NSF-BSF: Synthesis and Analysis of Novel Microresonator Combs

频率梳源是一种频率标尺，它能以惊人的精度测量频率——相当于测量地球和太阳之间距离的位移，其位移是原子宽度的100倍。频率梳用于基础物理实验、化学、环境和医学传感、时间和频率传输以及雷达系统。第一个频率梳是由庞大的激光系统制成的，而在过去的十年中，微谐振器（毫米大小的光学设备）可以产生频率梳的发现引起了科学兴趣的大量涌现。然而，几乎所有的频率梳都使用被称为孤子的短光脉冲。微谐振器中的孤子很难获得，浪费了产生它们的光泵功率，并且热不稳定。我们将研究有可能解决这些问题的新型波形。在我们的理论研究中，我们将使用我们开发的一套独特的计算工具，据我们所知，目前还没有其他研究小组使用过。这些工具可以快速确定如何获得这些波形，并确定它们在噪声和热效应存在下的稳健性。这使我们能够摆脱“反复尝试”的实验工作，这种实验工作迄今为止主要局限于单个孤子的研究。计算工具将通过网络普遍提供。我们期望它们将在其他系统中发挥作用，包括经济和生物系统，以及其他光学系统。为了开展这项理论工作并对这些想法进行实验测试，我们组建了一个团队，其中包括马里兰大学巴尔的摩分校（UMBC）、耶路撒冷希伯来大学、普渡大学和法国国家科学研究中心的科学家。UMBC是一个以多元化和教育创新而闻名的少数民族服务机构，我们希望本科生和研究生都能参与这项研究。我们所有的学生都将受益于强大的理论和实验合作，并有机会与来自不同国家的学生和教师互动。本研究的主要技术目标是研究在微谐振器中产生频率梳的波形的潜力，而不是单个孤子。我们将集中讨论余弦波和孤子分子。初步工作表明，余弦波具有较大的稳定区域，可以通过提高泵浦功率简单地获得，具有鲁棒性，并且可以具有较大的带宽。在正常色散状态下可以得到余弦波和暗孤子分子，而不是单（亮）孤子，这增加了可以获得频率梳的材料系统的数量。为了实现这一目标，我们将使用一套基于动力系统理论和统计力学的计算工具，我们已经开发并将继续开发这些工具。这些工具将使我们能够确定在存在噪声的情况下，系统参数空间中替代波形的可访问性，稳定性和鲁棒性。这项研究的第二个目标是证明这些理论工具的实用性，并使它们广泛地提供给研究界。在确定了参数空间中存在稳定波形的位置后，我们将与CNRS和普渡大学的实验合作者合作，利用他们现有的实验基础设施，分别基于晶体谐振器和氮化硅谐振器，测试和完善理论预测。我们期待一个迭代的过程，在这个过程中，理论工作导致新的实验，实验指导理论工作的方向。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Frequency comb sources are frequency rulers that make it possible to measure frequencies with phenomenal accuracy - equivalent to measuring a shift in the distance between the Earth and the Sun of 100 times the width of an atom. Frequency combs are used in basic physics experiments, for chemical, environmental, and medical sensing, for time and frequency transfer, and in radar systems. The first frequency combs were made from bulky laser systems, and the discovery in the past decade that microresonators (mm-size optical devices) can produce frequency combs has led to an outpouring of scientific interest. However, almost all frequency combs use short optical pulses called solitons. Solitons in microresonators are hard to obtain, waste much of the optical pump power that is used to generate them, and are thermally unstable. We will study novel waveforms that have the potential to solve these problems. In our theoretical studies, we will use a unique set of computational tools that we developed and that to our knowledge no other research group has at present. These tools make it possible to rapidly determine how these waveforms can be obtained and to determine their robustness in the presence of noise and thermal effects. That allows us to move away from the "cut-and-try" experimental work that has mostly limited studies to date to single solitons. The computational tools will be made generally available via the Web. We expect that they will be useful in other systems, including economic and biological systems, as well as other optical systems. To carry out this theoretical work and test these ideas experimentally, we have assembled a team that includes scientists at the University of Maryland Baltimore County (UMBC), the Hebrew University in Jerusalem, Purdue University, and the French Centre National de Recherche Scientifique. UMBC is a minority-serving institution with a reputation for diversity and educational innovation, and we anticipate involving undergraduate as well as graduate students in this research. All our students will benefit from the strong theoretical-experimental collaboration and the opportunity to interact with students and faculty from different countries.The principal technical goal of this research is to study the potential of waveforms other than single solitons for creating frequency combs in microresonators. We will focus on cnoidal waves and soliton molecules. Preliminary work indicates that cnoidal waves have a large region of stability, can be simply accessed by raising the pump power, are robust, and can have large bandwidths. Cnoidal waves and dark soliton molecules can be obtained in the normal dispersion regime, in contrast to single (bright) solitons, which increases the number of material systems in which frequency combs can be obtained. To achieve this goal, we will use a set of computational tools, based on dynamical systems theory and statistical mechanics, that we have developed and will continue to develop. These tools will allow us to determine where in the system parameter space the alternative waveforms are accessible, stable, and robust in the presence of noise. A secondary goal of this research is to demonstrate the utility of these theoretical tools and make them widely available to the research community. Having identified where in the parameter space stable waveforms exists, we will work with our experimental collaborators at the CNRS and Purdue to test and refine the theoretical predictions, taking advantage of their existing experimental infrastructure, which is based on crystalline resonators and silicon-nitride resonators, respectively. We anticipate an iterative process in which the theoretical work leads to new experiments, and the experiments guide the direction of the theoretical work.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.