快速协同模拟研究光学谐振器中孤子模式的缓慢演化

中文摘要 AI 辅助

物理和生物系统中的复杂模式通常通过由少数关键变量控制的缓慢集体动力学而涌现。在非线性光学谐振器中，耗散克尔孤子提供了一个重要例子，其中分离良好的孤子之间的相互作用可以在远长于特征损耗和增益时间尺度的时间尺度上演化。直接数值模拟这些动力学具有挑战性，因为刚性迫使传统方法以非常小的时间步长解析许多快速阻尼的自由度。我们提出了一种数值方案，即协同方法，该方法消除这些快速阻尼的自由度并保留缓慢演化的模式，使得时间步长比传统方法中使用的步长大许多数量级。应用于驱动克尔腔中的孤子分子，该方法实现了$10^3$到$10^5$的加速，同时捕捉实验室时间尺度上的动力学。我们使用它来模拟三孤子分子的完整相互作用动力学和八孤子分子的演化。该方法为研究具有广泛分离时间尺度的非线性系统中的缓慢模式形成提供了一个高效框架。

英文摘要

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

发表机构

• University of Maryland, Baltimore County（马里兰大学巴尔的摩分校）
• Racah Institute of Physics, The Hebrew University（希伯来大学拉卡物理研究所）

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