Temporal pulse engineering of spectral evolution in a synthetic frequency lattice

Precise experimental control and characterization of electron wave packet dynamics driven by external optical fields remain a fundamental challenge, particularly at ultrafast temporal and submicroscopic spatial scales. To overcome these challenges, we introduce a photon-based simulation platform employing a traveling-wave electro-optic phase-modulated waveguide. In our setup, the incident electromagnetic pulse serves as an analog to the electron wave packet, while the traveling-wave modulation simulates the external optical driving field. Our experimental study systematically explores pulse evolution under three distinct regimes defined by the relation between the pulse duration (Δt) and the modulation period (T). When the pulse duration is significantly shorter than the modulation period, we observe a uniform spectral shift analogous to electron acceleration in Dielectric Laser Accelerators (DLA), where spectral phase gradients represent electron momentum accumulation. Conversely, when the pulse duration greatly exceeds the modulation period, discrete diffraction patterns emerge, closely resembling the discrete sideband features of electron-photon coupling observed in Photon-Induced Near-Field Electron Microscopy (PINEM). Notably, in the intermediate regime (T/4 < Δt < T/2), the pulse spectrum exhibits Airy-function-type characteristics with self-healing effects. These experimental results provide critical insights into electron-wave interactions under external optical fields and establish a robust, programmable framework for further investigation.