Infrared PINEM developed by diffraction in 4D UEM

Significance

One of the most significant advances made is the ability to visualize nanoscale objects and to determine their shapes (through imaging) and their atomic-scale structure (through diffraction). Furthermore, for optical excitation of the nanostructure the photon-induced near-field EM (PINEM) imaging results in the mapping of nanostructure plasmonics with high spatial–temporal resolution. Here, we show that PINEM can be exploited in the infrared region with greater sensitivity, and that diffraction can be implemented for structural dynamics. Just as importantly, the time resolution of ultrafast EM (UEM), which already far exceeds, by 10 orders of magnitude, that of conventional EM, may be further enhanced by IR PINEM and photon gating with the unprecedented energy resolution (0.63 eV) reported here for UEM.

Abstract

The development of four-dimensional ultrafast electron microscopy (4D UEM) has enabled not only observations of the ultrafast dynamics of photon–matter interactions at the atomic scale with ultrafast resolution in image, diffraction, and energy space, but photon–electron interactions in the field of nanoplasmonics and nanophotonics also have been captured by the related technique of photon-induced near-field electron microscopy (PINEM) in image and energy space. Here we report a further extension in the ongoing development of PINEM using a focused, nanometer-scale, electron beam in diffraction space for measurements of infrared-light-induced PINEM. The energy resolution in diffraction mode is unprecedented, reaching 0.63 eV under the 200-keV electron beam illumination, and separated peaks of the PINEM electron-energy spectrum induced by infrared light of wavelength 1,038 nm (photon energy 1.2 eV) have been well resolved for the first time, to our knowledge. In a comparison with excitation by green (519-nm) pulses, similar first-order PINEM peak amplitudes were obtained for optical fluence differing by a factor of more than 60 at the interface of copper metal and vacuum. Under high fluence, the nonlinear regime of IR PINEM was observed, and its spatial dependence was studied. In combination with PINEM temporal gating and low-fluence infrared excitation, the PINEM diffraction method paves the way for studies of structural dynamics in reciprocal space and energy space with high temporal resolution.

Since its invention in the 1930s by Knoll and Ruska (1), the electron microscope has become a powerful tool in the fields of physics, chemistry, materials, and biology. A great variety of techniques related to the electron microscope has been developed in image, diffraction, and energy space (2, 3), with the spatial and energy resolutions of the transmission electron microscope now reaching 0.5 Å with Cs corrector (4) and sub-100 meV with electron monochromators (5, 6), respectively.

To these capabilities of spatial and energy resolution has been added the high resolution in the fourth dimension (time) by the development of four-dimensional ultrafast electron microscopy (4D UEM) (7–9), currently enabling nanoscale dynamic studies with temporal resolution that is 10 orders of magnitude better than the millisecond range of video-camera-rate recording in conventional microscopes. In 4D UEM, ultrafast time resolution is reached by using two separate but synchronized ultrashort laser pulses, one to generate a probing electron pulse by photoemission at the microscope cathode and the other to excite the specimen into a nonequilibrium state. The state of the specimen within the window of time of the probe pulse can be observed by recording the probe electron packet scattered from the specimen in any of the different working modes of the microscope, such as image and diffraction (10), energy spectrum (11), convergent beam (12), or scanning transmission electron microscopy (TEM) (13). Scanning the time delay between arrival of the pump and probe pulses at the specimen, which is controlled by a precise optical delay line, allows the evolution of the specimen to be traced.

One of the important techniques developed in, and unique to, UEM is photon-induced near-field electron microscopy (PINEM) (14). PINEM has extended the capability of UEM to observation of light–electron interactions near nanostructures or at an interface, which offers exciting prospects for the study of dynamics of photonics and plasmonics at the nanometer scale (15). The three-body interaction of photon, electron, and nanostructure relaxes momentum conservation and leads to efficient coupling between photons and electrons (16). In PINEM, an ultrashort optical pulse is used to excite evanescent electromagnetic fields near a nanostructure or at an interface. When the probe electron packet is in spatiotemporal overlap with these evanescent or scatter fields, some of its electrons can absorb/emit one or more scattered photons and then be detected by their contributions to displaced energy peaks in the electron energy spectrum. These displaced peaks appear as discrete sidebands to the zero-loss peak at separations given by the photon energy (hν) of the pump optical pulse. When using energy filtering to select for imaging only those electrons gaining energy, the resulting PINEM image reflects the strength and topology of the excited near field around the nanostructure or interface.

