Ultrabroadband Spacetime Nanoscopy of Terahertz Polaritons in a van der Waals Cavity

ABSTRACT

Guiding, storing, and processing light at the nanoscale hinges on understanding how polaritons — hybrid quasiparticles of light and matter — propagate and interfere in both space and time. This work introduces a synchrotron‐based technique, SYnchrotron SpaceTimE Mapping (SYSTEM), which captures real‐time evolution of polariton wave packets with ∼10 nm spatial and sub‐100 fs temporal resolution across an ultrabroadband 5–50 THz range. Here, SYSTEM directly visualizes the creation, interference, and decay of multiple high‐quality Fabry‐Pérot phonon polariton cavity modes in an α‐MoO₃ microcavity. These real‐space, real‐time observations reveal wave‐packet dynamics and cavity resonances with record‐high quality factors (Q ≈ 100) in the single‐digit terahertz regime near 9 THz. SYSTEM thus offers a powerful and broadly applicable platform for probing and engineering ultraslow, deeply subwavelength polaritons, opening new avenues for tailoring light–matter interactions and advancing next‐generation THz nanophotonic technologies.

This work introduces SYnchrotron SpaceTimE Mapping (SYSTEM), which captures real‐time evolution of polariton wave packets with ∼10 nm spatial and sub‐100 fs temporal resolution across an ultrabroadband 5 to 50 THz range. Here, SYSTEM directly visualizes the creation, interference, and decay of multiple high‐quality Fabry‐Pérot phonon polariton cavity modes in an α‐MoO₃ microcavity.

1. Introduction

Polaritons are hybrid quasiparticles that emerge from the strong coupling between light and matter excitations. They provide unique opportunities for controlling light at the nanoscale, notably including sub‐diffraction‐limited light confinement. Particular interest has been generated by combining polaritonic light control with the flexibility of tailored material properties of two‐dimensional 2D and van der Waals materials [1–3].

When using polaritons for guiding and processing optical information at the nanoscale, one needs to know the characterizing properties of a polaritonic wave packet, e.g., phase and group velocity, as well as decay length and lifetime. Due to the strong confinement and high momentum of many polaritonic excitations, real‐space studies of polaritonic dispersion require an experimental approach with sub‐diffraction‐limited spatial resolution. Recently, super‐resolution far‐field techniques have been demonstrated for ultrafast tracking of exciton polaritons in the visible and near‐infrared spectral range [4]. For the exploration of lower‐energy polaritons, such as phonon and plasmon polaritons in the mid‐infrared and terahertz spectral range, scattering‐type scanning near‐field optical microscopy (s‐SNOM) based techniques have proven successful [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]. Using s‐SNOM, properties of polaritonic wave packets such as the phase and group velocity can be indirectly obtained by analyzing the dispersion in frequency space using asymmetric Michelson interferometry [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. Some studies using s‐SNOM or ultrafast electron microscopy demonstrated time‐resolved nanoscopy of polariton propagation, thereby enabling direct probing of polariton wave packets [20, 21, 30, 31, 38, 39, 40]. However, such real‐time studies have so far been limited to either very low frequencies below ≤2 THz [21, 30, 31] or mid‐infrared frequencies at above ≥23 THz [20, 38, 39, 40]. Here, we employ the high spectral brightness of broadband infrared synchrotron radiation [16, 41, 42, 43] to fill this terahertz (THz) spectral gap in nano‐spectroscopy, demonstrating a new experimental s‐SNOM‐based method that we refer to as SYnchrotron SpaceTimE Mapping (SYSTEM). Our method covers the entire spectral range from ≥5.4 THz to beyond 50 THz in a single scan. We demonstrate SYSTEM studies with ∼10 nm spatial resolution and a temporal resolution of ∼10 fs (see methods), enabling efficient characterization of polariton wave packets across an unprecedented spectral range.

Hyperbolic phonon polaritons combine extreme light confinement with long polaritonic lifetimes and high quality‐factors [8, 9, 10, 11, 12, 16, 18, 19, 20, 25, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47]. This combination is very promising for infrared nanoresonators [18, 19, 27, 29, 37, 44, 45, 46, 47], and may even enable hyperbolic quantum processors [48]. To reduce surface scattering losses and obtain low‐loss nanoresonators, it is useful to employ highly confined polariton modes, resulting in a large momentum mismatch with free‐space modes. One of the most‐studied in‐plane anisotropic hyperbolic polariton hosts is molybdenum trioxide (MoO₃), which is a van der Waals material providing low‐loss phonon polariton modes across the mid‐infrared and terahertz spectral range [9, 10, 11, 12, 16, 25, 26, 27, 32, 33, 34, 35]. Here, we employ SYSTEM to simultaneously characterize all MoO₃ polariton modes in real space and time from around 5 THz up to mid‐infrared frequencies. Notably, we find that our MoO₃ structure acts as an extremely efficient THz nanoresonator at a central frequency of 8.7 THz with a lower limit for the quality factor of about 100. While similar values were previously demonstrated at mid‐infrared frequencies [18, 27, 44, 47], such quality factors are unprecedented in the single‐digit THz range.

1.1. Results

The experimental realization of SYSTEM is sketched in Figure 1a. We employ the ultrabroadband infrared radiation from the infrared beamline 22‐IR‐2 at the National Synchrotron Light Source II, Upton, USA. For SYSTEM data to provide undistorted information about polariton properties, it is essential that the infrared radiation and all optical elements provide sufficiently broad and flat spectral response, which is optimally fulfilled for our synchrotron‐based setup (Methods). Except for the light source, the setup resembles similar setups previously employed in the mid‐infrared spectral range [20]. In short, infrared radiation is guided onto a diamond beam splitter, which splits the beam into a sample and a gate pulse. The sample pulse is guided to the tip of an atomic force microscope (AFM) and launches a polariton wave packet in the sample. The wave packet travels through the sample at the group velocity v_G. It is reflected at the sample edge (sketch at the bottom of Figure 1c) and then again scattered from the AFM tip. The scattered light is guided back to the beam splitter and then detected with a suitable broadband detector. At the same time, the gate pulse is reflected at a movable reference mirror and then interferes with the sample pulse at the detector. Additional details on the experimental setup are provided in the Methods section.

FIGURE 1.

