The metasurface is composed of a suitably engineered array of nanobeams designed to perform either 1st- or 2nd-order spatial differentiation. We experimentally demonstrate the 2nd-derivative operation on an input image, showing the potential of all-optical edge detection using a silicon metasurface geometry working at a numerical aperture as large as 0.35.

Cathodoluminescence spectroscopy (CL) allows characterizing light emission in bulk and nanostructured materials and is a key tool in fields ranging from materials science to nanophotonics. Previously, CL measurements focused on the spectral content and angular distribution of emission, while the polarization was not fully determined. Here we demonstrate a technique to access the full polarization state of the cathodoluminescence emission, that is the Stokes parameters as a function of the emission angle. Using this technique, we measure the emission of metallic bullseye nanostructures and show that the handedness of the structure as well as nanoscale changes in excitation position induce large changes in polarization ellipticity and helicity. Furthermore, by exploiting the ability of polarimetry to distinguish polarized from unpolarized light, we quantify the contributions of different types of coherent and incoherent radiation to the emission of a gold surface, silicon and gallium arsenide bulk semiconductors. This technique paves the way for in-depth analysis of the emission mechanisms of nanostructured devices as well as macroscopic media., Comment: 8 figures. Includes supplementary information

We study the propagation of light in a three-dimensional double-periodic Ag/TiO2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength range of interest the positive index m=1 harmonic dominates the propagation of light in the orthogonal direction. These results are corroborated by numerical simulations and optical refraction experiments on a double-periodic Ag/TiO2 multilayer metamaterial prism in the 380-600 nm spectral range, which show that positive refraction associated with right-handed harmonics dominates. Studying the isofrequency contours we find that despite the occurrence of multiple harmonics the double-periodic structure can act as a flat lens: for a slab consisting of an integer number of unit cells all harmonics are degenerate and constructively interfere at the image plane. This work identifies important considerations relevant to the design of many three dimensional periodic metamaterials., Comment: 11 pages, 7 figures

We present a transparent conducting electrode composed of a periodic two-dimensional network of silver nanowires. Networks of Ag nanowires are made with wire diameters of 45-110 nm and pitch of 500, 700 and 1000 nm. Anomalous optical transmission is observed, with an averaged transmission up to 91% for the best transmitting network and sheet resistances as low as 6.5 {\Omega}/sq for the best conducting network. Our most dilute networks show lower sheet resistance and higher optical transmittance than an 80 nm thick layer of ITO sputtered on glass. By comparing measurements and simulations we identify four distinct physical phenomena that govern the transmission of light through the networks: all related to the excitation of localized surface plasmons and surface plasmon polaritons on the wires. The insights given in this paper provide the key guidelines for designing high-transmittance and low-resistance nanowire electrodes for optoelectronic devices, including thin-film solar cells. For these latter, we discuss the general design principles to use the nanowire electrodes also as a light trapping scheme.

We use spatially and angle-resolved cathodoluminescence imaging spectroscopy to study, with deep subwavelength resolution, the radiation mechanism of single plasmonic ridge antennas with lengths ranging from 100 to 2000 nm. We measure the antenna's standing wave resonances up to the fifth order and measure the dispersion of the strongly confined guided plasmon mode. By directly detecting the emitted antenna radiation with a 2D CCD camera we are able to measure the angular emission patterns associated with each individual antenna resonance. We demonstrate that the shortest ridges can be modeled as a single point dipole emitter oriented either upward (m=0) or in-plane (m=1). The far-field emission pattern for longer antennas (m>2) is well described by two interfering in-plane point dipoles at the end facets giving rise to an angular fringe pattern, where the number of fringes increases as the antenna becomes longer. Taking advantage of the deep subwavelength excitation resolution of the cathodoluminescence technique, we are able to determine the antenna radiation pattern as function of excitation position. By including the phase of the radiating dipoles into our simple dipole model we completely reproduce this effect. This work demonstrates how angle-resolved cathodoluminescence spectroscopy can be used to fully determine the emission properties of subwavelength ridge antennas, which ultimately can be used for the design of more complex and efficient antenna structures., Comment: 25 pages, 7 figures

We propose a design for a plasmonic copper metamaterial with a negative index of refraction at visible/near-infrared wavelengths. Using numerical simulations, we demonstrate negative refraction by a copper metamaterial prism, and perform a parameter extraction technique to verify the sign of the effective, electric permittivity and magnetic permeability. Our proposed design has a figure of merit comparable to similar silver-based metamaterials operating in the visible/near-infrared range. These findings have implications for the design of low cost plasmonic devices and negative-index metamaterials in the visible / near-infrared., Comment: 4 figures Inclusion of additional simulations referee request addition and correction of references, journal formatting style

We identify a route towards achieving a negative index of refraction at optical frequencies based on coupling between plasmonic waveguides that support backwards waves. We show how modal symmetry can be exploited in metal-dielectric waveguide pairs to achieve negative refraction of both phase and energy. By properly controlling coupling between adjacent waveguides, a metamaterial consisting of a one-dimensional multilayer stack exhibiting an isotropic index of -1 can be achieved at a free-space wavelength of 400 nm. The general concepts developed here may inspire new low-loss metamaterial designs operating close to the metal plasma frequency., Comment: 8 pages, 7 figures

We present ultrafast optical switching experiments on 3D photonic band gap crystals. Switching the Si inverse opal is achieved by optically exciting free carriers by a two-photon process. We probe reflectivity in the frequency range of second order Bragg diffraction where the photonic band gap is predicted. We find good experimental switching conditions for free-carrier plasma frequencies between 0.3 and 0.7 times the optical frequency: we thus observe a large frequency shift of up to D omega/omega= 1.5% of all spectral features including the peak that corresponds to the photonic band gap. We deduce a corresponding large refractive index change of Dn'_Si/n'_Si= 2.0% and an induced absorption length that is longer than the sample thickness. We observe a fast decay time of 21 ps, which implies that switching could potentially be repeated at GHz rates. Such a high switching rate is relevant to future switching and modulation applications.

We present ultrafast all-optical switching measurements of Si woodpile photonic band gap crystals. The crystals are spatially homogeneously excited, and probed by measuring reflectivity over an octave in frequency (including the telecom range) as a function of time. After 300 fs, the complete stop band has shifted to higher frequencies as a result of optically excited free carriers. The switched state relaxes quickly with a time constant of 18 ps. We present a quantitative analysis of switched spectra with theory for finite photonic crystals. The induced changes in refractive index are well described by a Drude model with a carrier relaxation time of 10 fs. We briefly discuss possible applications of high-repetition rate switching of photonic crystal cavities.