Strong-field nano-optics

The present status and development of strong-field nano-optics, an emerging field of nonlinear optics, is discussed. A nonperturbative regime of light-matter interactions is reached when the amplitude of the external electromagnetic fields that are driving a material approach or exceed the field strengths that bind the electrons inside the medium. In this strong-field regime, light-matter interactions depend on the amplitude and phase of the field, rather than its intensity, as in more conventional perturbative nonlinear optics. Traditionally such strong-field interactions have been intensely investigated in atomic and molecular systems, and this has resulted in the generation of high-harmonic radiation and laid the foundations for contemporary attosecond science. Over the past decade, however, a new field of research has emerged, the study of strong-field interactions in solid-state nanostructures. By using nanostructures, specifically those made out of metals, external electromagnetic fields can be localized on length scales of just a few nanometers, resulting in signficantly enhanced field amplitudes that can exceed those of the external field by orders of magnitude in the vicinity of the nanostructures. This leads not only to dramatic enhancements of perturbative nonlinear optical effects but also to significantly increased photoelectron yields. It resulted in a wealth of new phenomena in laser-solid interactions that have been discovered in recent years. These include the observation of above-threshold photoemission from single nanostructures, effects of the carrier-envelope phase on the photoelectron emission yield from metallic nanostructures, and strong-field acceleration of electrons in optical near fields on subcycle timescales. The current state of the art of this field is reviewed, and several scientific applications that have already emerged from the fundamental discoveries are discussed. These include, among others, the coherent control of localized electromagnetic fields at the surface of solid-state nanostructures and of free-electron wave packets by such optical near fields, resulting in the creation of attosecond electron bunches, the coherent control of photocurrents on nanometer length and femtosecond timescales by the electric field of a laser pulse, and the development of new types of ultrafast electron microscopes with unprecedented spatial, temporal, and energy resolution. The review concludes by highlighting possible future developments, discussing emerging topics in photoemission and potential strong-field nanophotonic devices, and giving perspectives for coherent ultrafast microscopy techniques. More generally, it is shown that the synergy between ultrafast science, plasmonics, and strong-field physics holds promise for pioneering scientific discoveries in the upcoming years.

Figure 1

Illustration of strong-field photoemission at nanostructures. Sharp metallic nanotips localize and enhance the incident optical excitation (blue pulse under the tip) at the apex. Nonlinear photoemission induces ultrafast electron emission (green bunches at the apex), and the trajectories are driven by the optical near field.

Figure 2

Localized surface plasmons. (a) LSP generation on a metallic nanorod written onto a glass substrate. (b) Spectral resonance of LSP coupling for a gold nanorod with 150 nm length and (inset) the position of the resonance peak as a function of nanoparticle size. (c) Field amplitude map (in units of the amplitude of the incident field) for a 150-nm-long gold nanorod calculated at the LSP resonance wavelength.

Figure 3

Properties of plasmonic dimers. (a) 2D field map consisting of two gold nanospheres with 100 nm diameter and 10 nm gap and (b) a bow-tie structure with 10 nm gap. (c),(d) Corresponding field amplitude map in units of the amplitude of the incident field. (e) Extinction spectrum of a plasmonic dimer with two gold spheres ($d=100\mathrm{nm}$, $d_{\mathrm{gap}}=10\mathrm{nm}$), and a bow-tie structure with 10 nm gap. (f) Field enhancement in the gap region as a function of gap distance at the resonant wavelength. Data are plotted on a double-logarithmic scale.

Figure 4

Properties of nanotips. (a) SEM image of a sharp, chemically etched, single-crystal gold taper with an apex radius of $\sim 7\mathrm{nm}$. From [583]. (b)–(d) FDTD simulation of the vectorial field around a gold nanotaper. This displays the electric-field component (b) $E_z$ (along the taper axis), and (c) $E_x$ (perpendicular). (d) The absolute value of the electric-field with the vector orientation indicated by arrows ([231]). (e) Dependence of field enhancement $E/E_0$ on tip material for freestanding tips with apex radius $R=10\mathrm{nm}$, cone semiangle of $\theta =20°$, and wavelength $\lambda =630\mathrm{nm}$. The solid lines represent contours of constant potential. From [49].

