Lightwave-driven electron emission for polarity-sensitive terahertz beam profiling

The generation and detection of electromagnetic radiation in the terahertz (THz) frequency range are key enabling technologies for the investigation of a wealth of light–matter interactions^1–7 as well as for material characterization, spanning from fundamental elements over electronic circuits, cancer cells, artisanal artwork, to explosives.^8–12 The THz source technology has matured tremendously over the past decades, enabling intense, coherent single-cycle THz pulses across the entire far-infrared region from table-top systems as well as accelerator-based THz sources with a very high average power and spectral coverage.^13,14 With the increasing pace of research and emerging applications in the THz range, the rapid profiling of more than the basic transverse intensity profile of THz beams is becoming more and more relevant. A large class of THz sources deliver quasi-single-cycle pulses with a very large bandwidth, where the peak electric field and its absolute polarity play a key role in the understanding of physical processes, such as THz generation from laser-driven plasmas,^15,16 field-driven electron emission,^17–19 and high harmonic generation,^20,21 and nonlinear semiconductor dynamics.²² These examples represent different manifestations of lightwave electronics,²³ where the instantaneous electric (or magnetic) field of the optical waveform determines the physics of the interaction between light and matter on a sub-cycle time scale.²⁴ The temporal shape of the electric field E(t) can be characterized by photoconductive sampling,²⁵ free-space electro-optic sampling,²⁶ and air biased coherent detection,^15,27 techniques that all rely on heterodyne optical sampling with a synchronous femtosecond laser pulse with at least the same bandwidth as the THz field.¹ The complete spatial profile $Ex,y,z,t$ can be characterized by similar techniques, by raster scanning of a single-point detector¹ or electro-optic sampling using a large-area detection crystal,²⁸ again with an ultrafast synchronized gate signal. Incoherent imaging with THz illumination from molecular gas lasers was described early on,²⁹ and today, beam profiling techniques for long wavelengths include pyroelectric,³⁰ VO_x microbolometer,^31,32 and thermopile³³ focal plane arrays (FPAs). All these incoherent methods measure the absorbed heat and are, therefore, sensitive only to the temporally integrated intensity of a THz beam without providing direct information about its field strength, polarization, or polarity.

Here, we demonstrate how electrons driven by a THz-induced field emission from an array of sub-wavelength antenna structures can excite and ionize the surrounding argon (Ar) gas³⁴ and use the resulting glow discharge to map the cross-sectional peak electric field distribution of THz field transients. We discuss the optimized design of the antenna structures and, then, characterize the field dependence of the Ar glow discharge and compare it to predictions obtained by the standard electron tunneling (Fowler–Nordheim) theory. We demonstrate that by designing the antenna structure in an asymmetric manner, it is possible to determine the absolute polarity of an asymmetric quasi-single-cycle THz-frequency lightwave. Finally, the arrangement of the antenna structures in an array enables imaging of the transverse profile of a focused THz beam, and we demonstrate this capability and the applications enabled by the strong nonlinearity of the emission process compared to conventional microbolometer imaging arrays.

An experimentally recorded image is shown in Fig. 1(f), and the basic concept is illustrated in Figs. 1(a) and 1(e). Here, THz single-cycle pulses are focused from the back side of a 525 μm-thick high-resistivity Si (HR-Si) substrate with 1 µm SiO₂ thermally grown on top.³⁵ On top of the oxide layer, antenna structures (Ti/Au, 10/200 nm) concentrate the field in a small central region. An SEM micrograph of the resulting antennas is shown in Fig. 1(b). The electric near-field at the metallic edges thereby reaches values >2 orders of magnitude larger than that of the incident peak electric THz field [Figs. 1(c) and 1(d)], which drives a field emission tunnel current J_FN from the antenna tips into free space according to the highly nonlinear Fowler–Nordheim (FN) equation,

where F is the externally applied electric field, β is the field enhancement factor at the emitter–vacuum interface, Φ is the emitter material work function, and a_FN and b_FN are the FN constants.³⁶ The emitted electrons subsequently undergo sub-cycle lightwave acceleration in the strong near-field and may eventually collide with and excite nearby argon (Ar) atoms, thereby creating a local microplasma with a glow discharge that is recorded with a standard CMOS camera. The Ar plasma glow discharge spectrum primarily reside in the near-IR and red region, where Si-based cameras are very sensitive.^37,38

