Time-Resolved EUV Momentum Microscopy

• Time-resolved extreme ultraviolet momentum microscopy is a pump–probe photoemission technique that combines EUV/XUV pulses with time-of-flight momentum mapping to capture full 3D electronic structures.
• It enables simultaneous acquisition of energy and in-plane momentum data, providing detailed band mapping and real-space imaging for advanced materials research.
• Leveraging both table-top HHG and FEL sources, the method produces multidimensional datasets that advance studies in non-equilibrium dynamics, exciton spectroscopy, and orbital tomography.

Searching arXiv for papers directly relevant to time-resolved extreme ultraviolet momentum microscopy. Querying arXiv for "time-resolved momentum microscopy extreme ultraviolet". Time-resolved extreme ultraviolet momentum microscopy is a pump–probe photoemission methodology in which ultrafast EUV or XUV probe pulses are combined with a momentum microscope—typically a time-of-flight instrument—to record the photoelectron distribution in energy and two in-plane momentum coordinates in parallel, and, in extended implementations, also as a function of delay, photon energy, polarization, or real-space region of interest. The field emerged from the convergence of high-repetition-rate high-harmonic generation beamlines, free-electron-laser sources, and full-field photoelectron optics, and it now spans table-top HHG instruments at $21.6$, $23.6$–$45.5$, and $26.5$ eV as well as FEL-based platforms operating from $25$ to $830$ eV (Fragkos et al., 3 Jul 2025, Heber et al., 2022, Keunecke et al., 2020, Kutnyakhov et al., 2019).

1. Measurement concept and operating principle

The defining distinction between momentum microscopy and conventional slit-based trARPES is the mode of acquisition. In a time-of-flight momentum microscope, the full azimuthal photoelectron momentum distribution is recorded in one shot, and the kinetic-energy axis is obtained from the electron flight time, so the instrument acquires a volumetric dataset $I(E,k_x,k_y)$ without scanning either momentum or kinetic energy (Jansen et al., 2020). In FEL implementations this has been described as direct mapping of 3D band structures in $(k_x,k_y,E)$ with about $2.5\times10^5$ data voxels and full surface-Brillouin-zone coverage up to $7~\mathrm{\AA^{-1}}$ diameter (Kutnyakhov et al., 2019). In a table-top multispectral HHG instrument, the simultaneous momentum field of view is $23.6$0 in both $23.6$1 and $23.6$2, with a $23.6$3 eV energy window (Heber et al., 2022).

The microscope optics can be operated in reciprocal-space or real-space mode. In reciprocal-space mode, the back focal plane of the objective lens constitutes an achromatic momentum image; in real-space mode, the emitting region on the sample is imaged instead. This duality is not an incidental convenience but a core methodological feature, because it permits real-space region selection before switching back to $23.6$4-space imaging. The exciton review emphasizes that this combination makes momentum microscopy practical for micron-scale exfoliated flakes, while the 2025 polarization-resolved instrument demonstrates real-space PEEM, $23.6$5-imaging, dark-field imaging, and sub-micron region-of-interest selection within one endstation (Reutzel et al., 2024, Fragkos et al., 3 Jul 2025).

EUV photon energies are central rather than optional. The exciton review states that photon energies larger than about $23.6$6 eV are required to probe large in-plane momenta, including valleys such as graphene $23.6$7 and TMD $23.6$8, and that EUV is likewise required for molecular orbital momentum fingerprints in photoemission orbital tomography (Reutzel et al., 2024). The 1 MHz graphene instrument makes the same point kinematically through the photoemission horizon,

$23.6$9

which is why $45.5$0 eV probing reaches the graphene $45.5$1 points and the full first Brillouin zone in one shot (Keunecke et al., 2020).