Figure 5

Working principle of plasmonic nanofocusing. The incident laser light is focused to a $\sim 5\mu \mathrm{m}$ spot size onto a line grating (a). The launched SPP wave packet propagates as an evanescent wave toward the apex, where it is spatially confined and partially scattered into the far field. (b) Representative single-crystal, sharply etched gold taper. The taper opening angle is around 20°, and the apex radius is roughly 10 nm; see the inset of (d). A grating is ion-beam milled onto the shaft at a distance of about $30\mu \mathrm{m}$ from the apex. (c) Wide-field image of light scattered from the taper. Light scattering from the grating is spatially well separated from the apex emission, revealing efficient plasmonic nanofocusing toward the apex. (a)–(c) From [555]. (d) Scanning electron microscope image of a monocrystalline and sharp gold taper equipped with a grating coupler. From [47].

Figure 6

High-spatial-resolution plasmonic-nanofocusing (PNS) spectra of a single nanorod. (a) Topography of a $40\times 10{\mathrm{nm}}^2$ gold nanorod. (b)–(d) PNS spectra were recorded at each pixel during the scan. PNS intensity scans in select energy ranges, mapping the optical mode profile of the nanorod with 5 nm resolution. (e),(f) Cross sections extracted along the white dashed lines in (a) and (c), respectively. From [174].

Figure 7

Harmonic generation from nanostructures. (a) Third-harmonic light generation from a resonant bow-tie nanostructure; see the SEM image in the inset. From [244]. (b) Schematic illustration (left panel) and efficiency of THG for different nanostructure geometries exhibiting different damping times. From [245]. (c) Schematic illustration and SEM image (inset) of a multiresonant nanoantenna pair for mode-matched SHG. From [102]. (d) SEM image (left panel) and illustration of broadband optical antenna for tunable SHG. From [16]. (e). Second-harmonic yield as a function of coupling distance of two neighboring nanoantennas (schematically depicted in the graph) for near-field sensing. The different arrangements of the nanoantennas are shown in the insets underneath. From [441].

Figure 8

Attempts for plasmon-enhanced HHG in gaseous media. (a) Schematic illustration of the gas excitation in plasmon-enhanced fields using bow-tie nanoantennas. (Inset) The enhanced near field in which the gas atoms are excited. (b) Scanning electron micrographs of bow-tie antennas used by (left image) [328] and (right image) [617]. (c) Extreme-ultraviolet spectrum from argon atoms excited in a plasmon-enhanced field in bow-tie antennas as shown in (b), left image. From [328]. (d) XUV spectrum showing exclusively incoherent fluorescence from neutral and singly ionized argon. From [617]. (e) Reproduction of the results shown initially by [328], with consideration of the possibility that the emission can stem from incoherent processes. From [243].

Figure 9

Nonlinear plasma excitation of gas atoms in tailored nanostructures. (a) Schematic illustration of four-step dissociation of nitrogen molecules in the vicinity of a terahertz-driven metallic antenna. From [296]. (b) XUV gas excitation in a hollow waveguide. (Inset) The excitation scheme, where low-energy, femtosecond laser pulses are enhanced at the end of the waveguide and excite injected noble gas atoms. The XUV-intensity hysteresis as a function of incident laser intensity indicates the bistable character of the underlying excitation mechanism. Adapted from [620].

Figure 10

High-harmonic generation from solids in plasmon-enhanced fields. (a) XUV high-harmonic spectrum from a sapphire target excited with plasmon-enhanced low-energy femtosecond pulses at 800 nm from a megahertz laser oscillator. (Inset) The structure used consisting of sapphire cones with gold coating. Adapted from [243] (b) UV high-harmonic spectrum from silicon using plasmonic enhancement of $2\mu \mathrm{m}\mathrm{fs}$ laser pulses in rod-type gold nanoantennas (see the SEM image in the inset). Adapted from [674].

Figure 11

High-harmonic generation from tailored solids. (a) Principle of high-harmonic generation in structured solids. (Left panels) Cones on a ZnO surface. (Right panels) Gallium-implanted regions in a silicon wafer. (b) HHG from ZnO cones (SEM image, left inset). The incident laser field is localized to the apices of the cones, which leads to enhanced HHG in subwavelength hot spots. The far-field intensity (middle inset) shows a distinct diffraction pattern of the third (red) and fifth (blue) harmonics of $2\mu \mathrm{m}$ fundamental laser pulses. The distribution of the fifth harmonic is shown in the right inset. (c) Third-harmonic emission from a gallium-ion-implanted Fresnel-zone-plate silicon target, as shown in the inset. (d) Focusing along the optical axis of the generated radiation to diffraction-limited spot size (see the mode profile of the main diffraction focus in the inset). (a)–(d) Adapted from [621]. (e) SEM image of a spiral zone plate in ZnO with a gradual depth profile. (f) Donut-shaped focus profile of the fifth harmonic generated in the spiral zone plate from a $2.1\mu \mathrm{m}$ fundamental driver. (e),(f) Adapted from [208]