Synchrotron Polariton Spacetime Mapping of MoO₃ Nanoresonator. (a) Experimental setup: Ultrabroadband infrared synchrotron radiation for THz‐to‐infrared nanoscopy. The distance dx refers to the distance between the atomic force microscopy tip and the nanoresonator edge. The relative position of the reference mirror, c·dt, with c the speed of light, is used to control the sample‐gate pulse time delay dt. (b) Real part ε’ of the frequency‐dependent dielectric permittivity ε of MoO₃ along its crystalline [010] and [001] direction, ε’_[010] and ε’_[001]. Spectral regions where ε’_[010] and ε’_[001] have opposite sign indicate hyperbolic polaritonic dispersion and are highlighted in grey. There are three major hyperbolic regions, labelled as (I), (II), (III). All of them are simultaneously excited due to the broad spectral range covered by the synchrotron radiation. (c) Bottom: Sketch illustrating polariton modes (arrows) being reflected at the edge of the MoO₃ nanoresonator. Top: Experimental spacetime map illustrating the propagation of polariton modes in MoO₃. The false color represents the second spatial derivative of the imaginary part of the near‐field signal as a function of space (position along the MoO₃ cavity) and time (time delay dt). There are three major polaritonic branches, matching the three hyperbolic spectral regions highlighted in (b). The branches are marked by dashed arrows, green: mode (III), orange: mode (I), blue: mode (II). The mode numbers – (III), (I), (II) from left to right in (c) – are assigned in order of ascending frequency, as illustrated in (b). (d) Dashed lines show experimental line profiles extracted at the positions of the arrows in (c). The full black lines in the background show an exponentially decaying sine wave fit to the data for profiles (I) and (II). The red curves show the corresponding exponential decay of the amplitude. (e) Applying the phase velocity operator (refer to text) to the spacetime map in (c) provides a spacetime map of the polariton phase velocity.

We study an antenna‐shaped, rectangular MoO₃ crystal (sketch in Figure 1a, detailed sample information in Methods and Supporting Information). Hyperbolic polaritons can propagate along the long antenna axis when the real part of the dielectric permittivity, ε’, has opposite sign along the in‐plane [001] and out‐of‐plane [010] direction. Figure 1b shows the dielectric permittivity along these two crystalline directions [12, 36]. There are three major hyperbolic bands for the MoO₃ resonator, which are highlighted in grey: (I) 260–340, (II) 540–850, and (III) 960–1010 cm⁻¹.

Figure 1c shows the SYSTEM data, i.e., an experimental spacetime map, that is acquired along the long symmetry axis, i.e., the [001] axis, of our MoO₃ cavity. The horizontal axis in Figure 1c corresponds to the position in space, which is given by the AFM tip position that is scanned along the line indicated by the black arrow in Figure 1a. For each point along this line, the time delay between sample and gate pulse is scanned via the position of the reference mirror. The vertical axis in Figure 1c shows the time delay of the gate beam in picoseconds, with zero corresponding to equal propagation times for sample and gate beam. In Figure 1c, we can clearly distinguish three “rays” emerging from each edge of the MoO₃ cavity (at ± 4 µm). The rays are composed of oscillating structures with positive (red) and negative (blue) amplitude, here appearing almost purple due to the fine detail. For illustration, we marked the three rays with arrows (green, orange, blue). As we will show in more detail later, these three rays correspond to polariton wave packets being launched in either of the three bands indicated in Figure 1b. Each of the three arrows in Figure 1c is labelled with the number of the corresponding polariton branch from Figure 1b. The assignment of each label can be verified by applying spectral bandpass filters to isolate each of the polariton branches as shown later (Figure 2). The three rays marked in Figure 1c propagate with different slopes in the space‐time map, corresponding to different group velocities [20, 21]. We calculate the group velocity v_G = 2·Δx /Δt from the slope Δx /Δt of the arrows. The factor of two arises as the polaritons are launched by the tip, i.e., they need to travel the distance between tip and cavity edge twice before being detected by the tip again [21]. We find group velocities of (I) 2.1, (II) 5.4, and (III) 0.4 µm/ps. For comparison, the speed of light in vacuum is c = 300 µm/ps, i.e., all polariton rays propagate at group velocities <2% the speed of light, illustrating the strong interaction between light and matter. Note that the group velocity can be tuned via the crystal thickness, with thinner/thicker crystals decreasing/increasing the velocity [8]. Using SYSTEM, we experimentally verify that a thicker crystal shows the expected higher group velocity (Supporting Information, Figure S2).

FIGURE 2.

Dispersion of MoO₃ Polariton Modes. (a) Synchrotron infrared nanospectroscopy converted from SYSTEM reveals polaritonic resonator modes of the MoO₃ cavity. The hyperbolic regions (I), (II), (III) are labelled following the definition in Figure 1b. (b) Spatial Fourier transform of the data in (a) illustrating the polariton dispersion and resonator modes in frequency‐momentum representation. The experimental dispersion agrees well with the calculated dispersion (Methods). (c,d,e) Experimental spacetime maps (left: overview, right: zoom) illustrating the propagation of polariton modes in the three main polaritonic MoO₃ Reststrahlen bands. The data is obtained from the spacetime map shown in Figure 1c by applying a spectral bandpass filter that approximately covers the spectral regions (I), (II), (III) as shown in Figure 1b. The cutoff frequencies of the bandpass filters are specified above each subfigure. Note that some of the spacetime maps (particularly left in c) show strong aliasing effects (beating patterns) as the pixel density of the figure is not sufficient to accurately display the high frequency oscillations. For the zoom‐ins (right) the features are sufficiently enlarged to avoid strong aliasing effects. The spacetime maps clearly illustrate the different phase (v_p) and group velocities (v_g) of the polariton packets.

Figure 1d shows experimental spacetime profiles extracted along the three arrows in Figure 1c (dashed lines). After the polariton wave packets are launched at time zero, we see an oscillation amplitude that decays with time. As all polaritons are launched at the same event, at first, the polaritons are not well separated. Due to the different group velocities of the polariton rays, the rays separate when propagating through spacetime within about 1 ps. Once the polariton rays are sufficiently well separated in spacetime, rays (I) and (II) can approximately be described as an exponentially decaying sine wave. The black lines in the background of Figure 1e show a fit to the experimental data. As derived in the Methods section (Figure 5), the frequency of the oscillation is directly proportional to the difference between the ray's phase and group velocity, v_p − v_g . Since the oscillation frequency is finite, this confirms that our polariton modes are not acoustic modes as for the latter v_p = v_g , which would result in a simple exponential decay [21]. For our modes, in Figure 1d, we find a 1/e lifetime of (2.7 +‐ 0.3) ps for ray (I) and (0.5 +‐ 0.1) ps for ray (II), which is illustrated by the red envelope in Figure 1d. Ray (III) is not well described by an exponentially decaying sine wave since polaritonic rays in Reststrahlen band (III) can propagate along both in‐plane directions [9, 36] and interference of different modes creates beating patterns that cannot be described by a single exponentially decaying sine wave [16, 38] (detailed explanation in Supporting Information).