2. Source classes and instrument architectures

Two source classes dominate the field: table-top HHG beamlines and FEL beamlines. The table-top 1 MHz graphene platform uses an ytterbium-doped fiber amplifier delivering $45.5$2 at $45.5$3 MHz and $45.5$4–$45.5$5 fs, compressed to $45.5$6–$45.5$7 fs at $45.5$8; the HHG branch is frequency doubled to $45.5$9 nm and generates the $26.5$0 harmonic at $26.5$1 eV in argon, with $26.5$2 meV bandwidth and an extracted probe pulse duration of $26.5$3 fs at the sample (Keunecke et al., 2020). A complementary 6 kHz instrument uses a $26.5$4 nm Ti:sapphire amplifier and a toroidal-grating monochromator to select odd harmonics from the $26.5$5 to the $26.5$6, spanning $26.5$7–$26.5$8 eV, and achieves a measured temporal response of $26.5$9 fs (Heber et al., 2022). A more recent monochromatic implementation operates at $25$0 eV and $25$1 kHz with a polarization-tunable XUV beamline, a small XUV footprint of $25$2, total energy resolution of $25$3 meV, and temporal resolution of $25$4 fs (Fragkos et al., 3 Jul 2025).

The FEL architecture extends the same measurement logic into the XUV and soft-x-ray range. At FLASH PG2, the available photon-energy range is $25$5–$25$6 eV, with demonstrated operation at $25$7 eV for valence-band time-resolved momentum microscopy and $25$8 eV for time-resolved core-level work (Kutnyakhov et al., 2019). The pulse structure there is $25$9 pulses per macrobunch, $830$0 MHz intra-bunch repetition rate, and $830$1 Hz macrobunch rate, corresponding to $830$2 probe pulses per second. After monochromatization and wavefront-tilt mitigation, the pulse duration at the sample is $830$3 fs for valence-band trMM and $830$4 fs for trXPS, while the experimental cross-correlation from laser-assisted photoemission is $830$5 fs (Kutnyakhov et al., 2019).

Table-top HHG and FEL instruments are therefore complementary rather than redundant. HHG platforms emphasize local accessibility, intrinsic pump–probe synchronization, and MHz-class repetition rates under low-per-pulse charge conditions; FEL platforms add broad tunability into the soft-x-ray regime, core-level access, tunable depth sensitivity, and large momentum reach (Keunecke et al., 2020, Kutnyakhov et al., 2019). The multispectral table-top instrument explicitly presents itself as a bridge between static 3D momentum microscopy and ultrafast XUV photoemission by adding photon-energy tunability for $830$6-resolved work (Heber et al., 2022).

3. Multidimensional data spaces and tomographic extensions

The minimal data structure of time-resolved EUV momentum microscopy is $830$7. In photon-energy-tunable implementations, this is generalized to $830$8, where $830$9 is reconstructed by varying $I(E,k_x,k_y)$0 under a free-electron-like final-state approximation: $I(E,k_x,k_y)$1 For graphene-covered Ir(111), the 6 kHz multispectral instrument used empirical parameters $I(E,k_x,k_y)$2 and $I(E,k_x,k_y)$3 eV, covered a $I(E,k_x,k_y)$4 interval of $I(E,k_x,k_y)$5, and reconstructed 3D Fermi-surface sheets from harmonic series spanning $I(E,k_x,k_y)$6 to $I(E,k_x,k_y)$7 eV (Heber et al., 2022).

A second extension is photoemission orbital tomography. In the plane-wave final-state approximation, the measured intensity is related to the Fourier transform of the emitting orbital: $I(E,k_x,k_y)$8 At fixed photon energy, the measurement samples $I(E,k_x,k_y)$9 on a hemispherical shell in 3D momentum space, with shell radius

$(k_x,k_y,E)$0

Varying $(k_x,k_y,E)$1 therefore supplies a family of hemispherical cuts through 3D momentum space (Bennecke et al., 25 Feb 2025).