Figure 12

Photoemission mechanisms and corresponding experimental results. (a) Multiphoton photoemission. (b) Tunnel-assisted below-threshold photoemission. (c) Optically induced tunneling. (d) Log-scale intensity plot of photoelectron yield with (red, upper curve) and without (blue, lower curve) static bias voltage on the tip, showing a reduction of the effective nonlinearity. (Inset) Interferometric autocorrelation of the excitation pulses recorded using photoelectron signal. Adapted from [557]. (e) Photoelectron spectra from a negatively biased tungsten tip, evidencing a step-shaped structure from one- and two-photon processes and subsequent tunneling emission. Adapted from [723]. (f) Fowler-Nordheim plots of dc tunnel emission (blue squares) and photo-field emission (red circles). Adapted from [270].

Figure 13

Experimental photoelectron spectra (dots) in comparison with TDDFT computation (solid lines) for different laser intensities. Adapted from [692].

Figure 14

(a),(b) Magnitude of the electron wave function as a function of distance from the sample and time in the multiphoton and quasistatic tunneling regimes, respectively. Electric force (dashed line) acting on the ejected electrons and their trajectories (solid white lines). Adapted from [715]. (c) Local electron density in TDDFT simulation. Adapted from [692].

Figure 15

(a) Photoemission probability within the modified SFA (dotted orange line), TDSE results obtained using Crank–Nicolson approach (solid green line), and Floquet calculations (dashed blue lines) for work function $W=5.5\mathrm{eV}$ and $\hslash \omega =1.56\mathrm{eV}$. Adapted from [715]. (b) Photoelectron yield as a function of intensity. Red lines indicate the decrease of the effective nonlinearity from 4.3 to 0.89 during the transition between photoemission regimes. Adapted from [151].

Figure 16

Rescattering plateau in above-threshold photoemission at laser intensities ranging from $0.55\times {10}^{11}$ (light blue, lowermost curve) to $1.3\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ (black, top curve), and $\hslash \omega =1.56\mathrm{eV}$. (Inset) Cutoff energies as a function of intensity. The plateau region begins at 9 eV and extends up to 20 eV with a soft cutoff. Adapted from [364].

Figure 17

Subcycle acceleration. (a) Scanning electron micrograph of the gold nanotip with the apex region (inset). (b) Electron emission map obtained by scanning the excitation focus ($3.8\mu \mathrm{m}$ wavelength) across the structure. (c) Interferometric autocorrelations of the excitation pulses recorded using a photoelectron signal. (d) Electron trajectories (solid lines) calculated in the ponderomotive regime. (e) The same trajectories in the subcycle regime. Adapted from [256]. (f) Photoelectron spectra measured at constant local near field and various excitation wavelengths ($1.2–8.9\hspace{0.17em}\hspace{0.17em}\mu \text{m}$, corresponding to curves moving from left to right). Adapted from [165].

Figure 18

Limiting cases of instantaneous nonlinear photoemission. For a given material, different regimes of photoemission and acceleration are accessed depending on the field localization and ponderomotive energy.

Figure 19

Experimental techniques for the probing of optical near fields. (a) In scanning near-field optical microscopy, a nanometer-sized probe is brought into close vicinity of a nanostructure, scattering light from the near field to the far field. (b) A beam of swift electrons passing close by or through a nanostructure impulsively excites plasmonic modes. The energy transferred during the process is measured as a loss of the electron kinetic energy, or the light emitted during radiative relaxation is detected as cathodoluminescence (CL). (c) Photoelectrons emitted from the sample surface after far-field illumination are imaged to yield a high-spatial-resolution map of the local field distribution. (d) If a plasmonic nanostructure is excited optically, an electron passing by or through can gain energy, enabling photon-induced near-field electron microscopy. (e) Electrons photoemitted by an ultrashort UV pulse are accelerated in the near field of a nanostructure, driven by a NIR pulse. Measuring the kinetic energy as a function of delay between the UV and the NIR driving field gives access to the temporal near-field structure.