The PINEM technique has been used to detect the evanescent near field surrounding a variety of structures with different materials properties and different geometries, such as carbon nanotubes (14), silver nanowires (14, 17), nanoparticles (16, 18), cells and protein vesicles (19), and several-atoms-thick graphene-layered steps (20). In addition, focused-beam PINEM has been used in scanning TEM mode to obtain induced near-field distributions for a copper grid bar (21), a nanometer gold tip (22), and a silver nanoparticle at the subparticle level (21). In a recent publication, three pulses, two optical and one electron, were introduced into the arsenal of techniques to gate the electron pulse and make its width only limited by the optical-pulse durations (23). Numerous general theoretical treatments (24–28) have successfully described the phenomenon, with detailed treatments quantitatively reproducing many unique features of these multifaceted experimental observations (17, 20–22).

Despite the growing body of PINEM studies, almost all previously published PINEM results were obtained in the image mode of the electron microscope using optical pulses with wavelengths of 500–800 nm. An exception is a single unresolved PINEM spectrum for 1,038-nm excitation published from this laboratory (25). Because the PINEM response of a material is governed by its optical properties and dimensions relative to the wavelength of light, excitation wavelength is an important parameter largely remaining to be explored experimentally.

Here we report the development of IR PINEM using excitation at the wavelength of 1,038 nm (photon energy 1.2 eV). The spatial- and fluence-dependent behavior of well-resolved IR PINEM induced at the edge of a copper grid bar is examined by combining nanometer-scale convergent-beam electron diffraction and diffraction-mode detection for electron-energy spectroscopy with an unprecedented energy resolution down to 0.63 eV at 200 keV. Different e-beam size effects were compared for PINEM generated by green and IR pump pulses. The spatial dependence of IR PINEM at the interface was studied at low-pulse fluence (linear regime) and high-pulse fluence (nonlinear regime). Diffraction of a gold crystal film was observed using the energy-resolved PINEM electrons produced by interaction with the scatter field of the adjacent copper grid edge. Notably, substantial PINEM peak amplitudes were achievable at dramatically lower fluence for IR pulses than for green pulses, opening up a possible path for studies of photosensitive materials. This general accessibility of strong PINEM signals is of particular importance for our primary interest of ultrafast dynamics, for which PINEM photon gating has the potential to vastly improve temporal resolution.

All PINEM experiments reported here were performed on the California Institute of Technology UEM-2 apparatus. The operation voltage on UEM-2 is 200 keV. The laser system used emits a train of ∼220-fs pulses with wavelength of 1,038 nm, set to operate at a repetition rate of 1 MHz. The laser output was frequency-doubled two successive times to provide the 259-nm pulses used to generate the electron packet (probe beam) at the 200-keV microscope photocathode source. The residual 1,038-nm and 519-nm optical pulses were each available for use as the PINEM pump beam to excite the near-field plasmons at the interface. All of the experiments were carried out with polarization set to be perpendicular to the interface and in the single-electron regime (8) to eliminate space-charge effects. In diffraction mode, a camera length of 920 mm and a spectrometer entrance aperture of 1 mm were used to obtain a small collection angle for better energy resolution.

PINEM: Image Mode and Diffraction Mode

Fig. 1 illustrates schematically PINEM measurements in image mode and diffraction mode of the microscope. For standard PINEM studies in image mode (Fig. 1A), the electron beam is unfocused and spread on the specimen, although focused beams have also been used. On the microscope view screen, a typical bright-field TEM image of one carbon nanotube is shown. By using an electron-energy-spectrometer entrance aperture which encompasses the nanotube area, the PINEM electron-energy spectrum is integrated over the entire area covered by the aperture when the optical and electron pulses are coincident on the specimen. In energy-filtered imaging using only those electrons that gain energy from photons, a PINEM image of the near field surrounding the nanotube is obtained. The dependence of the near-field signal on delay between the optical and electron pulses can be extracted from the recorded PINEM energy spectrum or image. The temporal response, as shown at the bottom of the figure, represents a convolution of the temporal profile of the induced field with those of both the optical and electron pulses.

Fig. 1.