It has previously been demonstrated how metal-based metasurfaces can be used to visualize the electric field of high-power THz transients by means of field enhancement and subsequent nonlinear effects such as field emission, electromigration, material breakdown, and THz-induced photoluminescence.^4,39,40 It has also been demonstrated how a plasma discharge can be used for THz detection, although without any metasurface implementation.⁴¹ 

The THz-driven field emission by tunneling can be a very effective process to liberate electrons. The effect can occur on a time scale shorter than the oscillation cycle of the THz field and was demonstrated from the tips of dipole antennas¹⁷ and across the narrow gap in split-gap dipole antennas.⁴² The effect has been used for the ultrafast control of tunnel currents from nanostructures in STM^3,18 and on 2D surfaces.⁴³ The incident electric field can be lifted into the field emission regime at MV/cm field strengths using metasurfaces with arrays of downscaled, generic resonant structures adapted from microwave research.^44–46 Moreover, the emitted electrons can, if accelerated to a sufficient kinetic energy, be used for collision-induced excitation of gas molecules surrounding the metasurface¹⁷ that, depending on the gas species, then leads to light emission in the UV, visible, and near-infrared regions. The functionality of such structures relies on the high electrical conductivity of metals such as gold (Au) that is used here. The high AC conductivity of metals spans well into the mid-IR regime, and the field enhancement factor β depends only weakly on the conductivity of the metal (see the supplementary material) and the process is, therefore, scalable in frequency up to at least 100 THz.

To enhance the field-emission process, we designed an array of sub-wavelength antenna structures optimized for interaction with a broadband THz single-cycle transient with bandwidth between 0.1 and 1.2 THz. The design and simulations were performed with CST (Computer Simulation Technology) Microwave Studio (MWS) and CST Particle Studio (PS) (Dassault Systems). If we define a field emission threshold as the field strength required to emit a single electron during the duration of the THz pulse (1 ps) from a representative area of 1 μm², we find this threshold field to be ∼5 · 10⁸ V/m. Therefore, a doubly resonant antenna structure was realized that gave the highest possible peak electric field response of the incoming THz transient in both time and space. This meant that design considerations in CST MWS relied on size and geometry sweeps over a range of well-known antenna structures from the microwave regime.

All simulations were performed in the time domain based on a hexahedral mesh. In volumes around the electron emission points at the antenna tips, the mesh was set to 40 × 40 × 40 nm³. When moving away from the emission points, mesh cells were allowed to expand up to 20% compared to their nearest neighbors. This resulted in a large cell asymmetry in volumes of less field variation. The largest mesh cell had at least one side that was 3.79 μm long, which was close to 100 times the smallest mesh cell. The incident electromagnetic field was treated as a linearly polarized plane wave, and the boundary conditions were periodic.

All simulations assumed a linear material response to keep the computational burden to a realistic level. Any nonlinear effect in Au on a ps time scale is insignificant as it was experimentally verified with an imaging IR thermometer that metal heating was below 1 °C in the strong THz field. The antenna design can be considered as two current loops driven by the same voltage bias, which is the incoming THz transient. The small loop is first optimized for a maximum peak field enhancement a few nm from the I-shaped tip by varying the width/height ratio. Afterward, the big current loop is introduced and the width is varied until a maximum peak field enhancement is again obtained. Finally, the big loop is “folded in” until a significant crosstalk between antenna parts starts to decrease the peak field enhancement again.

After CST MWS optimization, CST PS was used to introduce an electron field emission and perform spatial and temporal mapping of emitted electrons using the Lorentz force law. An animated rendering of the emission under vacuum conditions can be found in the supplementary material, Multimedia 1. Space charge effects are included in the simulations. The color scale indicates the electron energy. Each particle in the simulation represents a charge density, which is not necessarily equal to one electron.

