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.