Nanoscale Femtosecond Coherent Radiation and Spatiotemporally Shaped Free Electron Wave Function

We study tunable, nanoscale, femtosecond coherent radiation based on a coupled nanowire pair structure, which is transversely excited by a strong, linearly polarized laser pulse. The structure can function as a nanoscale undulator: the electrons moving through the nanogap are driven by a spatially periodic, transverse optical near field. We show that the near field can actively shape the electron wave function by inducing both a periodic oscillation and a quantum squeezing of its width. We then validate this theoretical framework by numerically solving the relativistically corrected time-dependent Schrödinger equation. The generated femtosecond pulse trains can be spectrally, temporally, and spatially controlled. This framework establishes the transverse optical near-field interaction as a novel mechanism for spatiotemporally shaping electron wave functions, thereby illuminating a path to a versatile platform for an on-chip femtosecond coherent light source and applications in free-electron quantum optics.