The structure consists of two coupled split-ring resonators of different circumferences and a common gap surrounded by a flat and a pointed electrode, which we shall refer to as the T- and I-tip, respectively. Each ring constitutes a current pathway, and for a circumference ratio of 3/2, both pathways give the capacitor-like tip arrangement its maximum charge accumulation and, hence, field enhancement due to the peak THz electric field at the same point in time and space [Figs. 2(a) and 2(b)]. In other words, the antenna structure is multi-resonant with its major resonance components being approximately in phase during the first 4–5 ps of interaction. Since the electron emission process is highly nonlinear and due to radiative losses, the initial time window of 4–5 ps following the interaction with the THz pulse is the only regime of interest. Our antennas are designed accordingly with a field enhancement performance that quickly degrades after 5 ps. Since J is a highly nonlinear function in E, and the electric field response of the antenna quickly dies out after THz excitation, it will, consequently, be mainly the peak electric field strength of the incident THz transient that determines the number of emitted electrons. Therefore, our metasurface can be used for the visualization of the peak electric field.

In the top plot of Fig. 2(a), we show a single-cycle THz pulse with a waveform determined in the experiment (gray, dashed curve) with a peak electric field of −100 kV/cm along with the simulated electrical currents that it induces in the antenna through the two cross sections shown in Fig. 2(b). In the bottom plot, the electric field enhancement β and the corresponding electric field are depicted as recorded 5 nm away from the antenna–vacuum interface above the I-tip and below the T-tip. The approximate location of the two points is indicated in Fig. 1(d). We see that the local, enhanced electric field is oscillating out of phase with respect to the incident electric field and that the temporal shape of the local field is significantly different from that of the incident field due to the frequency-dependent field enhancement factor. The maximum field enhancement in time for the used THz pulse is β = 132. The purple, vertical lines in Fig. 2(a) indicate the three most pronounced peaks in the electric field at a field polarity that enables only electron emission from the I-tip. By following these lines to the top plot, one can see that they closely correspond to situations where the current flow to the two tips is zero. This situation is indicative of a resonant antenna behavior where the largest field enhancement on the tip corresponds to that where the capacitive-like gap is charged with its maximum electric charge.

In Fig. 2(b), an image of the surface current distribution at 6.4 ps, where the electric field enhancement assumes its global maximum, is shown. Not only can it be seen that the current flow to the tips is close to zero, but it is also apparent that there is a complicated current flow with multiple nodes around the entire antenna structure, which would not be the case for a single resonant antenna such as an electric dipole. This flow originates from the beating between the two main resonances pertaining to the two rings, which collectively make up a broad enhancement spectrum at the I-tip as shown in Fig. 2(c). The spectrum is obtained from the Fourier transform of a 30 ps long time domain simulation, where the ringing originating from the resonant behavior has died out. This particular antenna is suitable for short THz laser pulses with a bandwidth between 0.1 and 1.2 THz. However, by simple geometrical scaling, this enhancement in spectrum can be moved to other parts of the infrared frequency spectrum since noble metals such as Au maintain excellent electrical conductivity properties all the way up into the near-IR range. This is supported by simulations described in the supplementary material.

The metasurface sample was made by growing a 1 µm thick thermal oxide layer on top and back of a standard 525 µm high-resistivity silicon wafer (HR-Si) with an electrical resistivity greater than 10⁴ Ω cm. The uniformity and exact thickness of the layer were not crucial and, therefore, not thoroughly investigated. Subsequently, a periodic antenna array was patterned using standard UV photolithography using a mask with a 1.5 µm tolerance and a resist with positive polarity. The antennas were designed to be 3 µm wide.

We placed the array on a SiO₂ buffer layer to suppress the nonlinear electrical breakdown effects in the silicon substrate due to the antenna near-fields, which reach strengths more than 2 orders of magnitude above their DC breakdown values. We have experimentally found that placing antennas directly on HR-Si leads to a reduced light emission and degradation of the metasurface in a matter of minutes, owing to the current paths in the substrate due to impact ionization and irreversible modifications of HR-Si induced by the strong electric field.^19,35

The SEM micrograph in Fig. 3 shows that a soft tapering of tips was nicely obtained. 10 nm Ti and 200 nm Au were deposited using the electron beam evaporation. The Ti layer was used for a better Au adhesion to the substrate. Lift-off was performed in N-methylpyrrolidone. The sample was cut at 10 × 10 mm². The antenna spacing was $x,y=74,148μm$⁠; thus, a sample held 135 × 67 = 9045 antennas optimized for a response between 0.1 and 1.2 THz.