Variant implementations of PINEM in UEM. (A) PINEM in image mode using a parallel electron beam and green optical pulses. The nanostructure specimen is seen as a bright-field image on the view screen and as an energy-filtered PINEM image or PINEM electron-energy spectrum after the spectrometer. The time-delay dependence of the PINEM signal shown at the bottom can be extracted from a series of spectra or images. (B) PINEM in diffraction mode using a focused nanometer electron beam and IR optical pulses. The ultrafast electron pulses are focused near the interface between a copper grid and gold film. A typical CBED pattern is observed on the view screen, and a small spectrometer entrance aperture is used to select a single diffraction spot for energy dispersion. After the spectrometer, an energy-filtered PINEM diffraction image or electron-energy spectrum is recorded. For a description of the time plot at the bottom, see A.

In the diffraction mode measurement illustrated here (Fig. 1B), the electron beam is focused to nanometer scale on a gold film in close proximity to a copper grid bar. On the view screen, a typical convergent-beam electron diffraction (CBED) pattern is observed; diffraction spots are enlarged (12). By using a smaller spectrometer entrance aperture to cover one single diffraction spot, the PINEM diffraction and energy spectrum can be obtained from only that chosen diffraction spot. In this concept of PINEM diffraction, the PINEM electrons exchange energy with the optical field scattered from the copper while being diffracted from a nanometer scale area of the gold specimen. This makes it possible to use a PINEM signal to study structural dynamics of a local area of a specimen of arbitrary structure and optical properties. The temporal confinement of the PINEM electrons can thus be exploited for greatly improved time resolution in diffraction studies (23, 29).

Another advantage of recording PINEM in diffraction mode is an improvement in the energy resolution in UEM operated at 200 keV, which reaches the 0.63-eV value. This improvement, attributed to the reduced dispersion effect of electron scattering in different directions, makes it easy to observe well-resolved PINEM peaks separated by the IR photon energy of 1.2 eV, as shown by the IR PINEM electron-energy spectrum in Fig. 1B. The PINEM signal dependence on interpulse time delay can again be extracted from the electron-energy spectrum (as described above for image mode) and is shown in Fig. 1B, Bottom.

PINEM: e-Beam Size and b-Material Effect

The distinction between the two types of experiment of Fig. 1 is further illustrated in Fig. 2 A and B. Fig. 2A shows an unfocused e-beam, spread to a diameter of about 1.7 µm, centered on the interface between vacuum (Upper Left) and a copper grid (Lower Right), indicated by the solid red line. The dashed circle represents the total e-beam illumination area, with no electrons passing through the copper grid due to its thickness (20-µm typical value). Under this e-beam condition, the resulting PINEM electron-energy spectrum is the integration of electron–photon interactions over the entire beam cross-section in the vacuum region. For such a large beam width, the PINEM response is very inhomogeneous, resulting in measurement of the average signal over the illuminated area.

Fig. 2.

(A) Unfocused e-beam experiments. The unfocused beam illuminates the interface between vacuum and copper grid. The dashed circle shows the e-beam coverage area (1.7 µm in diameter). (Scale bar, 500 nm.) (B) Focused e-beam experiments. The e-beam is focused to nanometer size (33-nm FWHM) at the interface between the vacuum and Cu grid. The e-beam is scanned away from the grid along the green arrow to obtain the distance dependence of the near field at the interface. (Scale bar, 500 nm.) The dashed circle shows the unfocused beam size from A for comparison. (C–F) PINEM electron-energy spectra obtained at t = 0 in diffraction mode at the interface between vacuum and Cu grid using two different e-beam sizes for two different wavelengths of the optical pulse. The energy loss is referenced to the original zero-loss energy of the incident electron beam. All of the electron-energy spectra have similar first PINEM peak ratio relative to the ZLP. (C) e-beam size 130 nm, green light (λ = 519 nm) with excitation fluence of 2.7 mJ/cm². (D) e-beam size 130 nm, infrared light (λ = 1,038 nm) with excitation fluence of 0.04 mJ/cm². (E) e-beam size 33 nm, green, 1.6 mJ/cm². (F) e-beam size 33 nm, infrared, 0.37 mJ/cm².

In contrast, in Fig. 2B a series of three e-beams focused to nanometer size (33-nm FWHM) is shown at the same image scale as Fig. 2A. In this case the resulting PINEM is contributed by the electron–photon interaction localized over a small range of b (impact parameter or distance from the interface) and all electrons are subject to a spatially homogeneous scattered light field. When the nanometer e-beam is scanned away from the grid along the green arrow (increasing b), the spatial profile of PINEM induced by the evanescent near field at the interface can be obtained, as done previously for green excitation (21).

