Abstract
Accessing the low-energy non-equilibrium dynamics of materials and their polaritons with simultaneous high spatial and temporal resolution has been a bold frontier of electron microscopy in recent years. One of the main challenges lies in the ability to retrieve extremely weak signals and simultaneously disentangling the amplitude and phase information. Here we present free-electron Ramsey imaging—a microscopy approach based on light-induced electron modulation that enables the coherent amplification of optical near fields in electron imaging. We provide simultaneous time-, space- and phase-resolved measurements of a micro-drum made from a hexagonal boron nitride membrane, visualizing the sub-cycle dynamics of two-dimensional polariton wavepackets therein. The phase-resolved measurement reveals vortex–anti-vortex singularities on the polariton wavefronts, together with an intriguing phenomenon of a travelling wave mimicking the amplitude profile of a standing wave. Our experiments show a 20-fold coherent amplification of the near-field signal compared with conventional electron near-field imaging, resolving peak field intensities in the order of a few watts per square centimetre, corresponding to field amplitudes of a few kilovolts per metre. As a result, our work paves the way for the spatiotemporal electron microscopy of biological specimens and quantum materials, exciting yet delicate samples that are currently difficult to investigate.
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All the key data that support the findings of this study are included in the article and its Supplementary Information. Further datasets and raw measurements are available from the corresponding author upon reasonable request.
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Acknowledgements
This work, especially the development and installation of the PELM, are part of the SMART-electron project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 964591. Measurements were conducted in the UTEM laboratory (I.K.) in the electron microscopy centre (MIKA) in the Department of Materials Science and Engineering, Technion. We acknowledge the Hellen Diller Quantum Center for supporting this research. The experimental effort is funded by the Gordon and Betty Moore Foundation, through grant GBMF11473 to I.K. A.N. acknowledges funding from the Swiss National Science Foundation (SNSF) through project P500PT_214469. S.T. acknowledges generous support from the Adams fellowship of the Israeli Academy of Science and Humanities; the Yad Hanadiv foundation through the Rothschild fellowship; the VATAT-Quantum fellowship by the Israel Council for Higher Education; the Helen Diller Quantum Center post-doctoral fellowship; and the Viterbi fellowship of the Technion—Israel Institute of Technology. F.H.L.K. acknowledges support from the government of Spain (PID2019-106875GB-I00; Severo Ochoa CEX2019-000910-S [MCIN/AEI/10.13039/501100011033], PCI2021-122020-2A funded by MCIN/AEI/10.13039/501100011033), the “European Union NextGenerationEU/PRTR (PRTR-C17.I1), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya (CERCA, AGAUR, 2021 SGR 01443)”.
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These authors contributed equally: T.B., H.N., H.H.S. and R.R. The sample fabrication was done by H.H.S. The hBN crystals were grown by E.J. and J.H.E. The measurements were performed by H.N., A.N., R.D., Y.A. and M.Y. The theory was developed by R.R., T.B., Q.Y. and J.C. The data analysis was performed by T.B. and R.R. The design and installation of the PELM in the electron microscope was performed by R.D., S.T.P., D.J.M. and G.M.V. The experiment was designed by T.B., H.H.S., H.N., A.N., S.T., Y.A., M.Y., R.D. and I.K. The work was supervised by F.C., G.B., F.H.L.K, G.M.V. and I.K. All authors contributed substantially to the analysis, discussion and writing of this work.
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Extended data
Extended Data Fig. 1 Reference non-uniformity correction.
(a) Energy filtered measurement with light induced only on the reference interaction. (b,c) Amplitude reconstruction for weak \({g}_{s}\) without (b) and with (c) correction. All the images are normalized to be between 0 and 1 such that the features are visible.
Extended Data Fig. 2 Phonon-polariton amplitude and phase reconstruction for different illumination intensities compared to conventional PINEM imaging.
Data acquired using three different average interaction strengths over the entire image: \(\left|{g}_{s}\right|\approx 0.4,\,0.8,\,1.4\), top to bottom, respectively. (a) conventional PINEM amplitude imaging for the three different interaction strengths and for different energy filtering (10 eV slit width, cutoff energy is marked at the bottom of each image), acquired for the same time-delay. (b) FERI amplitude imaging for the same electron dose on the sample. As predicted by theory (Fig. 4 of the main text), the largest amplification is seen for the weakest interaction strength. The right column shows FERI phase images for the different interaction strengths.
Extended Data Fig. 3 Sample images.
(a,b) TEM images of the investigated hBN flake. The experimental results shown in the main text could be reproduced in different windows of the flake, however, the highlighted window (b) gave the best coupling efficiency and thus strongest signal. (c) Electron diffraction pattern of the hBN flake highlighted in (b), confirming that the whole flake is mono-crystalline. (d) Optical microscope image of the investigated hBN flake. Different colors correspond to different hBN thicknesses and are formed due to optical interference in the hBN and substrate. The investigated window shows a uniform thickness.
Extended Data Fig. 4 Image post-processing revealing the phonon-polaritons properties.
(a) The relative phase scan produces the FERI tilted raw measurements which are used to reconstruct the amplitude and phase (b). (c1-4) The process for the ellipse estimation: (c1) convert the amplitude reconstructed image to black and white by thresholding. (c2-3) perform morphological image processing59. (c4) estimate the ellipse equation through connected component analysis. (d) Perform an affine transformation on the reconstructed images using the inverse of the estimated ellipse equation.
Supplementary information
Supplementary Information
Supplementary Sections 1–4.
Supplementary Video 1
Phonon-polariton PINEM delay scan in the hBN micro-drum. Each frame in this video corresponds to an energy-filtered electron image. The delay between the laser pulse impinging on the sample and the electron probe pulse is increased for each frame by 50 fs. This allows us to construct the time evolution of the phonon-polariton dynamics, showcasing the ‘hopping’ effect discussed in the main text.
Supplementary Video 2
Phonon-polariton PINEM delay scan in the hBN micro-drum. Each frame in this video corresponds to an energy-filtered electron image. The delay between the laser pulse impinging on the sample and the electron probe pulse is increased for each frame by 10 fs. This allows us to construct the time evolution of the phonon-polariton dynamics, showcasing the ‘hopping’ effect discussed in the main text.
Supplementary Video 3
FERI phase scans of phonon polaritons in the hBN micro-drum. Each frame in this video corresponds to an energy-filtered electron image. The video is a scan over the sample–reference relative phase for gs,max = 1.4 using sub-cycle delay steps, allowing one to reconstruct the phase of the field at the sample. The reconstruction is based on the FERI optimization expression discussed in Methods.
Supplementary Video 4
FERI phase scans of phonon polaritons in the hBN micro-drum. Each frame in this video corresponds to an energy-filtered electron image. The video is a scan over the sample–reference relative phase for gs,max = 0.8 using sub-cycle delay steps, allowing one to reconstruct the phase of the field at the sample. The reconstruction is based on the FERI optimization expression discussed in Methods.
Supplementary Video 5
FERI phase scans of phonon polaritons in the hBN micro-drum. Each frame in this video corresponds to an energy-filtered electron image. The video is a scan over the sample–reference relative phase for gs,max = 0.4 using sub-cycle delay steps, allowing one to reconstruct the phase of the field at the sample. The reconstruction is based on the FERI optimization expression discussed in Methods.
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Bucher, T., Nahari, H., Herzig Sheinfux, H. et al. Coherently amplified ultrafast imaging using a free-electron interferometer. Nat. Photon. 18, 809–815 (2024). https://doi.org/10.1038/s41566-024-01451-w
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DOI: https://doi.org/10.1038/s41566-024-01451-w