Figure 20

Scanning near-field optical microscopy of nanoplasmonic fields. (a) SNOM images of individual gold nanoparticles with 40 nm diameter. A local enhancement in light transmission through an aperture-type SNOM probe at certain colors is the signature of resonant light scattering by the nanoparticle. Scans are $750\times 750{\mathrm{nm}}^2$. From [330]. (b) Scattering-type SNOM imaging of 14-nm Au particles. When an AFM tip is scanned across a particle (left image), a large enhancement in scattered signal intensity is measured (center image). The deduced SNOM signal is shown in the right image. From [242]. (c) (Top left image) Topography and (top right image) SNOM image of a $\sim 50\text{−}\mathrm{nm}$ gold nanoparticle measured with white-light illumination through a fiber aperture probe. The scattering spectrum of the particle is shown in red together with simulations (solid black and dashed blue curves) based on a forced-oscillator model. From [445].

Figure 21

Time-resolved imaging of nanoplasmonic modes. (a) Plasmonic hot spots on a nanostructured gold film imaged by plasmonic-nanofocusing four-wave mixing (FWM) SNOM. (Left images) FWM signal and topography. Distinctly different dephasing times of the hot spots are found. From [353]. (b) Time-resolved two-photon photoluminescence SNOM imaging of the plasmon dynamics of a gold nanorod with length $l_{\mathrm{rod}}=615\mathrm{nm}$. (Top panel) SNOM image taken at a fixed time delay of 25.6 fs between two phase-locked excitation pulses. The standing-wave pattern along the horizontal axis, displayed in units of $l_{\mathrm{rod}}$, maps the resonantly excited eigenmode of the rod. A series of images taken as a function of delay times maps the lifetime of the plasmon mode. From [480].

Figure 22

Electron-beam-based imaging of nanoplasmonic modes. (a) EELS spectra obtained at three different positions on a Ag nanoprism (scanning electron microscopy image on the left): on a corner (A), on the edge (B), and in the center (C). Underneath are EELS images of the nanoprism showing the spatial distribution of the modes centered at 1.75, 2.70, and 3.20 eV. From [472]. (b) EELS maps of a split-ring resonator (image on the left) recorded at resonance energies of 0.37, 0.63, and 0.86 eV. From [689].

Figure 23

Photoemission electron microscopy images taken from a silver grating. (a) PEEM image using single-photon photoemission by a Hg lamp. (Inset) SEM image of the grating. (b) Two-photon photoemission image using 400-nm light with $p$ polarization. (c) The electron yield recorded from the topmost of the four hot spots marked in (b) is an interferometric time-resolved cross correlation of the laser pulse with the LSP. The inset magnifies a portion of the scan outside the pulse overlap, showing the shift of the LSP oscillation (blue symbols) with regard to the laser pulse optical interference (gray curve). (d) Details of the marked part in (b) for different time delays between pump and probe pulses. A clear variation of the oscillation phase can be observed after a time delay of approximately 20 fs. From [365].

Figure 24

Nanoplasmonic field imaging with PEEM. (a) PEEM images of a propagating surface plasmon polariton along a silver wire, recorded at time steps of 2 fs. The position of the upper maxima (see the maximum marked with a black arrow) depends on the temporal delay between the pump and the probe pulse, showing that it stems from SPP propagation dynamics on the nanowire. From [443]. (b) PEEM combined with an ultrafast pulse shaper and a learning algorithm (upper sketch) is used to illuminate a nanostructure consisting of three dimers of metal disks (marked with white circles in the first PEEM image). The upper left PEEM image is recorded with $p$-polarized laser light, the right-hand upper and lower images are recorded after optimization of the pulse shape for emission from regions A and B, respectively (regions A and B are marked with yellow squares). Adaptive optimization of the relative emission strength from regions A and B leads to increased (red, upper curve) and decreased (blue, lower curve) differences of electron yield from the two regions with respect to the unshaped laser pulse (black, curve in the middle). From [2]. (c) Surface plasmon polaritons with orbital angular momentum are optically excited via a slit in the shape of a spiral on a gold surface. The plasmons travel toward the center of the structure and form a plasmonic vortex. The images are taken at slightly different temporal delays between pump and probe pulse. From [628]. (d) Two plasmonic antennas are at the focus points of an elliptical cavity, and only one is illuminated by a sequence of ultrashort pulses. The photoemission recorded from the initially illuminated antenna shows coherent energy transfer between the two antennas. From [6]. (e) The fringe spacing of a LSP image is clearly reduced after illuminating a photochromic molecular switch with UV light, demonstrating control of the plasmon dispersion. This can be used to move the focal point of a plasmonic lens by 500 nm. From [232].