FIGURE 5.

Oscillation frequency at the center of a wave packet. The sketch provides a geometrical derivation of the oscillation frequency observed at the center of the wave packet in a spacetime map (experimental SYSTEM data presented in Figure 1d). Grey arrows represent the phase velocity, i.e., isophase lines in spacetime. The orange arrow represents the group velocity. We are interested in the intersections between the group velocity arrow and the isophase lines. The time difference Δx/v_g=1/f between these intersections explains the oscillation frequency f observed in the linecut along the group velocity vector presented in Figure 1d.

The spacetime map (Figure 1c) also contains direct information on how the polariton phase velocity evolves as a function of space and time. This can be visualized by applying the phase‐velocity operator, defined as $-2\frac{\partial }{\partial t}/\frac{\partial }{\partial x}$, to the spacetime map where the factor of two considers tip‐launched polaritons (see Methods). Rewriting this as an equation, the phase‐velocity map can be calculated from the spacetime map ϕ via: ${\mathrm{v}}_{\mathrm{p}}[\varphi (x,t)]=-2\frac{\partial \varphi (x,t)}{\partial t}/\frac{\partial \varphi (x,t)}{\partial x}$, as displayed in Figure 1e. In addition to the absolute value of the phase velocity in the order of a few 10 µm/ps, the map reveals that the phase velocity of polariton ray (III) is negative relative to the direction of propagation, while it is positive for rays (I) and (II). As the propagation direction is defined as positive (negative) for polaritons reflected from the left (right) edge, the sign of the phase velocity observed in Figure 1d also changes depending on the edge that ray is reflected from. For hyperbolic materials, polariton modes with positive and negative phase velocities in the same material are commonly observed [9, 20, 49]. A negative (positive) velocity is typically found for spectral regions that combine negative (positive) out‐of‐plane permittivity with positive (negative) in‐plane permittivity, which is a direct consequence of the hyperbolic dispersion relation [8, 19, 20, 44].

Taking a Fourier transform along the temporal axis of our SYSTEM raw data provides a conventional broadband infrared nanospectroscopy data set (Methods). Figure 2a shows the resulting data in real space (horizontal direction, matching Figure 1c) and temporal frequency (vertical direction). The polariton branches (I) and (II) around 9 and 18 THz, respectively, are well resolved. The fringes across the entire width of the crystal illustrate how the polariton cavity modes evolve as a function of incident light frequency. Due to the long polariton propagation length, counterpropagating polaritons can interfere and form standing wave patterns (polaritonic resonator modes). For polariton branch (I), these resonator modes are particularly clear around 9 THz and will be analyzed in detail later. Just below 30 THz, our data shows Reststrahlen band (III) as a bright stripe. Due to the narrow width of band (III), the fringes are not well resolved. Other bright regions in Figure 2a indicate surface polariton modes, polariton modes of the substrate, or hyperbolic phonon polariton modes propagating along the other in‐plane crystalline direction. Here, we will focus our analysis on modes (I–III) propagating along the [001] direction; modes propagating along the perpendicular direction are analyzed in the Supporting Information.

The polariton dispersion can be illustrated by also applying a Fourier transform along the spatial direction to the data in Figure 2a. The resulting data (Figure 2b) shows the spectrum as a function of both temporal (vertical axis) and spatial frequency (momentum, horizontal axis). As such, Figure 2b directly illustrates the dispersion of all three hyperbolic phonon polariton modes along the MoO₃ [001] direction. For comparison, we provide the calculated polariton dispersion in the Methods section, which agrees well with the experimental dispersion shown here. For bands (I) and (II), the dispersion is positive (increasing polariton momentum with increasing frequency). For band (III), the dispersion is relatively flat but slightly negative. For any of the bands (I)‐(III), the dispersion shows only low curvature for a large part of each spectral band, i.e., the group velocity does not vary much within the studied momentum range. This matches the three well‐defined “rays” in the spacetime map in Figure 1c. We note that this applies only to the central momentum range observed in the experiments, and the dispersion flattens for higher momentum (refer to calculations in Figure 4).

FIGURE 4.

Calculated polariton dispersion. The calculated imaginary part of the p‐polarized reflection coefficient, Im(r_p), visualizes the polariton dispersion for a stratified medium representing the sample discussed in Figures 1, 2, 3 and Figure S1. The two panels show the polariton dispersion along the main crystallographic in‐plane axes: (a) along the long resonator axis, i.e., the MoO₃ crystallographic [001] direction, which is the main direction studied in discussed in Figures 1, 2, 3, and (b) along the short resonator axis, i.e., the MoO₃ crystallographic [100] direction, which is studied in Figure S1.

By applying a spectral bandpass filter to the ultrabroadband spacetime map in Figure 1c, we can derive separate spacetime maps for each of the polaritonic bands. We employ a frequency bandpass (see Methods) with cutoff frequencies approximately matching the polaritonic bands. Figure 2c shows the resulting spacetime map for the frequency range from 960–1010 cm⁻¹, covering band (III). We find a single polaritonic ray, with properties matching those of ray (III) in Figure 1c. Measuring the angle between the time axis and fixed‐phase wavefronts allows us to read the phase velocity v_p of the rays (marked by arrow in Figure 2c), which is in the order of −(40 ± 30) µm/ps. The negative sign of the phase velocity matches to the phase‐velocity map in Figure 1e, agrees with literature [9, 49], and can directly be seen from the negative slope of the wavefronts in Figure 2c. For bands (I) and (II) in Figure 2d,e, we apply spectral bandpass filters from 260–340 and 540–700 cm⁻¹, respectively. For both bands, both the group and phase velocity are positive (each marked by arrows in Figure 2d,e). We observe phase velocities of (21 ± 6) µm/ps for band (I), and (38 ± 7) µm/ps for band (II). Note that each wave packet is composed of a distribution of phase velocities, since each polariton branch covers a finite range of momentum k (Figure 2b) and, hence, contributes different phase velocities v_p = ω/k, with angular frequency ω=$2\pi c\stackrel{\sim }{\nu }$, wavenumber $\stackrel{\sim }{\nu }$ and speed of light c. As such, the specific phase velocity value that we read from the spacetime maps in Figure 1d,e represents the dominating component for our experiment at a specific time.