The 2025 table-top 3D-POT experiment is directly relevant because it demonstrates the exact instrument stack required for future delay-dependent 3D orbital movies: a femtosecond HHG-EUV source, a time-of-flight momentum microscope recording the full $(k_x,k_y,E)$2 distribution without scanning, and a sparse-data reconstruction algorithm that reduces the number of required photon-energy projections (Bennecke et al., 25 Feb 2025). In that work, single harmonics from $(k_x,k_y,E)$3 to $(k_x,k_y,E)$4 eV were available, $(k_x,k_y,E)$5 photon energies with $(k_x,k_y,E)$6 eV spacing were accessible, and measured orbital maps were collected at ten photon energies from $(k_x,k_y,E)$7 to $(k_x,k_y,E)$8 eV. Each photon-energy dataset required two hours at a typical total count rate of $(k_x,k_y,E)$9 electrons/s. The analysis showed that seven photon energies give a good balance of reliability and speed, and that under favorable constraints even four photon energies can already yield a full 3D reconstruction, reducing a static 3D dataset to $2.5\times10^5$0 hours (Bennecke et al., 25 Feb 2025).

This reduction in projection number is methodologically important because a fully time-resolved 3D-POT experiment would require scanning both photon energy and pump–probe delay. The paper explicitly identifies the resulting future data space as $2.5\times10^5$1 and presents sparse cyclic-projections reconstruction as the route that makes such 5D datasets plausible on a table-top system (Bennecke et al., 25 Feb 2025).

4. Scientific applications

A first application class is non-equilibrium band mapping in quantum materials. In graphene, the 1 MHz $2.5\times10^5$2 eV instrument resolves the full first Brillouin zone, the six Dirac cones, the dark corridor, anisotropic hot-carrier distributions, and sidebands shifted by the pump photon energy of $2.5\times10^5$3 eV; a full 3D static band map with good signal quality is obtained in $2.5\times10^5$4 minutes (Keunecke et al., 2020). The same platform visualizes the pump-induced anisotropy at $2.5\times10^5$5 fs and its azimuthal thermalization by $2.5\times10^5$6 fs (Keunecke et al., 2020).

A second class is ultrafast valley and band-population dynamics. At FLASH, the valence-band trMM study of bulk $2.5\times10^5$7-WSe$2.5\times10^5$8 recorded volumetric $2.5\times10^5$9 maps before and after optical excitation at $7~\mathrm{\AA^{-1}}$0 eV and tracked excited populations from the $7~\mathrm{\AA^{-1}}$1 valleys into the lower-lying $7~\mathrm{\AA^{-1}}$2 valleys. The extracted dynamics show a fast decay component of $7~\mathrm{\AA^{-1}}$3 fs at $7~\mathrm{\AA^{-1}}$4, a population maximum at $7~\mathrm{\AA^{-1}}$5 delayed by $7~\mathrm{\AA^{-1}}$6 fs, and a fast decay component of $7~\mathrm{\AA^{-1}}$7 fs there; the $7~\mathrm{\AA^{-1}}$8 fs lag is interpreted as the temporal signature of intervalley scattering (Kutnyakhov et al., 2019).

A third class is exciton spectroscopy. The exciton review argues that momentum microscopy provides direct access to the energy landscape of bright and dark excitons and to the momentum coordinate fundamental to the exciton wavefunction, and that EUV pulses are indispensable because photon energies larger than about $7~\mathrm{\AA^{-1}}$9 eV are required to probe the relevant large in-plane momenta (Reutzel et al., 2024). The method can identify bright and dark excitons in TMDs, reveal scattering from initially bright $23.6$00-excitons into dark $23.6$01-excitons, and, more generally, extract information not only on the electron component but also on the hole component of the former exciton (Reutzel et al., 2024). The same review emphasizes that photoemission orbital tomography can reconstruct real-space properties of exciton wavefunctions in both 2D semiconductors and organic materials (Reutzel et al., 2024).