Figure 25

Principles of rescattering-based near-field probing. (a) Schematic drawing of the electron rescattering in the vicinity of a metal nanosphere. (b) Scheme of the experimental setup for nanoplasmonic near-field measurement with photoelectrons (black arrows). (c) Femtosecond-pulse-induced electron spectra for different nanoparticles (resonant, redshifted, and blueshifted nanorods as well as resonant bow ties) recorded by setting $25\mathrm{GW}/{\mathrm{cm}}^2$ focused laser intensity. Spectra are recorded by a time-of-flight spectrometer. (b),(c) From [149]. (d) Photoelectron spectrum with the spectral cutoff point indicated from which field enhancement is extracted. From [532].

Figure 26

Measurements of field enhancement factor on different nanostructured samples. (a),(b) SEM images of plasmonic nanoparticle samples. (c),(d) Plasmonic photoemission electron spectra as a function of focused laser intensity for the corresponding samples plotted in logarithmic false color representation. The white dashed lines show the linear dependence of the spectral cutoffs. (e),(f) Maximum plasmonic field enhancement values extracted from the electron spectral cutoffs according to Eq. (3.3) as a function of intensity for the corresponding samples, confirming the robustness of the measurement method. The horizontal lines show the simulated field enhancement values. From [532].

Figure 27

Attosecond streaking. (a) Concept of an attosecond streaking experiment during which an attosecond XUV pulse interacts with atoms from a gas flow in the presence of a few-cycle laser pulse. The released photoelectrons suffer a change of their initial velocities that is proportional to the vector potential of the field at the instant of release. From [229]. (b) The streaking spectrogram represents a series of kinetic energy spectra of electrons, emitted via attosecond XUV pulses and accelerated via a NIR-streaking field as a function of XUV-NIR delay. The trace represents the vector potential and enables the reconstruction of the streaking field waveform. From [348]. (c) Proposed combination of attosecond streaking with photoelectron-microscopy “atto-PEEM” to spatially and temporally resolve local plasmonic fields. From [640].

Figure 28

Streaking measurement from a nanotaper sample. (a) The energy shift of the streaking trace versus the time delay between the XUV and NIR pulses, shown by the white data points, was extracted by fitting a Fermi function (red) to the cutoff. (b) Reference streaking measurement in neon gas. The neon streaking trace is shifted in time by $250\pm 50$ as relative to the nanotaper trace. (c) Reconstruction of the local electric near field (green line) and vector potential (red line overlapping with the symbols) at the nanotaper surface from the measured streaking curve (symbols). The error bars indicate 95% confidence intervals of the Fermi fit. From [197].

Figure 29

Terahertz-near-field streaking at nanotips. (a) Realization of terahertz-near-field streaking measurement at nanotips via nonlinear photoemission with near-infrared pulses. (b) The local terahertz-near-field waveform at the apex of a gold nanotip is obtained from streaking spectrograms encoding electron kinetic energies as a function of streaking delay. From [705].

Figure 30

Near-field imaging with electron microscopy (a) Implementation of near-field imaging via electron microscopy with femtosecond-electron pulses. (b) Sequence of raw images for different terahertz-electron delays. (c) Extracted electric-field vectors at three different delays, scale bar $100\mu \mathrm{m}$. (a)–(c) Adapted from [566]. (d) Imaged electron beam with and without terahertz-streaking field. (e) Deflection diagrams for different delays, recorded with an uncompressed and terahertz-compressed electron bunch. (d),(e) From [744].

Figure 31

(a) (Top panel) Nonlinear photoemission into a terahertz near field enables the control of propagation, time structure, and energy of ultrashort electron pulses. (Bottom panel) Simulated energy compression after short propagation of a NIR-emitted electron ensemble via emission into a distinct phase of the terahertz near field, visualized for an equi-temporal set of snapshots. At the desired distance from the tip, the electron pulse reaches minimal velocity spread. Adapted from [706]. (b) (Top panel) Intense near-infrared pulses excite carriers in a nanotip. Time-delayed terahertz fields liberate hot electrons via field emission. (Bottom panel) In the streaking spectrograms, hot electron emission appears as the additional feature at 95 eV, tracing the electron relaxation (marked). Adapted from [257]. (c) (Top panel) Schematic of SPP clocking via terahertz nanostreaking. Propagating surface plasmon polaritons (SPPs) are excited at a grating coupler and emit electrons upon arrival at the apex. The propagation delay is clocked via the instant of emission and streaking by the terahertz near field. (Bottom panel) Experimental streaking spectrogram for grating excitation and terahertz acceleration from the apex. The time delay from $\tau =0$ encodes the SPP propagation time. From [707].