Fig. 2 C–F compares PINEM spectra recorded in diffraction mode at two pump wavelengths and two e-beam diameters (d), all with similar amplitudes for their n = ±1 PINEM peaks (ΔE = ± hν). The probe beams in each case pass close to the copper edge (b ∼ d/2) in vacuum and the temporal overlap between electron and photon pulses is maximized (i.e., at delay t = 0). Shown in Fig. 2C is the PINEM electron-energy spectrum excited by green (519-nm) optical pulses at a fluence of 2.7 mJ/cm². The energy loss is referenced to the original zero-loss energy of the incident electron beam. The e-beam size used is 130 nm, obtained by controlling the condenser lens strength and using a smaller condenser aperture. Because there is no substrate there are no diffraction peaks; only the central directed beam was selected for dispersion in the spectrometer by a small entrance aperture. The discrete peaks of the PINEM energy spectrum at a separation of 2.4 eV are very well resolved, and up to 6-photon absorption and emission can be observed with the amplitude of each successive peak decreasing by a factor of ∼2. The first gain/loss peak shows a 48% amplitude ratio relative to that of the zero-loss peak (ZLP).

For comparison, at the same interface and using the same e-beam size and position, Fig. 2D shows the PINEM electron-energy spectrum for 1,038-nm excitation at a fluence of 0.04 mJ/cm², also with n = ±1 PINEM peak amplitudes 48% of the ZLP. However, in this case only two gain/loss peaks, separated by an energy of 1.2 eV, are seen and well resolved. Thus, for the same experimental conditions and the same relative amplitude of the n = 1 peaks obtained for green and IR, the IR fluence is a factor of greater than 60 times lower. Similarly, in Fig. 2 E and F, green- and IR-induced PINEM spectra are compared for a smaller e-beam size of 33 nm adjacent to the same copper–vacuum interface. The green fluence (1.6 mJ/cm²) is again much higher (now a factor of ∼4) than that of the IR (0.37 mJ/cm²) to produce similar n = 1 peak amplitude ratios.

Comparisons between Fig. 2 C and E and between Fig. 2 D and F show the effect of change in e-beam size (accompanied by a change in impact parameter in this case) for PINEM at the copper interface excited by the same light pulses. Similar PINEM generated by lower excitation fluence for the smaller e-beam size (33 nm) than for the larger size (130 nm) is consistent with the weak interaction limit of PINEM theory and a near field decaying away from the interface. This is the trend seen for green excitation, but not for IR excitation (see below).

PINEM in Diffraction Mode: Energy Resolution

Fig. 3A is an expanded view of the IR PINEM spectrum of Fig. 2D, showing the two discrete gain and loss peaks. The zero-loss energy spectrum obtained under the same conditions, but at t = −3 ps (before the optical pump pulse arrival) is shown in Fig. 3B. The energy resolution is 0.63 eV, the best energy resolution reported in UEM at 200 keV. The energy resolution in the microscope is measured from the FWHM of the ZLP. The energy resolution is mainly determined by the width of the energy spread provided by the electron source, which is typically between 1 and 2 eV for the tungsten filament or heated LaB₆ source and 0.5–1 eV for a Schottky or cold field-emission source without electron monochromator (30). In pulsed UEM systems, most of which use thermionic sources, resolution is typically above 1 eV at an operating energy of 200 keV (31).

Fig. 3.

(A) PINEM electron-energy spectrum obtained at the interface between the vacuum and Cu grid using an e-beam size of 130 nm in diffraction mode, under IR (1,038 nm) excitation fluence of 0.04 mJ/cm². (B) The zero-loss energy spectrum obtained in diffraction mode, at t = −3 ps showing the energy resolution of 0.63 eV determined by the Gaussian fit (solid line). (C) Dependence of PINEM peak amplitudes on distance away from the grid–vacuum interface. The e-beam (33 nm) was scanned along the green arrow in Fig. 2B. The solid lines show exponential fits, yielding damping constants of 164 nm and 60 nm, respectively for the first- and second-order PINEM peaks. (Inset) Illustration of the geometry and x coordinate of the thin strip (dark gray) to which Eq. 1 applies. The light-gray block represents schematically the actual Cu grid bar used in our experiments. (D) Time-delay dependence of the first and second PINEM peak amplitudes. The solid lines are Gaussian fits (FWHM: 910 fs, 640 fs). (E) Bright-field UEM image showing the interface of gold film and Cu grid under unfocused e-beam illumination. (Scale bar, 1 µm.) (F) [1$\overline{1}$ 0] zone axis, CBED pattern from an 11-nm-thick gold single-crystal film using a focused e-beam (300 nm). (Scale bar, 5 nm⁻¹.)

