Extracting light from silicon is a longstanding challenge in modern engineering and physics. While silicon has underpinned the past 70 years of electronics advancement, a facile tunable and efficient silicon-based light source remains elusive. Here, we experimentally demonstrate the generation of tunable radiation from a one-dimensional, all-silicon nanograting. Light is generated by the spontaneous emission from the interaction of these nanogratings with low-energy free electrons (2–20 keV) and is recorded in the wavelength range of 800–1600 nm, which includes the silicon transparency window. Tunable free-electron-based light generation from nanoscale silicon gratings with efficiencies approaching those from metallic gratings is demonstrated. We theoretically investigate the feasibility of a scalable, compact, all-silicon tunable light source comprised of a silicon Field Emitter Array integrated with a silicon nanograting that emits at telecommunication wavelengths. Our results reveal the prospects of a CMOS-compatible electrically-pumped silicon light source for possible applications in the mid-infrared and telecommunication wavelengths. Extracting light from silicon is a longstanding challenge. Here, the authors report an experimental demonstration of free-electron-driven light emission from silicon nanogratings and investigates the feasibility of a compact, all-silicon tunable light source integrated with a silicon field emitter array.

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Towards integrated tunable all-silicon free-electron light sources.

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral prec...

Optical Excitations with Electron Beams: Challenges and Opportunities

Do the prior history and the wave-packet size and form of a free electron have a physical effect in its interaction with light? Here we answer these fundamental questions on the interpretation of the electron quantum wave function by analyzing spontaneous and stimulated emissions of a quantum electron wave packet, interacting with a general, quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission and absorption of photons depends on the preinteraction-history-dependent size, exhibiting spectral cutoff when it exceeds the interacting radiation wavelength. Furthermore, stimulated emission of an optically modulated electron wave packet has a characteristic harmonic emission spectrum beyond the cutoff, which depends on the modulation features. In either case, there is no wave-packet-dependent radiation of the Fock state, and particularly the vacuum state spontaneous emission is wave-packet independent. The classical-to-quantum transition of radiation from the point-particle to the plane-wave limits, and the effects of wave-packet modulation indicate a way of measuring the wave-packet size of a single electron wave function, and suggest an alternative direction for exploring light-matter interaction.

Spontaneous and stimulated emissions of a preformed quantum free-electron wave function

We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.

Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission.

The Smith-Purcell effect, observed when an electron beam passes in the vicinity of a periodic structure, is a promising platform for the generation of electromagnetic radiation in previously unreachable spectral ranges. However, most of the studies of this radiation were performed on simple periodic gratings, whose radiation spectrum exhibits a single peak and its higher harmonics predicted by a well-established dispersion relation. Here, we propose a method to shape the spatial and spectral far-field distribution of the radiation using complex periodic and aperiodic gratings. We show, theoretically and experimentally, that engineering multiple peak spectra with controlled widths located at desired wavelengths is achievable using Smith-Purcell radiation. Our method opens the way to free-electron-driven sources with tailored angular and spectral responses, and gives rise to focusing functionality for spectral ranges where lenses are unavailable or inefficient.

Spectral and spatial shaping of Smith-Purcell radiation

Time-varying media have recently emerged as a new paradigm for wave manipulation, due to the synergy between the discovery of highly nonlinear materials, such as epsilon-near-zero materials, and the quest for wave applications, such as magnet-free nonreciprocity, multimode light shaping, and ultrafast switching. In this review, we provide a comprehensive discussion of the recent progress achieved with photonic metamaterials whose properties stem from their modulation in time. We review the basic concepts underpinning temporal switching and its relation with spatial scattering and deploy the resulting insight to review photonic time-crystals and their emergent research avenues, such as topological and non-Hermitian physics. We then extend our discussion to account for spatiotemporal modulation and its applications to nonreciprocity, synthetic motion, giant anisotropy, amplification, and many other effects. Finally, we conclude with a review of the most attractive experimental avenues recently demonstrated and provide a few perspectives on emerging trends for future implementations of time-modulation in photonics. 

Photonics of time-varying media

Double-slit experiments—where a wave is transmitted through a thin double aperture in space—have confirmed the wave–particle duality of quantum objects, such as single photons, electrons, neutrons, atoms and large molecules. Yet, the temporal counterpart of Young’s double-slit experiment—a wave interacting with a double temporal modulation of an interface—remains elusive. Here we report such a time-domain version of the classic Young’s double-slit experiment: a beam of light twice gated in time produces an interference in the frequency spectrum. The ‘time slits’, narrow enough to produce diffraction at optical frequencies, are generated from the optical excitation of a thin film of indium tin oxide near its epsilon-near-zero point. The separation between time slits determines the period of oscillations in the frequency spectrum, whereas the decay of fringe visibility in frequency reveals the shape of the time slits. Surprisingly, many more oscillations are visible than expected from existing theory, implying a rise time that approaches an optical cycle. This result enables the further exploration of time-varying physics, towards the spectral synthesis of waves and applications such as signal processing and neuromorphic computation. A temporal version of Young’s double-slit experiment shows characteristic interference in the frequency domain when light interacts with time slits produced by ultrafast changes in the refractive index of an epsilon-near-zero material. 

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Double-slit time diffraction at optical frequencies

The Smith-Purcell effect is observed when an electron beam passes in the vicinity of a periodic structure. We propose a method to shape the spatial and spectral far-field radiation using complex periodic and aperiodic gratings.

We report a switchable time-varying mirror, composed of an indium-tin-oxide--gold bilayer, displaying a tenfold modulation of reflectivity ($\mathrm{\ensuremath{\Delta}}R\ensuremath{\approx}0.6$), which saturates for a driving-pump intensity ${I}_{\mathrm{pump}}\ensuremath{\approx}100\phantom{\rule{0.2em}{0ex}}\mathrm{GW}/{\mathrm{cm}}^{2}$. Upon interacting with the saturated time-varying mirror, the frequency content of a reflected pulse is extended up to 31 THz, well beyond the pump spectral content (2.8 THz). We interpret the spectral broadening as a progressive shortening of the mirror rise time from 110 fs to below 30 fs with increasing pump power, which is confirmed by four-wave-mixing experiments and partially captured by a linear time-varying model of the mirror. A temporal response unbounded by the pump bandwidth enables applications for spectral manipulation from time-varying systems with impact for communication networks, optical switching, and computing. 

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Romain Tirole

Papers

Photonics of time-varying media

Spectral and spatial shaping of Smith-Purcell radiation

Double-slit time diffraction at optical frequencies

Spectral and spatial shaping of Smith-Purcell radiation

Saturable Time-Varying Mirror Based on an Epsilon-Near-Zero Material