Figure 32

Field-driven current across a symmetric tunnel junction. (a) Scanning electron microscopy image of the contacted, symmetric bow-tie antenna with an 8-nm-wide gap. (b) Reconstructed electric field of the applied few-cycle laser pulse with the carrier-envelope phase (CEP) set to 0 (blue curve having maximal amplitude at 0 fs) and $\pi /2$ (red curve) by inserting dispersive material in the beam path. (c) Total current over the bow-tie antenna as a function of the CEP variation. Shown are eight individual measurements (thin gray curves) and their average (thick red curve). The black symbols indicate the fundamental symmetry of the electric fields of the applied NIR laser pulses. From [567].

Figure 33

Nanoplasmonic vacuum-tube diode. (a) Optical microscopic image of the two metal nanotips facing each other. (b) Schematic of the two tips in the focus of a few-cycle laser pulse. The sharper tip functions as the cathode and the blunter as the anode, labeled $C$ and $A$, respectively. (c) Laser-induced current between the two tips as a function of the laser focus position for three different tip-tip distances. The curves are offset for clarity. Positive current means the electrons travel from cathode to anode. Negative currents are measured when the blunter tip is illuminated and are shown here magnified by a factor of 50. From [259].

Figure 34

Chip-scale realizations of plasmonic switches. (a) SEM image of asymmetric nanojunctions with pointed emitters ($E$) opposing flat collectors ($C$). Scale bar, $2\mu \mathrm{m}$. (Inset) Close-up of thee emitter-collector region. Scale bar, 200 nm. (b) The unipolar photocurrent measured as a laser focus is raster scanned across the chip, color coded and overlaid on the SEM. Scale bar, $5\mu \mathrm{m}$. (a),(b) From [309]. SEM image of asymmetric nanojunctions with diamond-shaped emitters (c) before and (d) after laser illumination, showing the structural change and decrease of the gap. (e) Current measured before (blue curve fluctuating around zero) and after (red curve) illumination, as a function of a stationary bias. The red curve can be well fitted with a Fowler-Nordheim curve (black). (c)–(e) From [755].

Figure 35

Achievable temporal resolution in ultrafast point-projection electron microscopy. The time-of-flight spread is shown for various acceleration voltages and tip-sample distances. The region with tip-sample distances below $10\mu \mathrm{m}$ is marked in gray to indicate that this region is difficult to reach in a pump-probe setup. From [530].

Figure 36

Point-projection electron microscopy images of a single freestanding carbon nanotube. The interference of electrons being scattered from the nanotube and electrons passing the nanotube unperturbed can be observed. (a) Laser-driven electron emission at 400 nm. (b) Electrostatic electron emission. The corresponding lineouts are shown in (c) for laser-driven emission and (d) for electrostatic tunneling. From [167].

Figure 37

UPEM of InP nanowires. (a) Image of the nanowire recorded at a negative time delay, i.e., before optical excitation. (b) Normalized difference image recorded at a positive time delay of 150 fs. The different behavior of the $p$-doped (upper) and $n$-doped (lower) parts of the nanowire are clearly visible. (c) Apparent width of the nanowire for the two regions and different time delays. (Inset) Extracted current in the nanowire calculated from the width of the wire. From [462].

Figure 38

Two examples of remotely driven electron emission from sharp gold tapers. (a) SEM micrograph of a sharp gold taper with a grating coupler. (b) Number of electrons emitted from the taper apex when raster scanning the taper through a laser focus. Electron emission can be observed only when the grating coupler or the taper apex are illuminated. A 50-fold increase in electron count rate is reached when illuminating the grating coupler compared to the taper apex. This is due to the efficient nanofocusing of surface plasmons at the taper apex after their launching at the grating coupler. (a),(b) From [684]. (c) Drawing of an extractor-suppressor geometry used to suppress unwanted direct electron emission from the grating coupler. For certain voltage settings, only those electrons emitted from the taper apex are extracted. (d) Demonstration of the setup shown in (c). Electrons emitted from the right side of the vertical line are suppressed, proving that grating illumination indeed leads to emission from the apex. (c),(d) From [592].

