Mode-locked lasers exhibit a rich diversity of nonlinear dynamics, often featuring the nontrivial coexistence of linear dispersive waves and coherent structures, especially in transient evolution involving multiple soliton pulses. The coexistence of solitons and an embedded dispersive wave background sets a challenge for characterizing and analyzing these transient dynamics. Here, we demonstrate the real-time full-field characterization of transient soliton dynamics in a mode-locked fiber laser using nonlinear Fourier transform (NFT) and high-bandwidth coherent homodyne detection, revealing new insights into the physics of optical soliton interactions within complex nonlinear systems. Such characterization includes the formation of multiple solitons amid wide relaxation oscillations, the switching of multiple solitons, and controlled soliton drifting with associated digital encoding. NFT proves its efficiency in separating and analyzing coherent structures among the dispersive wave radiation in fiber lasers. By implementation of the inverse NFT, the corresponding pure soliton distribution can be reconstructed. These findings shed new light on ultrafast transient dynamics in optics.

中文翻译：

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通过非线性傅里叶变换揭示光孤子辐射和编码


锁模激光器表现出丰富的非线性动力学多样性，通常具有线性色散波和相干结构的非平凡共存，尤其是在涉及多个孤子脉冲的瞬态演化中。孤子和嵌入式色散波背景的共存为表征和分析这些瞬态动力学带来了挑战。在这里，我们演示了使用非线性傅里叶变换 （NFT） 和高带宽相干零差检测在锁模光纤激光器中对瞬态孤子动力学进行实时全场表征，揭示了对复杂非线性系统中光孤子相互作用物理学的新见解。这种表征包括在宽弛豫振荡中形成多个孤子、多个孤子的切换以及具有相关数字编码的受控孤子漂移。NFT 证明了它在分离和分析光纤激光器中色散波辐射中的相干结构方面的效率。通过实现逆 NFT，可以重建相应的纯孤子分布。这些发现为光学中的超快瞬态动力学提供了新的思路。