Frequency comb shaping through staggered phase flux in fast gain lasers

Optical frequency-comb devices are essential in telecommunications, sensing, and metrology. Yet, precise in-situ control of their spectral envelope remains challenging. We demonstrate a spectral shaping technique leveraging path-dependent phase engineering in the synthetic lattice of cavity modes in a ring-shaped laser with ultrafast gain recovery. By modulating the laser at its repetition rate and twice this frequency, we create a 1D triangular ladder with a staggered phase flux, which breaks time-reversal symmetry. This enables continuous tuning of a strong central lobe across the full bandwidth of our Quantum Cascade Laser frequency comb at 1340cm$^{-1}$. Our method offers unprecedented spectral control at the light generation stage in any fast gain active device, opening new opportunities in waveform engineering for ranging, data transmission, and sensing.