Also affecting the energy resolution are aberrations of the electron spectrometer, which can be almost eliminated by curving the polepieces of the magnetic prism and by using weak multipole lenses for fine tuning (30). However, in actual experiments, the electrons are scattered by the specimen in different directions, especially when there is strong diffraction in a crystalline specimen. Due to inherent characteristics of the magnetic prism, electrons scattered in different directions hit different targets on the detector in energy space after passing through the spectrometer, which decreases the energy resolution, especially in image mode. In fact, when recording electron-energy spectra, it is not necessary to collect all of the scattered electrons, part of which can be filtered out without harming the results.

In the spectrometer, there are three important parameters for optimization of the experimental conditions: the entrance aperture angle (γ), the object size, and the maximum collection angle (β). In diffraction mode, these three parameters can be adjusted unambiguously and independently; γ is controlled by the spectrometer entrance aperture, object size is determined by the selected area aperture, or by the size of the illuminated area, and β can be adjusted by the camera length depending on the size of the spectrometer entrance aperture. In our focused e-beam diffraction case, the object size is limited by the nanometer-scale area illuminated by the focused electron beam. To improve energy resolution, a choice of suitable size of the spectrometer entrance aperture and camera length ensures that only a single diffraction spot, consisting of electrons scattered in the same direction, is selected to form the electron energy spectrum. The maximum collection angle β used here is about 7 mrad.

IR PINEM: Spatial and Temporal Dependence in the Linear Regime

To observe the spatial localization of electron–photon interactions in the PINEM effect excited by IR pulses at the interface of vacuum and Cu grid, the focused e-beam with a size of 33 nm was scanned into vacuum away from the Cu grid along the green arrow in Fig. 2B. A low IR optical pulse fluence of 0.04 mJ/cm² was used to remain in the linear regime. As shown in Fig. 3C, the spatial dependence of the amplitudes of first- and second-order PINEM peaks decays quasi-exponentially with b. The values shown are direct amplitude measurements in spectra recorded with a constant exposure and electron flux. The solid lines are exponential fits, corresponding to decay constants of ∼164 nm and 60 nm for n = 1 and n = 2, respectively. Fig. 3D shows the time dependence of the first- and second-order peaks extracted from time-resolved PINEM energy spectra obtained at the interface using e-beam size of 130 nm at an IR pulse fluence of 0.04 mJ/cm². The Gaussian fits indicated by the solid line give FWHM values of 911 fs for n = 1 and 642 fs for n = 2.

For understanding of the expected topology of the PINEM signal at the copper grid edge, it is pertinent to give here a brief account of previous theoretical descriptions relevant to the situation. The scattering of the electron packet traveling through the scattered electromagnetic wave of a nanoparticle or an interface induced by an optical pulse can be treated in the regime of the time-dependent Schrödinger equation (25). The theoretical study has shown that PINEM can be related to optically driven charge-density distributions of nanoparticle plasmons (28). The PINEM intensity is approximately proportional to the absolute square of the field integral ${\tilde{F}}_0$ (i.e., $I_{PIN}\propto {\left|{\tilde{F}}_0\right|}^2$). For the case of an infinite thin strip with axis perpendicular to both the propagation direction and polarization direction of the incident light pulse, as represented in dark gray in Fig. 3C (Inset), a near-field approximation of the field integral derived in the weak-interaction limit has been given as (20)

$${\tilde{F}}_0\approx -i{\tilde{E}}_0{\chi }_b\hspace{0.17em}\frac{h}{2}\{e^{-\mathrm{\Delta }{k}_e\left|x-\left(w/2\right)\right|}-e^{-\mathrm{\Delta }{k}_e\left|x+\left(w/2\right)\right|}\},$$ [1]