A fourth class is polarization-resolved and dichroic photoemission. The $23.6$02 eV, $23.6$03 kHz instrument demonstrates linear, Fourier, and circular dichroism in photoelectron angular distributions from photoexcited 2D materials (Fragkos et al., 3 Jul 2025). In this architecture, the XUV polarization angle is rotated continuously through the $23.6$04 nm half-wave plate driving HHG, and the signal is decomposed voxelwise through

$23.6$05

The resulting observables distinguish $23.6$06- and $23.6$07-polarized matrix elements, expose Fourier dichroism through $23.6$08, and reveal valley-contrasting structure in 2H-WSe$23.6$09 and nonequilibrium dichroism in 2H-MoTe$23.6$10 (Fragkos et al., 3 Jul 2025).

A fifth, presently theoretical, class is attosecond photoelectron momentum microscopy. For aligned pentacene, the attosecond study predicts that delay-dependent photoelectron momentum maps at $23.6$11 eV can image coherent charge migration even when angle-integrated spectra are essentially independent of delay, because the evolving signal is carried by momentum-space structure rather than by the total yield (Reuner et al., 2023). The calculation explicitly includes the spectral broadening of a $23.6$12 fs, $23.6$13 eV probe pulse, with each line broadened to about $23.6$14 eV, and shows that the momentum degree of freedom can be the only place where the attosecond dynamics remain visible (Reuner et al., 2023).

5. Performance envelope, efficiency, and comparison with analyzer-based trARPES

The practical performance of time-resolved EUV momentum microscopy is governed by a characteristic tradeoff between information throughput and charge density. The comparison study that placed a time-of-flight momentum microscope and a hemispherical analyzer in the same $23.6$15 eV, $23.6$16 kHz trARPES setup makes this explicit (Maklar et al., 2020). In that apparatus the momentum microscope collected the full photoemission horizon up to $23.6$17, but the delay-line detector was effectively limited to about one electron per pulse, i.e. $23.6$18 counts/s. With a $23.6$19m field aperture, the transmission was about $23.6$20 and the effective detector quantum efficiency about $23.6$21, corresponding to detection of about $23.6$22 of all emitted electrons, compared with about $23.6$23 for the hemispherical analyzer (Maklar et al., 2020). Yet the momentum microscope also exhibited detectable probe-space-charge distortions above about $23.6$24 emitted electrons per pulse, roughly an order of magnitude earlier than the hemispherical analyzer, and the depth of focus followed an inverse-square dependence on field-aperture diameter, $23.6$25 (Maklar et al., 2020).

This comparison clarifies why full-field imaging is transformative for global band mapping but not universally superior for every ultrafast problem. The momentum microscope can acquire the full $23.6$26 distribution efficiently, whereas the analyzer is faster for targeted time traces in a known region. In the WSe$23.6$27 benchmark, 4D momentum-microscopy datasets required $23.6$28 hours or more, whereas analogous hemispherical-analyzer time traces on selected regions required $23.6$29–$23.6$30 hours (Maklar et al., 2020). The paper’s concise conclusion is that the two spectrometers are complementary rather than hierarchical (Maklar et al., 2020).

Across the field, representative resolution numbers reflect the diversity of optimization strategies. The 6 kHz multispectral instrument reports $23.6$31 fs temporal response, total energy resolution of $23.6$32 meV at $23.6$33 eV, and effective momentum resolution of $23.6$34 (Heber et al., 2022). The 2025 polarization-resolved platform reports $23.6$35 meV total energy resolution, $23.6$36 meV time-of-flight contribution, and $23.6$37 fs temporal resolution (Fragkos et al., 3 Jul 2025). The FLASH instrument reaches $23.6$38 fs cross-correlation, $23.6$39 meV energy resolution under FEL operation, and $23.6$40 momentum resolution (Kutnyakhov et al., 2019). These figures should be read alongside source-side constraints such as the $23.6$41 meV bandwidth and $23.6$42 fs probe duration of the $23.6$43 eV, 1 MHz graphene beamline (Keunecke et al., 2020).