Our measurements provide both spatio‐temporal information (SYSTEM) and momentum‐frequency information (nanospectroscopy). This allows us to visualize and quantify high‐quality cavity modes, revealing both the temporal dynamics and spectral mode structure in direct comparison. Figure 3a shows an enlarged view of the spacetime map of the MoO₃ polariton band (I), showing the full measured temporal dependence with a total time delay of 10 ps, from around −1 to + 9 ps. This time is sufficient for the polariton ray to cross the entire crystal: After being launched at either edge at time zero, the two polariton rays cross in the center of the cavity after ∼4 ps, and then reach the opposite cavity edge after a little less than ∼8 ps. After reaching the opposite cavity edge, the rays are reflected again. This reflection is more apparent for a thicker crystal where the group velocity is faster and, thus, the reflection appears earlier in time (Supporting Information, Figure S3).

FIGURE 3.

Terahertz Polariton Interference and Resonator Modes in MoO₃ Nanocavity. (a) Experimental synchrotron spacetime map showing polariton propagation in the spectral range from 260–340 cm⁻¹. The figure shows a larger spatial and temporal range compared to Figure 2e, enabling a more detailed analysis. A polaritonic ray is launched at each edge of the MoO₃ cavity at t = 0. At t ≈ 4 ps, both polaritonic rays meet in the center of the cavity, forming an interference pattern. (b) Synchrotron infrared nanospectroscopy in the spectral range from 264–320 cm⁻¹ (zoom‐in of Figure 2a). Several high‐quality polaritonic resonator modes can be observed, from a fundamental mode at ∼8.0 THz, up to resonator modes of order ≥12 at ≥9.3 THz. (c) Point spectrum extracted from (b) at the center of the cavity (x = 0). Each peak (dip) corresponds to an even‐order (odd‐order) resonator mode as labelled in the figure. (d) Spatial Fourier transform of the data shown in (b) illustrating the dispersion of the resonator modes.

When the polariton decay length is comparable to (or larger than) the nanocavity width, polaritonic resonator modes are expected to form. This condition is fulfilled for the MoO₃ polariton band (I), which has a 1/e decay length L = T·v_G = 5.6 µm, comparable to our cavity width of 8 µm. Figure 3b,c show the synchrotron infrared spectrum of the nanocavity in the frequency range of band (I). The spectrum clearly reveals resonator modes of multiple orders (n ≥12), where the mode‐order n corresponds to the number of nodes in the mode profile. Even‐order (odd‐order) modes show a maximum (minimum) at the center of the cavity. For example, the lowest even‐order mode (n = 2) is at 268 cm⁻¹, the 12th‐order mode is at 308 cm⁻¹. The resonator modes are well‐pronounced, with relatively sharp transitions between each mode order, suggesting a high mode quality factor. To quantitatively evaluate the quality factor, we extract a point spectrum at the center of our cavity. This corresponds to a vertical cut at x≈0 through the hyperspectral data in Figure 3b. The resulting point spectrum is displayed in Figure 3c. The cavity modes induce a deep modulation of the spectrum. For example, at the even‐order mode n = 6 at 285 cm⁻¹, the signal at the cavity's center is enhanced up to a value of S_{n = 6}/S_Au = 0.75. At the following odd‐order mode, n = 7 at 288 cm⁻¹, the signal at the cavity's center is decreased to a value of S_{n = 7}/S_Au = 0.38. This results in a modulation depth of 2 (S_{n = 6} ‐ S_{n = 7}) / (S_{n = 6} + S_{n = 7}) = 65%. The spectral width of the modes decreases with increasing mode order, matching the flattening dispersion with increasing frequency (Figure 3d). For mode indices n>∼6 we observe a width of Δ$\stackrel{\sim }{\nu }$≤3.4 cm⁻¹, which corresponds to the spectral resolution of our setup. As such, the minimum spectral width is an upper limit of the actual spectral width. This also suggests that the highest mode order observed here may be limited by the spectral resolution. Nevertheless, for mode n = 12 at $\stackrel{\sim }{\nu }$ = 307 cm⁻¹, the spectral width Δ$\stackrel{\sim }{\nu }$ already corresponds to a resonator quality factor of Q = $\stackrel{\sim }{\nu }$/Δ$\stackrel{\sim }{\nu }$≥93. The corresponding resonator mode lifetime [47] T = 2Q/ ω ≥ 3.2 ps is among the best of any polaritonic nanoresonators [18, 27, 37, 47]. It exceeds the extracted wave‐packet lifetime for band I since the wave packet consists of a mode distribution that includes modes with a shorter lifetime.

1.2. Conclusion

We introduce a novel technique, synchrotron spacetime mapping (SYSTEM), to directly characterize polariton propagation in space and time with a temporal resolution under 100 fs and spatial resolution on the order of a few 10 nm. In principle, even sub‐nanometer resolution might be achievable, as recently demonstrated for related optical near‐field techniques [22]. Our method provides direct access to properties of THz polariton wave packets such as their average group velocity, phase velocity, and lifetime over 10s of THz spectral range. Out of the many polariton bands we can simultaneously resolve in a MoO₃ nanocavity, a special focus of our analysis is the one centered at around 9 THz. For this band, our SYSTEM study finds an average group velocity of 2.1 µm/ps and 1/e polariton lifetime of 2.7 ps. Some modes within this band have an even longer lifetime, allowing us to build a nanocavity with at least 3.2 ps resonator lifetime. The resulting quality factor is in the order of ∼100, a record for the single‐digit terahertz range and comparable to the best mid‐infrared polariton cavities (comparison with literature values in Supporting Information) [18, 27, 29, 37, 44, 47, 50, 51, 52, 53]. We attribute the high quality of our terahertz nanocavity to the combination of the intrinsically low material losses of MoO₃ phonon polaritons [9, 12, 27], hexagonal boron nitride as a flat and low‐loss substrate, and low reflection losses due to the high mode confinement of ∼50. The demonstrated combination of terahertz polaritons with high‐quality nanocavities may pave the way toward novel terahertz nanophotonics applications. SYSTEM offers a direct approach to accessing the envelope and phase information of wave packets, making it a valuable tool for both fundamental nanophotonics research and the development of novel polariton‐hosting materials. As a publicly accessible user program, this capability will be crucial for the future design of nanophotonic devices, including optical computing, compact optical sensors, and on‐chip photonic devices.

