Nanoscale Femtosecond Coherent Radiation and Spatiotemporally Shaped free electron Wavefunction

We study tunable nanoscale femtosecond coherent radiation based on a coupled nanowire pair (CNP) structure that is excited by a strong laser. The structure functions as a nanoscale undulator (NU): the electrons moving through the nanogap are driven by a spatially periodic, transverse optical near-field. We show that the transverse near-field can actively shape the electron wavefunction 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 Schr\"odinger equation (RC-TDSE). 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 to spatiotemporally shape electron wavefunctions, which illuminates a path to versatile platform for on-chip femtosecond coherent light source and the application in free-electron quantum optics.