Acquisition speed can nevertheless be striking when the observable matches the full-field architecture. The $23.6$44 eV graphene platform obtains a full static 3D band map in $23.6$45 minutes at $23.6$46 MHz (Keunecke et al., 2020). The multispectral $23.6$47–$23.6$48 eV instrument acquires photon-energy-dependent Fermi-surface maps in $23.6$49–$23.6$50 hours per harmonic (Heber et al., 2022). The polarization-resolved $23.6$51 eV system records full polarization-modulated datasets at count rates of $23.6$52 electrons/s over $23.6$53 hours (Fragkos et al., 3 Jul 2025). In all cases, high repetition rate is the enabling condition because it permits low electrons per pulse while retaining usable average count rates.

6. Limits, methodological controversies, and future directions

The present limitations are partly instrumental and partly conceptual. First, time-resolved EUV momentum microscopy is intrinsically surface sensitive, and some applications—especially orbital tomography—require a well-ordered adsorbed molecular layer with known orientation (Bennecke et al., 25 Feb 2025). Second, several reconstruction schemes depend on approximations such as the plane-wave final-state approximation, real-space support constraints, symmetry assumptions, or sparsity priors (Bennecke et al., 25 Feb 2025, Jansen et al., 2020). In the 3D-POT demonstration, residual background generated ambiguities, including phase flips in weak momentum-space lobes, and the finite momentum cutoff of $23.6$54 limited the real-space resolution to about $23.6$55 Å (Bennecke et al., 25 Feb 2025). Third, fixed-energy monochromatic instruments maximize stability and polarization control but do not provide $23.6$56 tunability; conversely, multispectral systems add $23.6$57 access at the price of lower flux per harmonic and longer acquisition times (Fragkos et al., 3 Jul 2025, Heber et al., 2022).

A persistent controversy concerns the relation between formal parallelism and practical throughput. The field comparison with a hemispherical analyzer shows that the momentum microscope’s global efficiency is curtailed by stronger susceptibility to space charge, depth-of-focus limits, and detector bottlenecks (Maklar et al., 2020). The 1 MHz graphene paper adds further practical constraints: the delay-line detector is effectively limited to about one photoelectron per pulse, the MCP ages above $23.6$58 counts/s, pump-induced low-energy electrons can consume detector bandwidth, and average-power heating can raise the sample holder temperature by about $23.6$59C at high repetition rate (Keunecke et al., 2020).

Attosecond and coherent extensions add another layer of complexity. The pentacene theory shows that attosecond probes inevitably broaden the spectrum strongly and make multiple ionization channels overlap, even though the momentum maps remain informative (Reuner et al., 2023). The phase-manipulated XUV pump–probe study at FERMI does not implement momentum microscopy, but it demonstrates independent phase and delay control of XUV pulse pairs, phase-cycling lock-in detection, and rotating-frame downshifting of attosecond oscillations into the femtosecond domain (Wituschek et al., 2019). This suggests a route toward phase-sensitive $23.6$60-resolved XUV spectroscopy, but that implication remains prospective rather than demonstrated in a momentum microscope (Wituschek et al., 2019).

Source engineering is also likely to broaden the method’s scope. The self-torque paper demonstrates EUV beams with time-varying orbital angular momentum generated in HHG and diagnosed through azimuthal frequency chirp (Rego et al., 2019). A plausible implication is that structured EUV beams could become a matrix-element control parameter in momentum microscopy, especially for chiral, magnetic, or topological observables, but such use is not yet realized in the cited momentum-microscopy experiments (Rego et al., 2019).

The most immediate future direction is explicit in the current literature: ultrafast multidimensional datasets that combine delay, photon energy, and full-field momentum detection. The multispectral table-top instrument already formulates the target hypercube as $23.6$61 (Heber et al., 2022). The 3D-POT work goes further and identifies $23.6$62 as the natural future data space for delay-dependent orbital tomography, with sparse-shell reconstruction reducing the photon-energy burden to the point where four photon energies per delay step may suffice after static characterization (Bennecke et al., 25 Feb 2025). In that sense, time-resolved EUV momentum microscopy is evolving from an efficient full-band mapper into a general platform for ultrafast wavefunction-sensitive spectroscopy.