Femtosecond Geometric Hermite-Gaussian Mode Generation from a Half-degenerate Laser Oscillator

Ultrafast structured light, featuring multidimensional spatial degrees of freedom (DoFs) and femtosecond-scale temporal characteristics, has garnered significant research interest. Frequency degeneracy provides a powerful intracavity mechanism to manipulate laser modes by simultaneously supporting multiple eigen frequencies, yet its application to femtosecond structured light generation remains insufficiently investigated. In this work, we demonstrate a half-frequency-degenerate cavity that directly generates femtosecond geometric Hermite-Gaussian (HG) modes. By introducing two-dimensional off-axis pumping, the oscillating laser modes can be tuned from single HG to geometric modes, accessing both geometric Gaussian and first-order HG beams. Leveraging the broad emission spectrum of Yb:KGW and SESAM-assisted Kerr-lens mode-locking (KLM), we demonstrated, for the first time, intracavity femtosecond geometric HG mode generation, delivering a pulse duration of 331 fs. An astigmatic mode converter (AMC) transforms the generated geometric HG modes into vortex pulses with multiple vortex cores. Our approach establishes a versatile platform for femtosecond structured light sources, whose high-peak-power and spatiotemporally structured characteristics are relevant to future explorations in high-capacity optical communications, microparticle manipulation, and strong-field physics.