The metasurface was placed as a sidewall in a small pressure control chamber with antennas pointing inward. The THz pulse was incident at normal incidence from the back, thus suffering from a 30% Fresnel reflection loss. The electron field emission and plasma generation were realized by introducing argon (Ar) gas in the chamber at variable pressures. The glow discharge light was imaged through a back window with a 20× microscope lens. The camera had a monochrome 2.8 megapixel CCD sensor (Lumenera Infinity 3-3URM).

We used a 3.4 W, 110 fs Ti:sapphire regeneratively amplified laser (Spectra-Physics Spitfire Ace) with a central wavelength of 800 nm for THz generation and detection. The repetition rate was 1 kHz. Quasi-single-cycle THz pulses were generated by optical rectification in a LiNbO₃ crystal using the tilted pulse front excitation scheme.^47,48 The THz pulses have energies of a few μJ and bandwidth from 0.1 to 1.2 THz, with a maximum at 0.5 THz. Free-space electro-optic (EO) sampling^26,49 with a 1-mm (110) ZnTe crystal was used to acquire THz time traces and estimate the peak electric field. THz beam profiling was performed in the THz focus by exchanging the ZnTe crystal with a metasurface imaging system or a microbolometer array (NEC, model IRV-T0831).

Depending on the relative orientation of the asymmetric gap to the incident peak field polarity, the maximum charge accumulation will happen either at the T-tip or at the I-tip. The strength and spatial distribution of the field emission associated with the charge accumulation will, therefore, depend on the incident field polarity, as discussed below and shown in Fig. 4. Consequently, we can distinguish between different polarities with an array of antennas of alternating orientation.

Metasurfaces that aim to enhance the incident electric field can significantly benefit from the field coupling between the individual surface elements.^44,50 However, for a beam profiling device, elements with such a non-local coupling would give an image where the imaged electric field at each pixel depended on the electric field distribution on the entire surface. Our antenna element is, therefore, designed to encapsulate the field enhancement inside the antenna itself to avoid the significant coupling with neighboring antennas [Fig. 1(d)]. Simulations (not shown) confirm that the local field enhancement is independent of the lattice spacing of the resonant structures when placed in an array. As a result, the light intensity from an arbitrary pixel can be interpreted as a measure of the electric field at the closest emission point. The decoupling of elements also makes it feasible to pack the individual antennas closely for an increased resolution. For further miniaturization, the current pathway in the largest split-ring is folded in bends to minimize its area [Figs. 1(b) and 1(c)].

In Fig. 4, we show the capability of the metasurface to be used for absolute polarity determination in two different ways. The insets in Figs. 4(a) and 4(b) illustrate two different simulated cases where an antenna is illuminated with a single-cycle pulse of opposite polarities. In the top configuration, overall, the highest field enhancement for the antenna occurs at the I-tip and the electron emission will, therefore, initiate here at low field strengths. However, when increasing the field strength, an additional emission from the T-tip starts to grow. Since the total emission area at the T-tip constitutes two tips and a long, flat side [points 2, 3 and 4 in Fig. 1(d)], its total emission increases faster than that at the I-tip. Therefore, even at lower field strengths at all emission surfaces compared to the I-tip, the T-tip emission surpasses that of the I-tip at some field strength. With the opposite polarity, the field enhancement at the T-tip is always larger than at the I-tip. Therefore, there will be no crossover of the main emission point from I-tip to T-tip. Thus, by illuminating an antenna with a well-known orientation, one can, in principle, determine the absolute polarity by observing whether this crossover happens.