2. Methods

2.1. Experimental Realization of Synchrotron Spacetime Mapping (SYSTEM)

The experimental realization of SYSTEM is sketched in Figure 1a. We employ the ultrabroadband infrared radiation from the infrared beamline 22‐IR‐2 at the National Synchrotron Light Source II, Upton, USA. The infrared synchrotron light source itself provides radiation covering the entire electromagnetic spectrum from microwaves to X‐rays. The spectral radiance of the synchrotron radiation is about three orders of magnitude larger compared to thermal blackbody radiation at ∼2000 K and its spectral bandwidth covers many orders of magnitude, from microwave frequencies through the infrared and visible to ultraviolet frequencies [54]. Limited by different optical elements, the pulses reaching the near‐field setup cover the spectral range from around 160 to 20 000 cm⁻¹, i.e., about two orders of magnitude. The lower frequency cutoff of ∼160 cm⁻¹ is given by absorption in a CsI window, the upper cutoff of around 20 000 cm⁻¹ is due to reflection off gold‐coated mirrors. The high spectral radiance and ultrabroad spectral coverage makes synchrotron radiation ideal for SYSTEM studies.

Using reflective optics, the infrared radiation is guided onto a diamond beam splitter, which splits the beam into a sample and a gate pulse. The sample pulse is guided to the tip of an atomic force microscope (AFM). We use a commercial AFM, a NeaScope near‐field microscope by Attocube, Germany. As such, the overall optical design as shown in Figure 1a resembles the optical design used in reference [20], with important differences being the light source, the optical materials and the detector as described in this section. As for other optical near‐field microscopy techniques, the spatial resolution of our method is given by the AFM tip radius, which is in the order of ∼10 to ∼100 nm. For our measurements, we use metal AFM tips (model 25PtIr200B‐H from RockyMountain Nanotechnology, USA). The tip oscillates at its resonance frequency of ∼60 kHz at an amplitude of around 100 nm. The light that is scattered from the AFM tip is guided back to the beam splitter and then detected with a suitable broadband detector. At the same time, the gate pulse is reflected at a movable reference mirror and then interferes with the sample pulse at the detector. Note that in this asymmetric Michaelson interferometer geometry, the gate pulse does not primarily interact with the sample but rather probes the scattered sample pulse [20]. To avoid light absorption in air, the whole experimental setup is either kept in vacuum (infrared MET beamline of the National Synchrotron Light Source II) or in a >99% nitrogen environment (optical table with SYSTEM setup). We use a liquid‐helium‐cooled Mercury‐Cadmium‐Telluride (MCT) detector as described in reference [42], which enables infrared near‐field microscopy studies in an spectral range from below 180 to beyond 1800 cm⁻¹, with some limited sensitivity beyond this range. For our experiment, the spectral width of our detector is the main limitation for the detected spectral width of the pulse. Importantly, the spectral width is sufficient to cover all relevant Reststrahlen bands of MoO₃ (Figure 1b). To reduce far‐field contributions to our near‐field signal, the detector signal is demodulated at higher harmonics nf of the tip tapping frequency f. The results shown in this manuscript use n = 2. For the data processing we use the Y‐channel of our lock‐in amplifier, i.e., we use Y = A_n  sin φ _n  with amplitude A_n and phase φ _n of the demodulated signal. The temporal dependence of the near‐field signal is acquired by moving the reference mirror position while the AFM tip is kept at a stationary position relative to the sample. This results in an interferogram of the near‐field signal at a fixed spatial position. Once the scan of the reference mirror is completed, the AFM tip is moved to the next spatial position. For the experiments shown in the present manuscript, the tip is moved along a straight line. For the experimental data in Figures 1, 2, 3, we chose a spatial step size of 30 nm. The whole process results in a 2D data file that contains the near‐field signal as a function of tip position x and time delay dt.

To obtain spacetime maps such as the ones shown in Figures 1c,2, 3, the raw data is processed in two main steps: (1) Spectral bandpass filtering to reduce spectral contributions outside of the frequency region of interest. (2) Taking the second derivative along the spatial direction to remove spatially constant contributions. Details of each step are described below:

(1) Spectral bandpass filter: The spectral bandpass filter was applied electronically, after the data acquisition, and consisted of the following three steps: (i) Fourier transform of the data along the temporal axis. (ii) Multiplication of the spectral data with a Planck‐taper window with lower and upper cutoff frequency matching the spectral region of interest. For Figure 1a, we chose a bandpass from 150 to 1050 cm⁻¹, i.e., covering all relevant Reststrahlen bands of MoO₃. For the other figures, the cutoff frequencies are mentioned in the figure caption. (iii) Reverse Fourier transform of the data to regain the temporal data.

(2) Second spatial derivative: To reduce noise, we first apply a Gaussian broadening along the spatial direction. We chose a Gaussian distribution with an eight‐pixel standard deviation. We then take the second spatial derivative. As described in reference [21], the derivative removes spatially constant contributions and, thus, reveals polaritonic contributions to the near‐field signal. Compared to the first derivative, the second derivative better preserves the symmetry of the polaritonic behavior. We note that alternative methods for removing the spatially constant background exist such as Fourier filtering or subtraction of average values [20, 30]. For our data, we find that these alternative methods generally provide comparable qualitative results.

2.2. Theoretical Description of SYSTEM Data Interpretation

In general, the electric field of the outcoupled signal can be expressed as

$$E_{sig}\left(x,t\right)=\int d\omega A\left(\omega ,x\right)e^{i\left(\omega t-\beta \left(\omega \right)x\right)}+c.c$$

where x denotes the position of the line‐scan on the sample, A(ω, x) denotes the position‐dependent spectrum of the signal pulse, β(ω) is the wavevector and in general can be nonlinear in ω, and c.c. refers to the complex conjugate. The initial phase is neglected in this expression as it only contributes a constant phase.

