Data-driven Design of Spatiotemporal Mode-locked Cavities for Variable-mode Femtosecond Emission and Performance Limits

Spatiotemporal mode locking (STML) enables femtosecond emission that exploits coupled spatial and temporal dynamics, but achieving targeted transverse modes with predictable limits remains difficult due to high-dimensional, nonlinear cavity parameter spaces. We present a data-driven framework that combines a fast digital twin of the cavity with experiment-in-the-loop learning to synthesize and switch among variable transverse modes while quantifying performance limits. A reduced-order propagation model provides millisecond evaluations for control, while Bayesian optimization and reinforcement learning map actuator settings to modal content, pulse energy, and jitter. Closed-loop experiments on a reconfigurable cavity validate inverse designs for TEM00{00}TEM10{10}multimode operation, revealing trade-offs among dispersion, Kerr nonlinearity, saturable absorption, and spatial filtering. We measure timing jitter, relative intensity noise, and spectral-temporal quality to bound achievable performance across modes and identify mode-dependent ceilings governed by gain bandwidth and B-integral. Results establish a general route to agile, specification-driven STML sources and provide actionable guidance on performance limits for variable-mode femtosecond lasers.