Figures and data
Schematic of the laser optics integrated into a USEM (ultrafast SEM) to allow for ponderomotive experiments.
a, A pulsed laser (green) intersects with a strobed electron beam (purple) orthogonally, making each interacting electron packet behave as though it passes through a concave cylindrical lens. The ponderomotive effect of the pulsed laser defocuses the electron beam and simultaneously imposes a phase shift. b, A cross-section of the USEM that shows the optical connections. The electron beam is typically focused to a tight point to achieve high resolutions, but the interaction expands a subset of the focused electrons. A set of periscopes were installed to allow for the longest propagation distance post-interaction but are not necessary for the ponderomotive interaction itself. c, An image of the gold foil (290 nm diameter holes) used for experiments, with the region of interest highlighted by a red box.
Pulsed-laser lensing of an electron beam using the ponderomotive effect.
a, Difference images were generated by subtracting the negative-time reference image, acquired 21-67 ps before the photons arrive, from the time-zero image, when the photon pulses overlaps the electron packets. After noise filtering, these experimental difference images (b, top) are compared with simulated counterparts (b, bottom). The colorbar indicates the difference intensity in percentage of peak image counts. Axes are provided to indicate directions parallel and perpendicular to the laser Poynting vector. A third arrow is used to show the near-diagonal direction of laser lensing due to the ponderomotive effect. Scale bar, 100 nm. c, A line profile of the difference intensity along the axis of pulsed-laser lensing due to the ponderomotive effect. The direction along which electrons are preferentially pushed is indicated by the larger black arrow. Experimental data is shown as filled yellow circles (±S.E.M.) with simulated data shown as a dashed line. c, Momentum shift (µrad) produced by the ponderomotive effect in the axis orthogonal to both beams. A 500-fs laser pulse (green wave packet, propagating left-to-right) intersects an electron packet that moves into the page (black outline). The continuous green lines mark the 12.5 µm laser-beam diameter, while the black ellipse (major axis ∼15 µm) shows the simulated electron-beam profile calculated from the experimental parameters in Supplementary Table S1. d, The ponderomotive effect generated by the pulsed laser (green wave packet propagating left-to-right; 12.5 µm beam bounded by solid green lines) imparts an equivalent phase shift of roughly 430 radians to the electron packets traveling into the page (black outline).
Maximizing pulsed-laser lensing by exploiting the ponderomotive effect over long periods of time.
a, Increasing the UV pulse energy (top, 0.25 nJ/pulse → middle, 0.5 nJ/pulse → bottom, 1.0 nJ/pulse) lengthens the photoelectron packet (top, 5.8 ± 1.9 ps → middle, 7.1 ± 1.1 ps → bottom, 13.4 ± 0.9 ps). An approximate twofold increase in electron pulse duration weakens the ponderomotive effect, as evidenced by a steady reduction in the intensity difference (top, −4.1 ± 1.1% → middle, −3.3 ± 0.2% → bottom, −3.0 ± 0.1%). b, A strong ponderomotive effect requires the pulsed laser and the electron packets to have maximum spatial overlap. Shifting the laser beam perpendicular to its axis illustrates how even slight misalignment weakens the interaction. The solid blue line shows the mean signal in the negative-time reference images, while the flanking dashed blue lines denote its error bounds within a standard error to the mean (± S.E.M.). c, Demonstration of stability of pulsed-laser lensing due to the ponderomotive effect. Filled yellow circles (± S.E.M.) denote the mean difference intensity at time zero, while filled blue circles (± S.E.M.) indicate the mean difference intensity at −21 ps.
Simulated properties of an electron beam post-laser interaction at 30 keV (solid) and 300 keV (dashed).
An electron pulse duration of 1 ps and a central unscattered beam diameter of 10 µm was assumed for all simulated values in this figure. Here, the laser parameters are varied to reach a mean phase shift of π/2. a, The required pulse energy in microjoules. The left (right) of the colorbar corresponds to 30 keV (300 keV) electrons and is on a linear scale. b, The r.m.s deviation from the mean phase shift. The colorbar values are displayed in radians but positioned on a log10-scale.
