Sugavanam Srikanth, Kopae Morteza Kamalian, Peng Junsong, Prilepsky Jaroslaw E, Turitsyn Sergei K
Aston Institute of Photonic Technologies, Aston University, Aston Triangle, Birmingham, B4 7ET, UK.
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200062, China.
Nat Commun. 2019 Dec 11;10(1):5663. doi: 10.1038/s41467-019-13265-4.
Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.
现代高功率激光器展现出丰富多样的非线性动力学特性，常常呈现出线性色散波与相干结构的非平凡共存现象。虽然经典傅里叶方法能够充分描述扩展的色散波，但对于时间局部化和/或非平稳信号的分析则需要更为细致入微的方法。然而，可用于同时表征局部化场和扩展场的数学方法尚未得到充分发展。在此，我们展示了基于扎哈罗夫 - 沙巴特谱问题的非线性傅里叶变换（NFT）如何能够作为一种信号处理工具，用于表示和分析嵌入色散辐射中的相干结构。我们利用锁模脉冲的全场实时实验测量来计算非线性脉冲光谱。为了对激光状态进行分类，我们提出了特征值概率分布的概念。我们给出了两种场归一化方法，并表明在适当的信号归一化条件下，NFT能够产生激光辐射的有效模型。
