In the Smith Purcell effect [1], an electron of velocity beta=v/c passes near a subwavelength periodic grating and emits radiation to the far field with a characteristic dispersion relation dependent on the elevation angle and the diffraction order.

Recent interest in spectral and spatial control over SP sources gave rise to radiation with shaped spectra [2], while recent theoretical works investigated the ability to control the spatial pattern and polarization by using 1D [2-4] and 2D [5] metasurfaces with subwavelength features that alter the near-field and thereby the far-field radiation. One such example, only described theoretically thus far, is that of spatial focusing of Smith-Purcell radiation with a metasurface lens[2,3] of varying periodicity along the electron trajectory. As high numerical-aperture lensing is predicted for these structures, they may serve, for example, as convenient couplers for spontaneously emitted light into optical fibers. These ideas, when proven for visible light, could be of tremendous importance for novel free-electron THz and X-Ray sources [6], for which it is challenging to fabricate efficient lenses.

In this work, we experimentally demonstrate for the first time a free-electron metasurface lens and characterize its far-field spectral and spatial emission pattern. For this purpose, we fabricated a 20um long, gold-on-glass metasurface of subwavelength periodicity varying between 163nm and 228nm according to [2], with an expected focal length of 17.32um at a central wavelength of 580nm. In our experiment, we used an electron beam with kinetic energy of 30 KeV in a scanning electron microscope and collected the emitted radiation with an angle resolved cathodoluminescence detection system. We measured the far-field spatio-spectral response of the metasurface in hyperspectral mode[7] which allows measuring the spectrum and emission angles of the source in a single shot. To compare our results with theory, we conducted a hybrid physical simulation using FDTD to calculate the emitted radiation and ray-tracing to model the collection system. A reasonable agreement between theory and experiment is achieved, where both the theoretical and the experimental hyper-spectra span a similar, broadband region and display oscillatory behavior. Finally, we measured a drastic change in the angular range per emitted wavelength between an ordinary SP grating with a 190nm period and our metasurface lens, implying a high numerical aperture for the lens. Our future plan is to further investigate the focusing properties of these lenses by scanning over the collection optics position.