We observe that the total emission strength is significantly different in the two configurations, which can, similarly, be used for absolute polarity determination. In Fig. 4(c), the latter method has been used by creating an antenna array with antennas assuming alternating orientations. One particular orientation dominates over the other in terms of total electron emission. In this case, by lowering the integration time on the CMOS camera, one obtains an image similar to that in Fig. 4(d). Three situations have been highlighted here. Situations 2 and 3 come from oppositely oriented antennas at the center of the THz beam with a high electric field strength. The main light emission in both situations come from the T-tip, with situation 3 being slightly brighter than situation 2, showing a field polarity configuration as in Fig. 4(a). The antenna orientation in situation 1 is the same as that in situation 3. However, in this situation, the antenna is located in a much lower field strength region and its main emission is, thus, from its I-tip, as expected. All three situations are outlined in the right-most panels to illustrate the main electron emission maps.

Our model for electron emission in Figs. 4(a) and 4(b) is based on the Fowler–Nordheim equation. To extract the value for the work function, we have taken a series of mode profile images at different incident THz field strengths. Experimentally, the incident THz pulses were variably attenuated by placing two wire grid polarizers in the beam and rotating the first one. For each image, we integrated the total light emission and used it for a Fowler–Nordheim plot. We find, with an effective work function, that Φ = 0.9 eV (see the supplementary material for details). This value differs significantly from the commonly accepted value of Φ = 5.1 eV of the work function of Au in vacuum. An unusually low value for the effective work function at THz frequencies has also been observed in ambient THz-driven scanning tunneling microscopy (THz-STM)³ and in THz-driven field emission from gold into a nitrogen (N₂) atmosphere.¹⁷ The lowering of the effective work function is still a somewhat controversial observation, but it appears reasonable that it originates from a combination of two effects, namely adsorbates and impurities on the gold surface and the surface topology of the gold. The interface is irregular on the sub-µm scale, and thus, the field enhancement factor β calculated for a perfectly regular structure may locally be underestimated.^3,17 There is a good agreement between the observed light emission as a function of THz field strength and the Fowler–Nordheim equation, which suggests that the electron-to-photon conversion is linear within the Ar glow discharge. The extracted work function is used in Fig. 5(a) to plot the emission current density as a function of both the incident THz peak electric field and the corresponding field at the I-tip, including a 30% Fresnel loss at the backside of the substrate. We have scaled the experimental data accordingly (see the supplementary material) to verify that we start to see light emission in the electron emission regime where tens of electrons are emitted. Considering that the vertical axis in Fig. 5(a) covers 30 orders of magnitude within four orders in the electric field, it is reassuring that our emission threshold is physically sensible. The experimentally determined threshold for a detectable light emission is 55 kV/cm, and the antenna at that point emits about 50 electrons/μm²/ps.

Figure 5(b) shows that the photon emission strength depends on the pressure of the surrounding argon gas in a nontrivial manner. Within the measured pressure range, we see that at a few mbar pressure, the light intensity is highest and vanishes rapidly when the pressure is lowered below 1 mbar (not shown here). At higher pressures, the light intensity decreases, approximately as I ∝ P^−0.7 [dashed, blue curve in Fig. 5(b)]. As discussed in further detail in the supplementary material, we attribute this dynamics to the interplay between the energy-dependent cross section for elastic electron scattering and excitation/ionization of the Ar atoms. Elastic scattering is most efficient at low energies, and excitation/ionization is most efficient at higher energies.⁵¹ 

