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We present a two-dimensional frequency comb, with distinct fixed repetition-rates in both the azimuthal mode dimension and an orthogonal dimension parametrized by the angular phase-velocity. We experimental demonstrate it using a single integrated microring bichromatically pumped.

 

We demonstrate Kerr-mediated all-optical synchronization of a dissipative Kerr solition with an external master laser in a single microring resonator. It enables passive frequency division for optical clock metrology applications. 

We demonstrate Kerr-mediated all-optical synchronization of a dissipative Kerr solition with an external reference laser in a single microring resonator. It enables passive stability transfer and frequency division for optical clock metrology applications.

 

Frequency combs have revolutionized the measurement of time and frequency since their invention in 2000, and have a wide array of applications to applications that range from basic science applications, to a wide array of sensing applications, to commercial applications, to military applications, and the list goes on. Noise poses a fundamental limit to these systems, and calculating its impact play a critical role in system design. Frequency combs are created by modelocked laser systems that emit a periodic train of short pulses. Laser systems are complex nonlinear systems and the usual method for determining the impact of noise is to carry out computationally-expensive Monte Carlo methods. That limits the parameter range over which it is possible to study the noise impact. We have developed a new approach based on dynamical systems methods. In our approach, we determine a stationary state of the laser system as parameters vary solving a root-finding problem [Wang1]. Starting from a stationary state, we determine all the eigenvalues and eigenvalues of the linearized system. The variance of the amplitudes of the eigenvalues obey either random walk of Langevin equations [Menyuk]. Starting from that point, we can determine the power spectral density of the key laser parameters (amplitude jitter, timing jitter, frequency jitter, phase jitter) [Wang2]. We applied this approach to SESAM lasers and found that we were able to reproduce a computation that took 20 minutes on a cluster with 256 cores with a computation that took less than 4 minutes on a desktop computer. 

A significant challenge in the modeling of short pulse fiber lasers is that with each successive generation there has been a dramatic increase in the amount by which the pulse varies over each round trip. Therefore, lumped rather than averaged models are required to accurately compute the periodically stationary (breather) solutions generated by these lasers. We use a spectral method to assess the linear stability of periodically stationary pulses in lumped models. This approach extends previous work by Menyuk and Wang on stationary pulses in averaged models. We first present a gradient based optimization method inspired by the work of Ambrose and Wilkening to compute periodically stationary pulses. Then, we use Floquet theory to characterize the linear stability of the pulses obtained using optimization in terms of the spectrum of the monodromy operator,M, obtained by linearization of the round trip operator about a periodically stationary pulse. 

Frequency combs, invented in 2000, have revolutionized frequency measurement and there- by impacted a host of applications. These include applications to military systems, medi- cine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to  ber lasers to mi- croresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these ap- proaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on  ber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 

Frequency combs, invented in 2000, have revolutionized frequency measurement and thereby impacted a host of applications. These include applications to military systems, medicine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to fiber lasers to microresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these approaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on fiber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 

We demonstrate numerically the deterministic generation of a dissipative Kerr soliton in coupled Si3N4 microrings resonators using electrically-controlled mode interactions. We use a constant pump power and linearly sweep frequency.