The electric field of reference arm can be denoted as

$$E_{ref}\left(t-\tau \right)=b\left(t-\tau \right)e^{i\left({\omega }_0\left(t-\tau \right)\right)}+c.c$$

where τ represents the delay introduced by the delay stage in the reference arm. b(t) = |b(t)|e ^iϕ(t) is the temporal envelope with a phase contribution ϕ(t), and ω₀ is the central frequency of the reference pulse.

Interferogram can then be expressed as [18]

$$I\left(x,\tau \right)={\int }_{-\infty }^{\infty }dt{\left(E_{sig}\left(x,t\right)+E_{ref}\left(t-\tau \right)\right)}^{2}dt$$

$$={\int }_{-\infty }^{\infty }dt\left({\left|E_{sig}\left(x,t\right)\right|}^2+{\left|E_{ref}\left(t-\tau \right)\right|}^2+E_{sig}\left(x,t\right)E_{ref}^{\ast }\left(t-\tau \right)\right)+c.c.$$

After applying spectral bandpass filters to I(x, τ) in its Fourier domain, the term that solely depend on t that correspond to zero‐frequency component in frequency domain is eliminated. By taking spatial derivatives on I(x, τ), the term that depend only on x is further eliminated, leaving only the term $E_{sig}(x,t)E_{ref}^{\ast }(t-\tau )$ and its complex conjugate in the integrand. For now, we first consider $\stackrel{\sim }{I}(x,\tau )$ without x‐ and τ‐ independent term:

$$\begin{array}{c}\hfill \stackrel{\sim }{I}\left(x,\tau \right)={\int }_{-\infty }^{\infty }dt{E}_{sig}\left(x,t\right)E_{ref}^{\ast }\left(t-\tau \right)+c.c.\\ \hfill ={\int }_{-\infty }^{\infty }dt\int d\omega A\left(\omega ,x\right)e^{i\left(\omega t-\beta \left(\omega \right)x\right)}{b}^{\ast }\left(t-\tau \right)e^{-i{\omega }_0\left(t-\tau \right)}\\ \hfill ={\int }_{-\infty }^{\infty }d\omega A\left(\omega ,x\right)e^{-i\beta \left(\omega \right)x}\int e^{i{\omega }_0\tau }{b}^{\ast }\left(t-\tau \right)e^{i\left(\omega -{\omega }_0\right)t}dt+c.c.\end{array}$$

By defining $t^{\prime }≔t-\tau$ and substituting, the second integral above can be evaluated as

$\int e^{i{\omega }_0\tau }{b}^{\ast }(t-\tau )e^{i(\omega -{\omega }_0)t}dt=\int e^{i{\omega }_0\tau }{b}^{\ast }(t^{\prime })e^{i(\omega -{\omega }_0)(t^{\prime }+\tau )}d{t}^{\prime }=e^{i\omega \tau }\int b^{\ast }(t^{\prime })e^{i(\omega -{\omega }_0)t^{\prime }}d{t}^{\prime }.$

Note that ${\stackrel{\sim }{E}}_{ref}^{\ast }(\omega -{\omega }_0)=\int b^{\ast }(t^{\prime })e^{i(\omega -{\omega }_0)t^{\prime }}d{t}^{\prime }$ is the complex conjugate of the Fourier transform of the reference beam with an offset ω₀.

Finally, $\stackrel{\sim }{I}(x,\tau )$ can be written as

$$\stackrel{\sim }{I}\left(x,\tau \right)={\int }_{-\infty }^{\infty }d\omega \left(A\left(\omega ,x\right){{\stackrel{\sim }{E}}^{\ast }}_{ref}\left(\omega -{\omega }_0\right)\right)e^{i\left(\omega \tau -\beta \left(\omega \right)x\right)}+c.c.$$

Therefore, the interferogram $\stackrel{\sim }{I}(x,\tau )$ corresponds to a renormalized wave packet of the near‐field signal with the weight given by ${\stackrel{\sim }{E}}_{ref}(\omega -{\omega }_0)$. The second derivative $\stackrel{\sim }{I}(x,\tau )$ with respect to x can be expressed as

$$\begin{array}{c}\hfill \frac{{\partial }^2}{\partial x^2}\stackrel{\sim }{I}\left(x,\tau \right)={\int }_{-\infty }^{\infty }d\omega \left(A\left(\omega ,x\right){{\stackrel{\sim }{E}}^{\ast }}_{ref}\left(\omega -{\omega }_0\right)\right)e^{i\left(\omega \tau -\beta \left(\omega \right)x\right)}\\ \hfill +c.c={\int }_{-\infty }^{\infty }d\omega \left(-\beta {\left(\omega \right)}^{2}A\left(\omega ,x\right)+\frac{{\partial }^{2}A\left(\omega ,x\right)}{\partial x^2}\right)\\ \hfill {{\stackrel{\sim }{E}}^{\ast }}_{ref}\left(\omega -{\omega }_0\right)e^{i\left(\omega \tau -\beta \left(\omega \right)x\right)}+c.c.\end{array}$$

This operation only modifies the shape of the wave packet through renormalization but does not alter the essential extraction of group and phase information.

2.3. Phase Velocity Operator

Figure 1e shows a spacetime map of the polariton phase velocity. This phase‐velocity map v_p(x,t) can be calculated from the regular spacetime map ϕ (Figure 1c) via: ${\mathrm{v}}_{\mathrm{p}}[\varphi (x,t)]=\frac{\partial \varphi (x,t)}{\partial t}/\frac{\partial \varphi (x,t)}{\partial x}$. Here, we discuss this calculation and derive the phase velocity operator.

