We experimentally study simultaneous generation and focusing of Smith-Purcell radiation by a free-electron-driven metalens, and explore theoretically metasurface lenses showing polarization control. Our work paves the way towards versatile and tunable free-electron metasurface light sources.
Electromagnetic metasurfaces provide coherent phase-control over light down to the subwavelength scale , enabling planar optical components with applications ranging from lensing  to holography . Directly embedding radiation mechanisms into metasurfaces  further adds active control over the intrinsic emission process. A promising route in this direction is the use of free electron radiation mechanisms. Notably, free electrons provide access to spectral ranges in which alternative approaches are usually unavailable or inefficient, such as the terahertz (THz), ultraviolet (UV), and X-ray regimes. Moreover, free electrons allow for spatially-selective excitation of nanophotonic components at unprecedented nanometric resolution, combined with ultra-broadband control over light emission by tuning the electron energy. Shaping, and in particular, focusing free-electron radiation for practical purposes, however poses a great challenge that has been only pursued theoretically thus far [5,7]. In Fig. 1, we depict a roadmap towards implementing focused and polarization-controlled free-electron light emission.
Fig. 1: Roadmap for different implementations of focused free-electron light emission using metalenses. a Illustration and simulation of our experiment: focused Smith-Purcell radiation from a chirped 1D metagrating (varying periodicity). Left panels show numerical FDTD simulations of focused radiation emission for different wavelengths (580nm focuses on-axis; 660nm focuses off-axis). b Our proposal for simultaneously focused and polarization-controlled free-electron light emission from a 2D split-ring resonator (SRR) chirped metasurface. Left panels show numerical FDTD simulations of focused emission, where the position of the electron beam relative to the SRR determines the emitted polarization (in conventional Smith-Purcell radiation, only the longitudinal polarization is allowed). c Vision for using atomically-thin van der Waals heterostructures with chirped layer thicknesses to allow for focused X-ray emission via the processes of coherent bremsstrahlung and parametric X-ray radiation , following the recent demonstration of X-ray emission from such periodic structures .
In this work, we provide the first experimental evidence of focused emission Smith-Purcell (SP) radiation in the visible and near-infrared spectral range by using chirped metagratings, namely SP metalenses. We fabricated both converging and diverging SP metalenses driven by free electrons at 30keV incident energy  in a scanning electron microscope (SEM). Our structures emit radial wavefronts that form a well-defined on-axis focal spot at a design wavelength of nm, while focusing off-axis for any other wavelength (see Fig. 1a). To experimentally study the desired lensing effects, we employ hyperspectral angle-resolved light detection, allowing us to recover the far-field radiation patterns of our metalenses as a function of optical wavelength and emission angle, as depicted in Fig. 2.
The results of our measurements, for both types of metalenses, are depicted in the left panels of Fig. 3, along with hybrid finite difference time domain (FDTD) and ray tracing simulations (middle panels). We find very good agreement between the measured and simulated data, as also evident from the cross-section of the hyperspectral data shown in the right panels of Fig. 3. In addition, the measured numerical apertures of the lenses for the nominal emission wavelength closely approach their design value of (angle cutoff denoted by white arrow in Fig. 3). Finally, the far-field signature of the opposite wavefront curvature emitted by the converging and diverging metalenses is discerned through two effects: first, the power distribution over wavelength, which has an opposite trend due to electron beam alignment and divergence; second, a defocusing aberration due to the imaging screen position that gives rise to opposing spectral slopes in the lower angular cutoff of the emission patterns (white dashed lines in Fig. 3).
Fig. 2: Experimental setup for far-field hyperspectral angle-resolved measurements. The experimental setup allows for simultaneous characterization of the far-field spectrum and angular emission profiles of a sample upon electron beam excitation. The metagrating structures are aligned parallel to the optical axis of a parabolic mirror, The electron beam is set to graze the grating structures at a few nm distance. Light emitted parallel to the sample plane (rays depicted as solid lines) is collected and collimated by the off-axis paraboloid (rays depicted as dashed lines), and imaged onto a diffraction grating, scattering it onto a CCD sensor, where the horizontal and vertical position in the CCD plane translate into a respective wavelength and emission angle.
In summary, we experimentally demonstrated metasurfaces that simultaneously generate and shape free-electron radiation, and characterized their far-field spectra. Our results pave the way towards source-embedded metasurfaces driven by free electrons with unprecedented spatial, spectral and polarization tunability (as seen by our simulations in Fig. 1b), operating in sought-after wavelength regimes where diffractive elements are scarce or inefficient, such as the extreme ultraviolet or X-ray ranges.
Fig. 3: Hyperspectral measurements and hybrid FDTD-ray tracing simulation results for both metalens types. a Experimental (left) and simulated (middle) hyperspectral images of the converging Smith-Purcell metalens. For the converging lens, power is distributed more towards the longer wavelengths, due to a slight angle between the sample and the electron beam and due to its divergence. Collection aberrations create a negative slope at the edge of the spectrum (white dashed line). Right: characteristic oscillations in the spectrum at a given observation angle (angles chosen to show best fit): simulation (blue line) vs. measurement (red line), for the converging lens at (angle cross-section marked as a red dotted line). b Experimental (left) and simulated (middle) hyperspectral image of the diverging Smith-Purcell metalens. In this case, power is distributed more towards the shorter wavelengths, and the slope of the spectrum (white dashed line) is positive. Right: cross-section for .
1. Bomzon et al Opt. Lett. 27, 1141 (2002)
2. Khorasaninejad, M. et al Science 352, 1190–4 (2016)
3. Zheng et al, Nat. Nanotechnol. 10, 308–312 (2015)
4. Li et al Nature Reviews Materials vol. 2 1–14 (2017).
5. Remez et al, Phys. Rev. A 96, 061801 (2017).
6. Su et al, ACS Photonics 6, 1947–1954 (2019)
7. Lai et al, Sci. Rep. 7, 11096 (2017)
8. Xi et al, CLEO2021 A.5 JTu3A.5 (2021)
9. Shentcis et al, Nat. Photonics 14, 686–692 (2020)