Optical amplification and transmission of attenuated multi-soliton based on spectral characteristics of Akhmediev breather

单模光纤中双分量Akhmediev呼吸子重现与光谱不对称性的实验观测

Experimental observation of recurrence and spectral asymmetry of the two-component Akhmediev breathers in a single mode optical fibre

本文通过实验、理论与数值模拟研究了单模光纤中双分量Akhmediev呼吸子的重现光谱动力学，揭示了基本呼吸子的光谱不对称性及二阶非简并呼吸子的复杂演化。

Manakov方程的高阶调制不稳定性与多Akhmediev呼吸子：跨越不稳定带之间稳定间隙的频率跳变

Higher-order modulation instability and multi-Akhmediev breathers of Manakov equations: Frequency jumps over the stable gaps between the instability bands

本文研究了Manakov方程的高阶调制不稳定性，发现初始边带对的选择会改变不稳定频率结构并引发离散谱内的频率跳变，通过数值模拟和精确的多Akhmediev呼吸子解验证了这一包含多个生长-衰减周期的复杂动力学。

Akhmediev breather signatures from dispersive propagation of a periodically phase-modulated continuous wave

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{ö}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for…

Growth rate of modulation instability driven by superregular breathers

We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolute difference of group velocities of SR breathers coincides exactly with the linear MI growth rate. This link holds for a series of nonlinear Schrödinger equations with infinite-order terms. For the particular case of SR breathers with opposite group velocities, the growth rate of SR breathers is consistent with that of each quasi-Akhmediev breather…

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be …

The linear and nonlinear instability of the Akhmediev breather

The Akhmediev breather (AB) and its M-soliton generalization $AB_M$ are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the constant unstable background; they describe the appearance of $M$ unstable nonlinear modes and their interaction, and they are expected to play a relevant role in the theory of periodic anomalous (rogue) waves (AWs) in nature. It is rather well established that they are unstable with respect to small perturbations of the NLS equation. Concerning perturbations of these solutions within the NLS dynamics, there is the f…

Surface polaritonic solitons and breathers in a planar plasmonic waveguide structure via electromagnetically induced transparency

We propose a scheme for the coupler-free excitation of surface polaritonic solitons and breathers in a planar plasmonic waveguide structure comprising of a transparent layer, a metal layer and a layer of three-level lambda-type atomic medium. In the proposed system, an enhanced Kerr nonlinearity is achieved via electromagnetically induced transparency (EIT) in the bottom atomic medium, which can be controlled through proper modulation of the frequency detunings and Rabi frequencies of the driving laser fields. This nonlinearity balances the dispersion in the system, thus providing the necessar…

Femtosecond Optical Superregular Breathers

Superregular (SR) breathers are nonlinear wave structures formed by a unique nonlinear superposition of pairs of quasi-Akhmediev breathers. They describe a complete scenario of modulation instability that develops from localized small perturbations as well as an unusual quasiannihilation of breather collision. Here, we demonstrate that femtosecond optical SR breathers in optical fibers exhibit intriguing half-transition and full-suppression states, which are absent in the picosecond regime governed by the standard nonlinear Schrödinger equation. In particular, the full-suppression mode, which …

Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band

Solitons on a finite a background, also called breathers, are solutions of the focusing nonlinear Schrödinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes Akhmediev breathers (AB), Kuznetsov-Ma (KM), and Peregrine solitons (PS), which have been successfully exploited to describe several physical effects. These families of solutions are actually only particular cases of a more general three-parameter class of solutions originally derived by Akhmediev, Eleonskii and Kulagin [Theor. Math. Phys. {\bf 72}, 809--818 (1…

Freezing Optical Rogue Waves by Zeno Dynamics

We investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation do…

Multi-soliton, multi-breather and higher-order rogue wave solutions to the complex short pulse equation

In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the $N$-bright soliton solution in a compact determinant form, then the $N$-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first- and second-order rogue wave solutions are given explicitly and illustrated by graphs. The asymptotic analysis is performed rigorously for both the $N$-soliton and the $N$-breather …

香农熵有助于优化频分复用极限学习机的性能

Shannon Entropy Helps Optimize the Performance of a Frequency-Multiplexed Extreme Learning Machine

本文引入光功率、相位和光谱的香农熵，优化了频分复用极限学习机（ELM）的系统参数，使其性能达到顶尖机器学习模型水平，并揭示了不同频率梳编码下的孤子结构与数据处理机制。