Conforti Matteo, Marini Andrea, Tran Truong X, Faccio Daniele, Biancalana Fabio
Opt Express. 2013 Dec 16;21(25):31239-52. doi: 10.1364/OE.21.031239.
Motivated by recent experimental results, we demonstrate that the ubiquitous pulse propagation equation based on a single generalized nonlinear Schrödinger equation is incomplete and inadequate to explain the formation of the so called negative-frequency resonant radiation emitted by optical solitons. The origin of this deficiency is due to the absence of a peculiar nonlinear coupling between the positive and negative frequency components of the pulse spectrum during propagation, a feature that the slowly-varying envelope approximation is unable to capture. We therefore introduce a conceptually new model, based on the envelope of the analytic signal, that takes into account the full spectral dynamics of all frequency components, is prone to analytical treatment and retains the simulation efficiency of the nonlinear Schrödinger equation. We use our new equation to derive from first principles the phase-matching condition of the negative-frequency resonant radiation observed in previously reported experiments.
受近期实验结果的启发，我们证明基于单个广义非线性薛定谔方程的普遍存在的脉冲传播方程是不完整的，不足以解释光学孤子发射的所谓负频率共振辐射的形成。这种缺陷的根源在于，在传播过程中脉冲频谱的正负频率分量之间不存在特殊的非线性耦合，而这一特性是缓变包络近似无法捕捉到的。因此，我们引入了一个基于解析信号包络的概念上全新的模型，该模型考虑了所有频率分量的完整频谱动力学，易于进行解析处理，并保留了非线性薛定谔方程的模拟效率。我们使用新方程从第一原理推导出先前报道的实验中观察到的负频率共振辐射的相位匹配条件。