where E₀ is the amplitude of the incident electric field, h is the strip height, w the strip width, $\mathrm{\Delta }{k}_e$ the momentum change of the electron, x the distance normal to the axis of the strip measured from the center of the strip width, and ${\chi }_b\approx [\left(w+h\right)/\left(w+\epsilon h\right)]\left(\epsilon -1\right)$, where ${\chi }_b$ is the material susceptibility and $\epsilon$ the dielectric function. From Eq. 1, the PINEM intensity is dependent on material properties, shape and size of the strip, the polarization and intensity of the optical pulse, and location. The decay length in the exponential terms is (Δk_e)⁻¹, where $\mathrm{\Delta }{k}_{\epsilon }={\omega }_p/{\nu }_{\epsilon }$ for light of angular frequency ω_p and an electron with velocity υ_e. This length is simply proportional to the wavelength of incident light; for 200-keV electrons and 1,038-nm light, (Δk_e)⁻¹ is 115 nm. Thus, for a strip much wider than the wavelength of light, the second term in Eq. 1 disappears, and the amplitude of the PINEM field is seen to decrease exponentially with distance away from the strip edge (located at w/2).

Although Eq. 1 is an approximation derived for a thin strip (on the nanometer scale), it provides qualitative agreement with the PINEM signal behavior shown in Fig. 3C for the case of the copper grid bar at low fluence. However, the height of the grid is in fact much greater than the wavelength of light. This micrometer extent of the specimen, represented by the light-gray slab in Fig. 3C (Inset), may introduce phase differences and inhomogeneity in the field interacting with the electrons, and such effects must be properly considered for a quantitative treatment of the signals observed here.

The above comments about the effect of the thickness of the grid bar are relevant to the comparison of Fig. 2 D and F also. The very large difference in fluence for similar PINEM signals when reducing the e-beam size is not expected from consideration of Eq. 1, but the thick grid and its relation to the wavelength of light may be responsible for the difference in IR and green behavior. Future experiments should examine the wavelength, fluence, and e-beam size dependence independently and for different structures.

Fig. 3E shows a bright-field image of the interface between a gold film and Cu grid illuminated by an unfocused e-beam. A typical CBED pattern of [1 $\overline{1}$ 0] zone axis gold single crystal is given in Fig. 3F, which was obtained at the interface using a 300-nm e-beam. The IR PINEM electron-energy spectrum can be obtained from each single diffraction spot or the central directed spot by using a suitably sized spectrometer entrance aperture. The study of structural dynamics for an arbitrary substrate at high temporal resolution is possible in this PINEM configuration using the power of PINEM photon gating (23, 29). In this technique, an optical PINEM pump pulse is fixed in time with respect to the electron pulse, thus gating a pulse of PINEM electrons of duration controlled by the optical pulse length. This subset of electrons, detected separately by energy filtering, becomes the probe for dynamics initiated by a second time-delayed ultrafast optical pulse focused on the specimen. The achievable time resolution is in this case limited only by the optical pulse lengths. Note also that there is no restriction on the type of specimen that may be studied in this scheme because the structural and material requirements for the generation of the PINEM signal are imposed exclusively on the grid bar.

IR PINEM: Nonlinear Phenomena

To further characterize the IR PINEM of the copper grid, the IR pump intensity was increased beyond the linear range. Fig. 4 A and B shows two IR PINEM electron-energy spectra recorded in diffraction mode using a 33-nm e-beam under excitation fluence of 0.08 mJ/cm² and 2.2 mJ/cm², respectively. As shown in Fig. 4A in the low-fluence regime, only weak first-order absorption/emission peaks are observed in the PINEM energy spectrum. However, in the high-fluence regime of Fig. 4B, the PINEM energy spectrum shows multiple discrete sideband peaks with up to 13 net photons absorbed and emitted. In contrast to PINEM energy spectra in the linear regime, the peak amplitudes in the orders from n = $\pm$2 to $\pm$4 are even higher than the zero-peak amplitude, which is called an “inverted distribution” behavior (25).

Fig. 4.

Nonlinear IR PINEM at the interface between the vacuum and Cu grid. (A and B) IR PINEM electron-energy spectra recorded in diffraction mode using a 33-nm e-beam under different IR excitation fluence of (A) 0.08 mJ/cm² and (B) 2.2 mJ/cm². (C) Distance dependence of IR PINEM peaks up to the 10th order obtained by scanning the 33-nm e-beam away from the interface under excitation fluence of 2.2 mJ/cm². (D) The energy resolution is 0. 7 eV measured from the zero-loss energy spectrum. (E) Time-and energy dependence of PINEM electron-energy spectra obtained at the interface for 130-nm e-beam and IR fluence of 1.25 mJ/cm².