Assuming a single‐frequency plane wave, the spacetime map ϕ(x, t) is described by a sine wave: ϕ(x, t) = sin (2π(x/λ − ft)) with wavelength λ and frequency f. Considering that the phase velocity v_p = fλ and using ω = 2πf, this can be written as ϕ(x, t) = sin (ω(x/v_p − t)). The derivatives of ϕ are $\frac{\partial }{\partial t}\varphi (x,t)=-\omega \cos (\omega (x/v_p-t))$ and $\frac{\partial }{\partial x}\varphi (x,t)=\omega /v_p\cos (\omega (x/v_p-t))$. Therefore, $-\frac{\partial \varphi (x,t)}{\partial t}/\frac{\partial \varphi (x,t)}{\partial x}=v_p$, i.e., for a plane wave, the phase velocity operator $-\frac{\partial }{\partial t}/\frac{\partial }{\partial x}$ calculates the phase velocity from the spacetime map. If we now assume that our spacetime map ϕ(x, t) can locally, i.e., in the local proximity of any point in the spacetime map, be approximated by a plane wave, the operator will accurately produce the local phase velocity v_p (x,t). Note that v_p (x,t) here refers to the local phase velocity observed in the spacetime map (as opposed to the physical phase velocity of the polaritons). For edge‐launched polaritons the phase velocity will generally be equal to this velocity. However, for tip‐launched polaritons, we will need to consider an additional factor of two as the polaritons need to travel any distance twice to be detected. Therefore, for tip‐launched polaritons, the phase velocity operator becomes $-2\frac{\partial }{\partial t}/\frac{\partial }{\partial x}$. This is the form that we use to obtain Figure 1e. Before applying the operator to our experimental data, we apply an appropriate Gaussian filter to reduce artifacts from the numerical spatial and temporal derivatives. We note that in regions with multi‐mode interference, reliable phase‐velocity readout is not possible. We therefore regard the phase velocity as not well‐defined where multiple modes overlap significantly.

2.4. Dielectric Permittivity of MoO₃ and hBN

We used literature data to calculate the dielectric permittivity for all relevant materials. The permittivity of the gold substrate was calculated from reference [55]. The permittivity of hBN was calculated from the parameters provided for isotopically pure h¹¹BN in reference [56]. To obtain the permittivity of MoO₃, we combined the mid‐infrared data provided in reference [36] with the far‐infrared data provided in reference [12]. The real part of the resulting permittivity is shown in Figure 1b for the crystalline [001] and [010] direction, which are most relevant for the polaritonic response along the long resonator axis. Figure S6 shows the dielectric permittivity along all three crystalline axes. For the analytical calculation of the polariton properties (Figure 4; Figure S5), the dielectric permittivity of the superstrate (>99% N₂) was assumed to be ε_N2 = 1.0, independent of the optical frequency.

2.5. Analytical Calculation of Polariton Properties

We calculate the imaginary part of the p‐polarized reflection coefficient, Im(r_p), for a stratified medium representing our sample, which consists of a MoO₃ thin film of thickness d_MoO3 = 88 nm on top of a thin film of hBN with thickness d_hBN = 83 nm on top of a gold substrate. The thicknesses d_MoO3 and d_hBN match the values measured via atomic force microscopy for the sample discussed in Figures 1, 2, 3 and Figure S1. The superstrate in the calculation is air/vacuum. Figure 4 shows false color displays of Im(r_p) as a function of momentum k (horizontal axis) and wavenumber ω (vertical axis). As maxima of Im(r_p) correspond to the resonance condition for polariton excitation, false color maps of Im(r_p) have become a common tool for the visualization of polariton dispersion [8]. Panels (a) and (b) illustrate the polariton dispersion along the long and short cavity axes, respectively. Comparing the experimental dispersion (Figure 2b) with the corresponding calculation of Im(r_p) along the long resonator axis (Figure 4a), we generally find good agreement.

2.6. Oscillation Frequency at the Center of a Wave Packet

Figure 1d presents linecuts through the spacetime map (Figure 1c) extracted along the center of each of the three wave packets. For wave packets (I) and (II), the extracted line profiles are well described by an exponentially decaying sine wave of frequency f. In the main text, we state that the frequency f is proportional to the difference v_p‐v_g between the average phase velocity v_p and the group velocity v_g of the wave packet. Figure 5 provides a geometrical derivation of the full expression for the phase velocity. We use the horizontal axis for space x and the vertical axis for time t. Grey arrows represent isophase fronts, i.e., the direction of the grey arrows represents the phase velocity in the spacetime map. The temporal distance between two grey arrows shall correspond to a full phase cycle of 2π. Assuming an average frequency f₀ of the wave packet, the vertical distance between the isophase arrows is given by 1/f₀ as marked in Figure 4. The orange arrow Figure 5 represents the group velocity. For the illustration, we assume that the phase velocity is larger than the group velocity, v_p>v_g, which can be seen from the different slope of the corresponding arrows. Intersections between the group velocity vector and the isophase lines represent a full phase cycle at the center of the wave packet, i.e., the time difference between two adjacent intersections is 1/f, with f the frequency of the decaying sine wave (Figure 1d). Using the sketch provided in Figure 4, we derive the following expression for f:

$$\frac{1}{f}=\frac{\mathrm{\Delta }x}{v_g}=\frac{1}{f_0}+\frac{\mathrm{\Delta }x}{v_p}$$

Eliminating Δx from the equation above and solving for f, this yields:

$$f=\frac{\left(v_p-v_g\right)}{v_p}{f}_0$$

For simplicity, in the derivation above we implicitly assumed edge‐launched polariton modes, but in the experiment we predominantly observe tip‐launched modes. However, the expression above remains the same for both tip‐ and edge‐launched modes: In a spacetime map, tip‐launched modes effectively behave like edge‐launched modes with half the group and phase velocity [21]. As only relative differences between the phase and group velocity matter in the expression above, any constant pre‐factor would cancel. The derived expression shows that the absolute value of the frequency f at the center of the wave packet can be both smaller and larger than the frequency f ₀ of light wave at a fixed point in space. The value is larger, f > f ₀, when the phase and group velocity have opposite signs, e.g., this is the case for MoO₃ band (III) [9]. For band (I) and (II), both velocities are positive and larger than zero, v_p > v_g > 0, resulting in f < f ₀. Notably, for acoustic polaritons, i.e., polaritons with a linear dispersion where v_p = v_g , the equation above predicts that the oscillation frequency f = 0. This means a line profile extracted along the center position of the wave packet (such as the ones shown in Figure 1d) would show a non‐oscillating exponential decay. This matches previous experimental and theoretical spacetime studies of acoustic plasmon polaritons in graphene [21].

2.7. Temporal Resolution of SYSTEM

There are different options for defining the temporal resolution of our technique, and the most useful definition depends on the scientific question one is trying to answer. In the following, we will discuss the following two questions related to the temporal resolution: (1) What is the time resolution for detecting optical phase changes? (2) What is the shortest pulse length/ wave packet that we can measure?

