Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators
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Date
2019-09-30
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Citation of Original Publication
Zhen Qi, et.al, Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators, Optica Vol. 6, Issue 9, pp. 1220-1232 (2019) ; DOI: 10.1364/OPTICA.6.001220
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©2019 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.
Access to this item will begin on 2020-09-30
©2019 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.
Access to this item will begin on 2020-09-30
Abstract
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.