Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators
Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators
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DOI：
10.1364/optica.6.001220
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发表时间：
2019-09-20
期刊：
影响因子：
10.4
通讯作者：
Menyuk, Curtis R.
中科院分区：
文献类型：
--
作者：
Qi, Zhen;Wang, Shaokang;Menyuk, Curtis R.
单孤子是更一般的波形的特殊极限，通常被称为椭圆余弦波或图灵辊。我们从理论和计算上研究了微谐振器中椭圆余弦波的稳定性和可达性。我们表明，他们是强大的，在对比单孤子，可以很容易地和确定性地访问在大多数情况下。它们的带宽可以与单孤子相媲美，在这种限制下，它们实际上是周期性的孤子串，并且对应于具有增加的功率的频率梳。我们全面探讨了三维参数空间，包括失谐，泵振幅，和模式周长，以确定稳定的解决方案存在。为了完成这项任务，我们使用了一套独特的计算工具，基于动力系统理论，使我们能够快速，准确地确定每个椭圆余弦波周期的稳定区域，并找到不稳定的机制和它们的时间尺度。最后，我们专注于孤子的限制，我们表明，单孤子的稳定区域几乎完全重叠的稳定区域的连续波和几个更高的周期性椭圆余弦波，有效地多个孤子列车。这个结果部分解释了为什么很难确定性地访问单个孤子。(C)根据OSA开放获取出版协议的条款，2019年美国光学学会
Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement