On-demand tailoring soliton patterns through intracavity spectral phase programming.

Multi-pulse oscillations are prevalent phenomena observed in mode-locked lasers and nonlinear microresonators, where the short- and long-range interactions between nonlinear wavepackets give rise to diverse pulse patterns such as soliton molecules, soliton crystals, and soliton bursts. However, these intricate nonlinear interactions are highly sensitive to the parameters of dissipative systems, leaving the properties of multiple pulses far from being controlled, which hampers their applications such as high-speed optical communication and material processing. In this study, we propose a universal approach for quantitatively tailoring multiple solitons in mode-locked fibre lasers through spectral phase programming, enabling the on-demand generation of soliton patterns with separations that follow from constant, geometric, or arithmetic sequences. By combining with spectral filtering, we demonstrate dual-colour soliton patterns in the same cavity, further highlighting the adaptability of soliton structures. Numerical simulations validate the experimental observations, demonstrating that the spectral phase modulates solitons to emit sub-pulses, which interact with other solitons to generate trapping potentials, thereby giving rise to diverse soliton patterns.