Transverse Electron-Beam Shaping with Light

Interfacing electrons and light enables ultrafast electron microscopy and quantum control of electrons, as well as new optical elements for high-sensitivity imaging. Here, we demonstrate for the first time programmable transverse electron-beam shaping in free space based on ponderomotive potentials from short intense laser pulses. We can realize both convex and concave electron lenses with a focal length of a few millimeters, comparable to those in state-of-the-art electron microscopes. We further show that we can realize almost arbitrary deflection patterns by shaping the ponderomotive potentials using a spatial light modulator. Our modulator is lossless and programmable, has unity fill factor, and could pave the way to electron wave-front shaping with hundreds of individually addressable pixels.

Popular Summary

Adaptive optics has led to breakthroughs in astronomy and deep-tissue imaging. Imaging techniques using deformable mirrors or spatial light modulators enable crisp images even if the light must pass through a turbulent atmosphere or millimeter-thick tissue. In electron optics, techniques of arbitrary beam shaping are just beginning to emerge. We demonstrate programmable shaping of free-electron beams based on the ponderomotive interaction between electrons and light.

An electron beam passing through a high-intensity light field will experience a phase shift proportional to the local light intensity. Taking a step toward applications in electron microscopy, we now shape the light-intensity distribution with a spatial light modulator. The light then interacts with a synchronized pulsed-electron beam, which enables us to imprint almost arbitrary ponderomotive phase distributions. We realize convex and concave electron lenses made from light and imprint more complex patterns, like a smiley. In contrast to other electron-shaping techniques, our scheme avoids losses, inelastic scattering, and instabilities due to the degradation of material-diffraction elements.

Our experiments pave the way to wave-front shaping in pulsed-electron microscopes with thousands of programmable pixels. This enables aberration correction and adaptive imaging. In the future, parts of an electron microscope might be made from light which could be adjusted to the specimens being studied, maximizing sensitivity while minimizing beam-induced damage.

Figure 1

Experimental setup: programmable ponderomotive deflection of electrons in free space. Outside of the vacuum chamber, the SLM-shaped laser distribution is formed in the conjugate plane ($CP$). In the specimen chamber, the electron beam interacts with a counterpropagating laser pulse in the interaction plane (IP). The induced electron phase modulations are proportional to the local laser pulse energy. Left: the modified SEM chamber door which allows for in- and outcoupling the shaped light fields (see also Appendix pp2).

Figure 2

Ponderomotive electron-light interaction: (a) An SEM objective lens (OL) focuses the electron pulse to a crossover slightly below the interaction plane. The objective aperture (OA) is set to $100\mu \mathrm{m}$. (b) Top: light intensity distribution (scale bar $93\mu \mathrm{m}$) before being demagnified ($5\times$) to the interaction plane. Bottom: observed electron intensity distribution (scale bar 1 mm) at the detector plane. (c) Wave optics (top) and ray optics (bottom) simulations of the detected electron beam shown in (b). (d) Detected electron distributions (scale bar 1.6 mm) when delaying the laser pulse with respect to the electron pulse by multiples of $\tau =666\mathrm{fs}$. The delay causes the interaction to take place in a plane where the light is not focused.

Figure 3

Lensing using ponderomotive potentials. (a) Detected electron distribution with concave (left, LG00), no (center), and convex (right, LG10) ponderomotive lens (scale bar 1 mm). (b) Focal length as a function of the laser pulse energy for LG00 (green and violet) and LG10 (orange) modes. The inset shows the respective light intensity distributions, measured in a plane conjugate to the interaction plane.

Figure 4

Programmable electron-beam shaping: detected electron distribution after interaction with shaped light fields. For (a)–(c), the SLM is used to add vertical trefoil, coma, or astigmatism (scale bar 1.1 mm) to the incoming light field. In (d), a Gerchberg-Saxton algorithm is used to shape the light field into a distribution resembling a smiley, which also appears in the detected electron distribution (scale bar 1.2 mm).

Figure 5

Measured target intensities with the CMOS (scale bar $33\mu \mathrm{m}$) in the conjugate plane before being demagnified ($5\times$) to the IP. (a) Concave and convex lens. (b) Programmable intensity modulation. (c) Smiley.

Figure 6

(a) Optical setup used to generate the desired laser intensity distribution. In order for the electrons to pass through the optical system, a 1.5-mm hole is drilled in the mirrors before and after the interaction plane. To minimize the laser intensity losses at the hole and, hence, to facilitate diffraction around it, a beam block is implemented in the algorithm. (b) The schematic of the adapted iterative GSA. For propagating the electric field from one plane to another, the Fresnel transfer function is used. This allows for introducing additional elements, like beam block, in the iterative algorithm.

Figure 7

(a) 3D drawing of the experimental setup, side view. (b) Series of simulated ponderomotive potentials (scale bar $45\mu \mathrm{m}$) in the conjugate plane after temporally displacing the laser pulse by multiples of $\tau$. The same linear scale is used for all images.

Figure 8

Normalized radial intensity distribution obtained from 31 single-electron detection events. The data points (10974) are smoothed out using a Savitzky-Golay filter with a window size of 601 and a polynomial order of 3. The fitted Voigt profile represents a convolution of a Gaussian profile with a FWHM of $20.4\mu \mathrm{m}$ and a Lorentzian profile with a FWHM of $95.2\mu \mathrm{m}$.

Figure 9

(a) Spatial intensity distribution of the LG10 beam measured in the conjugate plane. (b) Residuals of a fit to the distribution. The fit function is a sum of a dominant LG10 mode and a minor LG00 mode. (c) Cross cut showing the fit (orange) and its LG10 (turquoise) and LG00 (blue) components, as well as the quadratic Taylor expansion around $\rho =0$ (violet). (d) Diameter of the electron beam at the detector as a function of the laser pulse energy, along with the theory and an error region due to our error in determining the waist of the dominant LG10 component.

Figure 10

(a) Spatial intensity distribution of the LG00 beam measured in the conjugate plane. (b) Residuals of a LG00 fit to the distribution. (c) Cross cut showing the fit (orange) and its quadratic Taylor expansion around $\rho =0$ (violet). (d) Diameter of the electron beam at the detector as a function of the laser pulse energy, along with the theory and an error region due to our error in determining the waist of the LG00 mode.