Panels (d)–(i) in Fig. 5 show a comparison between scanning a microbolometer camera [(d) and (g)] and our metasurface [(e) and (h)] through the focal point of a THz beam focused with an off-axis paraboloidal mirror with an effective focal length of 50.8 mm (2 in.). Due to the discrete nature of the resonator array, the vertical lines in panels (e) and (h) represent a row or column of resonators. To get a more comprehensive visualization of the beam profile, panels (f) and (i) are binned versions of the metasurface data integrated over each period of the array (see the supplementary material for further details). Panels (d), (e), and (f) represent the projection of the beam profile onto the x (horizontal) axis, and panels (h), (i), and (j) represent the y (vertical) projection. All original cross-sectional images can be found in the supplementary material. The apparent cross section of the profile measured with the metasurface is comparable to that measured with the microbolometer camera. Due to the strongly nonlinear relation between the THz field strength and emission strength, a more narrow distribution is expected, so our observation is somewhat unexpected. However, we attribute this observation to several experimental factors. First, the digital dynamic range of the CMOS camera images is 8 bits, so the limited dynamic range leads to a certain amount of saturation of the images (see the supplementary material). A camera with a higher bit depth would remove this artifact and lead to a more narrow apparent beam profile. Additionally, it is known that the microbolometer camera has a better sensitivity at higher THz frequencies³² and, therefore, tends to report a frequency-integrated beam profile of a broadband THz beam that is narrower than the actual beam profile in the <1 THz frequency range where the metasurface has its highest sensitivity in this experiment. Hence, a direct comparison of the beam profile widths makes little sense. More importantly, the beam profile comparison reveals that while the microbolometer camera records the beam profile across the full region, the metasurface only detects a signal in the narrow region near the focus where the peak field strength is highest. This is quantified in Fig. 5(c), where the integrated signals along the z direction from the two cameras are compared. The microbolometer records the average power of the THz beam, which is independent of the focusing conditions, and hence, the transversely integrated signal is approximately constant. The slight roll-off at the start end of the range is due to the size of the beam profile exceeding that of the sensor array. In contrast, the metasurface records a signal only in the region close to the focal plane, with a FWHM of the response of less than 12 mm. Hence, the metasurface is well suited for the efficient localization of the focal plane, even in a single-pixel version without imaging capabilities. The beam profile projections show that the focused THz beam has a certain amount of astigmatism in the form of different positions of the focal plane for the two projections. This astigmatism is reproduced in the metasurface images. It is worth noticing that given the fast response of the metasurface, it is possible to use it for single-shot THz imaging, as shown in the supplementary material.

In conclusion, we have demonstrated a new method for THz beam profiling that simultaneously measures the peak electric field and unambiguously determines the absolute polarity of single-cycle pulses. We use a metasurface that enables a lightwave-driven electron emission when excited with a short THz transient and subsequent light emission in the visible region originating from an electron-induced local argon plasma discharge. An absolute calibration of the incident peak electric field strength is possible for a given antenna structure and gas pressure. Further enhancements in sensitivity are expected by improvements in the antenna design and tighter manufacturing tolerances. A significant advantage of our metasurface-based THz visualization method is its scalability and low fabrication costs; the size of the focal plane array can readily be increased to the full size of a standard wafer, and it can be fabricated by the standard UV lithography and metal evaporation. This is in contrast to other THz beam profiling options, where the focal plane array is typically limited to a very small size, fabrication is expensive, and dedicated readout electronics is required.

We expect our approach to be broadly applicable to the far- and mid-infrared spectral range by straightforward geometric scaling of the antenna dimensions. This indicates the sensitivity across the THz and mid-IR ranges, although the sensitivity to absolute polarity becomes less relevant in the mid-IR, at least with current sources in this range that are almost exclusively limited to multi-cycle, symmetric pulse shapes. Finally, since our technique effectively uses up-conversion from the THz to the visible regime, standard silicon CMOS or CCD detectors can be used for imaging, making it more cost effective than using a focal plane array designed to operate in the THz frequency range directly.

See supplementary material for raw data for field dependence of electron emission, Fowler-Nordheim description of emission data, single-shot imaging, pressure dependence of the emission strength, alignment and saturation of the metasurface images, raw data for scans through the THz beam focus and a simulated sweep of the electrical conductivity for an antenna. In addition, a Particle-in-Cell simulation of the electron emission from an antenna can be found as a video file.

The use of the Linac Coherent Light Source, SLAC National Accelerator Laboratory, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-76SF00515. M.C.H. was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. 2015-SLAC-100238-Funding. We also acknowledge the funding from the Independent Research Fund Denmark (ULTRA-TED).

The authors have no conflicts to disclose.

Simon Jappe Lange: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Matthias C. Hoffmann: Data curation (equal); Formal analysis (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Peter Uhd Jepsen: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.