Fiber lasers are a paradigm of dissipative systems, which distinguish themselves from a Hamilton system where energy is conservative. Consequently, pulses generated in a fiber laser are always accompanied by the continuous wave (CW). Under certain hypothesis, pulses generated in a fiber laser can be considered as a soliton, a product of a Hamilton system. Therefore, all the descriptions of solitons of a fiber laser are approximate. Coexistence of solitons and the CW from a fiber laser prevents unveiling of real nonlinear dynamics in fiber lasers, such as soliton interactions. Pulse behavior in a fiber laser can be represented by the state of single pulse, the state of period doubling of single pulse, the states of two pulses either tightly bound or loosely distributed, the states of three pulses, and various combinations of the above-mentioned states. Recently, soliton distillation was proposed and numerically demonstrated based on the nonlinear Fourier transform (NFT) [J. Lightwave Technol. 39, 2542 (2021) [CrossRef] ]. Solitons can be separated from the coherent CW background. Therefore, it is feasible to isolate solitons from CW background in a fiber laser. Here, we applied the NFT to various pulses generated in a fiber laser, including single pulse, single pulse in period doubling, different double pulses, and multiple pulses. Furthermore, with the approach of soliton distillation, the corresponding pure solitons of those pulses are reconstructed. Simulation results suggest that the NFT can be used to identify soliton dynamics excluding CW influence in a fiber laser, which paves a new way for uncovering real soliton interaction in nonlinear systems.

中文翻译：

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非线性傅里叶变换启用光纤激光辐射的特征值谱研究

光纤激光器是耗散系统的一种范例，它与能量保守的哈密顿系统不同。因此，光纤激光器中产生的脉冲总是伴随着连续波 (CW)。在某些假设下，光纤激光器中产生的脉冲可以被认为是孤子，是哈密顿系统的产物。因此，对光纤激光器孤子的所有描述都是近似的。孤子和来自光纤激光器的 CW 的共存阻止了光纤激光器中真实非线性动力学的揭示，例如孤子相互作用。光纤激光器中的脉冲行为可以用单脉冲状态、单脉冲倍周期状态、两个脉冲紧密结合或松散分布的状态、三个脉冲的状态、以及上述状态的各种组合。最近，基于非线性傅立叶变换 (NFT) [J. 光波技术。39 , 2542 (2021) [CrossRef] ]。孤子可以从相干的 CW 背景中分离出来。因此，在光纤激光器中将孤子与连续波背景隔离是可行的。在这里，我们将 NFT 应用于光纤激光器中产生的各种脉冲，包括单脉冲、倍周期单脉冲、不同的双脉冲和多脉冲。此外，通过孤子蒸馏的方法，这些脉冲的相应纯孤子被重建。仿真结果表明，NFT 可用于识别光纤激光器中排除 CW 影响的孤子动力学，这为揭示非线性系统中的真实孤子相互作用开辟了新途径。