Temporal resolution for tracking phase changes: We use an interferometric method to detect phase changes. Starting from an incident probe wave packet, we use a beam splitter to create two copies of the wave packet. One of these copies is used to probe the sample and experiences a change in amplitude and phase. The other copy is used as a reference packet with a controlled phase delay (via the moveable reference mirror). We obtain the optical phase via interference between the sample and reference wave package. Neglecting the finite signal‐to‐noise ratio of our measurement, the accuracy of our phase measurement is given by the accuracy of controlling the reference mirror position. As such, a lower limit for the corresponding temporal (phase) resolution, δt, of our setup is given by the accuracy and repeatability of our reference mirror positioner (PIHera by Physik Instrumente (PI), Germany), δx = 14 nm. Here, we are interested in relative mirror positions (relative to x = 0, t = 0). Using Gaussian error propagation, the uncertainty of relative mirror positions will be $\sqrt{2}$ δx. As the reference beam travels the optical distance δx twice at the speed of light c, the temporal resolution is given by δt = 2 $\sqrt{2}$δx / c = 0.13fs. While the actual measurement uncertainty of δt might be larger, e.g., due to thermal drift of optical components, the measurement uncertainty of δt is not currently a limiting factor for the temporal resolution of our method. In the experiment, we choose a reference mirror step size that is several orders of magnitude larger than the uncertainty discussed above. For instance, the SYSTEM measurements on sample #1, discussed in Figures 1, 2, 3 and Figure S1, (sample #2, discussed in Figures S2–S4) were acquired with 1200 (2048) reference mirror steps over a total distance of 1500 µm, resulting in a spatial step size of dx = 1.25 µm (0.73 µm) and temporal step size dt = 8.3 fs (4.9 fs). The step size dt is much larger than the temporal resolution δt.

Shortest measurable pulse length: The shortest pulse length that we can experimentally access is given by the measured temporal length of the incident pulse. As a first approximation, for our interferometric method, the pulse length will be inversely proportional to its spectral width. The measured spectral width is determined by the light source, the optical elements and detector, i.e., all instrument components, as well as the sample. To estimate the intrinsic spectral width/ pulse length of the instrument, we measure a gold reference sample, which provides a spectrally broad flat optical response in the infrared frequency range that we are interested in. Figure 6 shows the measured near‐field interferogram of a gold reference sample. For clarity, the signal was normalized by retracting the average signal value and dividing by the maximum peak height. The inset provides a detailed view of the central pulse around dt = 0. The signal amplitude remains below 10% of the main peak for |dt|>0.05 ps, and the central pulse clearly has a length of less than 0.1 ps, providing an estimate for the shortest wave packet we can measure. For most spacetime maps, we apply spectral bandpass filters to reduce contributions from outside our spectral range of interest. For example, we apply a bandpass filter from 150 to 1050 cm⁻¹ to the data shown in Figure 1c. The dashed line in the inset illustrates the impact of this filter on the measured pulse shape. The pulse length remains below 0.1 ps. As the pulse length is inversely proportional to the spectral width, this short pulse length is a direct consequence of the broad spectral width covered by our system.

FIGURE 6.

Pulse shape measured on a gold reference sample. The figure shows the normalized experimental near‐field signal (interferogram) measured on a gold reference sample as a function of the time delay dt. As gold provides a spectrally broad flat response in our infrared spectral range of interest, the measured pulse length provides an estimate for the shortest pulse length accessible with our SYSTEM setup. The inset shows a detailed view of the measurement, focusing on the region around dt = 0. The central pulse is shorter than 0.1 ps. The dashed line illustrates the pulse shape modification by a spectral bandpass filter with cutoff frequencies at 150 and 1050 cm⁻¹.

Note that the synchrotron radiation itself is pulsed due to the bunched structure of the electron beam that is used to create the synchrotron radiation. The pulse length of the National Synchrotron Light Source II is in the order of ∼10 ps [42, 54]. As the temporal resolution of our SYSTEM setup is shorter by orders of magnitude, clearly the temporal resolution of SYSTEM is not limited by the pulse length of the infrared radiation.

2.8. Synchrotron Infrared Nanospectroscopy

Synchrotron infrared nanospectroscopy was performed using the infrared nanospectroscopy setup at the 22‐IR‐2 beamline of the National Synchrotron Light Source II using the setup previously described in reference [42]. While the process of raw data acquisition is the same as for SYSTEM, the data processing significantly differs for both techniques. Conventional infrared nanospectroscopy uses a Fourier transform along the temporal dimension to get access to the spectral information; the temporal information is not usually directly studied. In contrast, SYSTEM provides direct access to the time‐resolved data via the data processing described in the corresponding methods section above.

2.9. Sample Preparation

The sample preparation has previously been described in reference [16]. Employing a flame‐growth approach, MoO₃ is naturally grown in the shape of nanoresonators without the need for artificial material structuring. This ensures ideal material properties for high‐quality nanoresonators [16, 27]. The growth of monoisotopic h¹¹BN crystals from metal solution has been previously described in reference [57]. We use a commercial ultra‐flat Au substrate that was template‐stripped from a Si wafer (100 nm‐thick Au film on glass, Platypus Technologies, USA). The hBN bulk samples were exfoliated and transferred to the Au substrate using low‐adhesion cleanroom tape. Then, the as‐grown MoO₃ structures were transferred onto the hBN on gold sample.

Conflicts of Interest

The authors declare no conflict of interest.

Author Contributions

L.W., G.L.C., and M.K.L. conceived the study. S.‐J.Y., H.Y., J.H., and X.Z. grew the MoO₃ crystals and fabricated the samples. E.J., and J.H.E. grew the hBN crystals. L.W. and S.‐J.Y. pre‐characterized the samples with support from C.C.H., T.F.H., J.A.F., D.N.B., G.L.C., and M.K.L. L.W. performed the measurements with support from C.C.H., G.L.C., and M.K.L. L.W. analyzed the experimental data with support from S.X., X.C., H.W., G.L.C., M.K.L. L.W. performed the analytical calculations with support from Z.D. S.X. derived the phase velocity operator with support from L.W. Y.L. derived the theoretical description of SYSTEM. L.W., C.C.H., D.N.B., G.L.C. and M.K.L. support the infrared nanospectroscopy facility at BNL. L.W. and M.K.L. drafted the manuscript with input from all other authors.

Supporting information

Supporting File: smll72141‐sup‐0001‐SuppMat.pdf

Wehmeier L., Xu S., Chen X., et al. “Ultrabroadband Spacetime Nanoscopy of Terahertz Polaritons in a van der Waals Cavity.” Small 22, no. 10 (2026): e05899. 10.1002/smll.202505899

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.