Figure 39

Ultrafast plasmon-driven point-projection electron microscopy. (a) Schematic of the setup. (b) SEM image of the 30-nm thin gold film sample. A double nanohole structure is milled into it such that it forms a small resonator with a gap region in the middle. (c) Series of shadow images recorded at the central part of the nanostructure shown in (b) for different time delays between the pump laser and the electron-probe pulse. (d) Shadow image without optical excitation of the sample. (e) Lineouts through three images shown in (c) and (d). A spatial resolution of 20 nm is found. (f) Temporal evolution along certain positions on the arrow shown in (d). The expansion of the cloud can be followed with a temporal resolution of less than 25 fs. From [683].

Figure 40

Inelastic electron-light scattering in optical near fields. (a),(b) Electrons traversing an intense optical near field at a nanostructure gain or lose energies in multiples of the photon energy. (c) The electron-energy spectrum after interaction (red curve, shown also in the inset) consists of multiple photon sidebands. $t=0$, electron and optical pulse are temporally overlap; $t=-2\mathrm{ps}$, electrons pass the nanostructure before the optical excitation. (d) Energy-filtered electron micrographs collecting electrons that gained between one and four photon energy quanta of an optically excited carbon nanotube (electron–laser pulse delay 0 ps) for two optical polarization directions (indicated as arrows). (a)–(d) From [39]. (e) Amplitudes of (upper panel) zero-loss peak and (lower panel) $n$th-order photon sidebands depending on the distance from the nanoparticle surface. From [737].

Figure 41

Energy-momentum matching in inelastic electron-light scattering. (a) Dispersion relation of electrons (blue curve, labeled as “Electron”), free photons (green curve, labeled as “free”), and photons within a dielectric medium (red curve, labeled as “retarded”). From [497]. (b) Energy-momentum conservation of a free electron and free photon via momentum broadening (horizontal ellipses) due to spatial confinement and energy broadening (vertical ellipse) due to temporal confinement. The solid green line (“Free Photon”) represents the dispersion relation of a free photon, and the dotted blue line represents the momentum change of a free electron at the given energy change. From [497].

Figure 42

Coherent optical modulation of a free-electron state. (a) An electron pulse traversing a localized optical near field acquired a sinusoidal phase modulation. (b) Electron-energy spectra at incident optical fields of 0, 0.023, 0.040, 0.053, and $0.068\mathrm{V/}\mathrm{nm}$ (bottom to top). (c) Level diagram of electron energies coupled by the optical near field. Different interfering quantum paths between the levels are indicated by arrows. (d) Experimental electron-energy spectra depending on (left panel) the incident optical-field strength compared to (right panel) a numerical simulation taking. From [186].

Figure 43

Ramsey interferometry with free-electron wave functions. (a) Schematic of the Ramsey interferometry approach for free electrons utilizing two phase-locked optical near fields. (b) Electron-energy spectra after the second interaction zone depending on the relative phase of the two near fields. $\theta$ denotes the orientation of a $\lambda /2$ plate, used for controlling the relative near-field phase. From [164].

Figure 44

Formation and characterization of attosecond electron pulse trains. (a) The first optical near field imprints a sinusoidal phase modulation on an ultrashort electron pulse. The second near field probes the temporal structure of the dispersed pulse. (b) Spectrogram showing the dependence of the electron-energy spectra on the relative phase between the two near fields. (c) Reconstructed Wigner function of the propagated electron pulse at the second interaction zone. The time marginal demonstrates the formation of an attosecond electron pulse train with spike widths of 655 as. From [524].

Figure 45

Mapping plasmonic modes with high-spectral selectivity. (a) Spatial map of inelastic electron scattering probability around a silver nanowire for a range of incident photon energies (given in the bottom line). The scattering probability is characterized by recording energy-filtered electron micrographs at the initial electron energy, thereby quantifying the local electron scattering probability. (b) Spatial Fourier transforms of the photon-energy-dependent scattering probability maps [shown in (a)] evaluated along the wire direction. (c) Fourier amplitude integrated in the spatial frequency range indicated in (b) as a function of the photon energy of the incident light field. From [519].