Fig. 4C depicts the nonlinear behavior of spatial dependence of IR PINEM peaks up to the 10th order obtained by e-beam (33 nm) scanning away from the interface between vacuum and Cu grid. The excitation fluence used here is 2.2 mJ/cm². As for Fig. 3C, the peak amplitudes are measured directly from spectra recorded under fixed conditions. Unlike the exponential decay of PINEM peak amplitude of the first- and second order in the linear regime (Fig. 3C), the nonmonotonic behavior of peak amplitude from order n = $\pm$1 to order n = $\pm$6 is very clear, in which the distance from the grid of maximum peak amplitude decreases with increasing order of absorption/emission. The energy resolution used in spatial dependence experiments is 0.7 eV, as shown in Fig. 4D.

Previous theoretical study predicted that in the weak-interaction limit the temporal dependence is precisely the convolution of incident electron packet and photon pulse profile, whereas for increasing interaction strengths broadening of the temporal width and deviation from Gaussian behavior is the direct result of nonlinear effects (32). The probability amplitudes for the PINEM peaks of each order n depend on the nth-order Bessel function of the first kind J_n(Ω), where $\text{Ω}=e{F}_0/\left(\hslash \omega \right)$ (25). At high field strength, the Bessel function has the asymptotic form

$$J_n\left(\text{Ω}\right)=\sqrt{\frac{2}{\pi \text{Ω}}}\cos \left(\text{Ω}-\frac{n\pi }{2}-\frac{\pi }{4}\right).$$ [2]

Thus, as the field in the high-fluence regime varies in space or time depending on the nature of the PINEM field, the probabilities display an oscillatory behavior. For the focused e-beam, due to well-defined impact parameter b, such oscillations with field variation in space are not averaged out (25). The rise and fall of PINEM amplitude with b in Fig. 4C is a consequence of this cosine-like behavior with respect to the changing strength of the scattered light field. Such oscillatory or nonmonotonic behavior of PINEM, seen in Fig. 4C and elsewhere (21, 22), represents the nature of electron–photon coupling in PINEM, coherent versus incoherent (25).

Fig. 4E gives the time- and energy dependence of PINEM electron-energy spectra obtained at the interface of copper grid using an e-beam of 130 nm, IR fluence of 1.25 mJ/cm². It shows symmetrical energy dependence for all orders and asymmetrical time dependence at low order. Such low-order time asymmetry was commented on by Kirchner et al. (33) in reference to time–energy patterns like those shown here, but using shorter optical pulses and 25 keV for the electrons. It is attributed to weak temporal asymmetry of the optical pulses that is highly magnified by the strong nonlinear PINEM response.

Outlook

Under focused electron beam conditions, PINEM experiments were carried out at an interface between vacuum and Cu grid in diffraction mode. The energy resolution remarkably reached the 0.63-eV value, which makes the observation of resolved PINEM peaks excited by IR (1,038 nm) possible. By comparing the PINEM effects between green and IR, the near-field enhancement in PINEM at the interface is shown to be much more sensitive to IR pulses, and this provides one promising way to investigate near-field effects using more gentle optical pulses without damaging the specimen before useful information is obtained, especially for biological sample visualization. PINEM diffraction was realized, to our knowledge, for the first time, which opens the door to studies of structural dynamics of materials by the PINEM-gating technique to reach a higher temporal resolution. The nonlinear PINEM effects by IR at high fluence will be further studied by combining the theoretical calculation to determine the nature of the multiple photon–electron coupling interactions, coherent or incoherent.

Going beyond the scope of this work, these results for IR irradiation and the earlier visible excitation (14, 15, 25) provide a suggestion of the opportunities that may arise when optical scanning through resonances is made possible using high-power, broadly tunable lasers. Further PINEM enhancement is expected, with a potential for additional applications in spectroscopy and plasmonics, already the subject of studies at high spatial and energy resolutions (34–38). The direct excitation of very low-energy modes, such as phonons and bond vibrations, may enable selected mode imaging in this domain of resonant excitation (36).