Spectral shaping of fast-gain frequency combs through phases in synthetic dimensions

Optical frequency comb devices have unlocked new capabilities in telecommunications, sensing, and metrology. Yet, precise in situ control of the comb spectral envelope remains extremely challenging. By introducing mode coupling with non-trivial phases, we demonstrate a spectral shaping technique that enables continuous tuning of a dominant spectral lobe across the full bandwidth of a semiconductor laser frequency comb. We achieve this jointly leveraging the engineered geometry of the synthetic lattice formed by the cavity modes of the laser and the coherent dynamics enabled by its fast-gain recovery. We use dual-tone modulation of the cavity at its repetition rate and twice this frequency with a controlled relative phase to couple the comb modes into a triangular lattice. The relative phase between the two tones defines a lattice phase that breaks time-reversal symmetry and steers the lattice dynamics through the fast gain. With this approach, we experimentally control the spectral envelope of the comb such that a targeted region contains more than twice the intensity expected from a uniform distribution, demonstrating tunable spectral selectivity. This capability, achieved directly at the light generation stage in a fast-gain device, opens routes for efficient programmable waveform engineering with potential applications in ranging, data transmission, and sensing.