Fig. 1

Design Principle for the broadband light source. a Formation of focused broadband transition radiation in interaction of an electron beam with an engineered planar lens. The structure is designed to effectively mimic a porous hemispherical geometry. b Schematic of the design principles that includes projection of incorporated holes in the hemispherical lens to a planar gold film. c Interaction of a 30 keV electron (incident from the top) with a mesoscopic hemispherical porous film positioned on a silica substrate. The electron passes through one of the holes at the center. Depicted in the figure is a snapshot of the simulated z-component of the electric field 22.55 fs after impact on the lens surface which indicates a clear focus. Color bar is in the dimensions of Vm⁻¹and scale bar is 1 μm. d CL spectra of the hemispherical structure computed at a plane positioned 5 micrometer below the structure. Inset: Temporal representation of the z-component of the electric field at the focal point in c. Time-averaged electron-induced electromagnetic wave packet at the energies e E = 0.6 eV and f E = 1.3 eV. Depicted is the magnitude of the Fourier transform of the z-component of the electric field in the xy and yz planes. Color bar is in arbitrary units and scale bars are 1 μm