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1. Dynamical Methods for Studying Stability and Noise in Frequency Comb Sources

   Curtis R. Menyuk, Brandon Wilson (May 2021, SIAM Conference on Applied Dynamical Systems)

   null (Ed.)

   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. 

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2. Dynamical Methods for Studying Stability and Noise in Frequency Comb Sources

   C.R. Menyuk, L. Courtright (November 2021, Progress in Electromagnetics Research Symposium 2021)

   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. 

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3. Stability and Noise in Frequency Combs: Harnessing the Music of the Spheres

   Menyuk, Curtis R. (January 2019, Colloquium talk: Boston University, Columbia University, Cornell University, University of West Virginia)

   Frequency combs have revolutionized the measurement of time and frequency and impacted a wide range of applications spanning basic physics, astrophysics, medicine, and defense. The key theoretical issues in understanding and designing frequency combs are finding regions in the adjustable parameter space where combs operate stably, determining their noise performance, and optimizing them for high power, low noise, and/or large bandwidth. Here, we present a unique set of computational tools that we have developed that allow us to efficiently address these issues. These tools combine 400-year-old dynamical systems theory with modern computational methods, and they are 3–5 orders of magnitude faster than standard evolutionary methods and provide important physical insight. We have applied these tools to frequency combs from passively modelocked lasers with fast and with slow saturable absorbers and to frequency combs from microresonators. Our methods predict improved operating regimes for combs that are produced from both the passively modelocked lasers and the microresonators. 

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4. Self-frequency-modulated laser combs

   https://doi.org/10.1063/5.0215583  

   Roy, Mithun; Zeng, Tianyi; Burghoff, David (August 2024, Applied Physics Letters)

   Optical frequency combs with equidistant frequency modes have revolutionized metrology and spectroscopy. The most widespread combs consist of periodic pulse trains generated by mode-locked lasers. However, it has recently been demonstrated that most semiconductor lasers based on Fabry–Pérot cavities, such as quantum well laser diodes, quantum cascade lasers, and quantum dot lasers, can enter an unconventional regime without traditional mode-locking mechanisms. The time-domain profile of these self-locked combs features a frequency-modulated (FM) wave with quasi-continuous-wave intensity and near-linear frequency chirp. The observation of the FM mode of operation in lasers with significantly different dynamics suggested that this mode is a fundamental operating state of semiconductor lasers, stemming from a deeper underlying mechanism. Thanks to recent theoretical and experimental advances, the origin of FM behavior has become clear. In this Perspective, we discuss the current status of FM combs in semiconductor lasers based on Fabry–Pérot cavities, focusing on their physical origin, modeling, characterization, bandwidth enhancement, and potential in future applications. 

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5. Defect-engineered ring laser harmonic frequency combs

   https://doi.org/10.1364/OPTICA.430896  

   Kazakov, Dmitry; Opačak, Nikola; Beiser, Maximilian; Belyanin, Alexey; Schwarz, Benedikt; Piccardo, Marco; Capasso, Federico (September 2021, Optica)

   A monochromatic wave that circulates in a nonlinear and dispersive optical cavity can become unstable and form a structured waveform. This phenomenon, known as modulation instability, was encountered in fiber lasers, optically pumped Kerr microresonators and, most recently, in monolithic ring quantum cascade lasers (QCLs). In ring QCLs, the instability led to generation of fundamental frequency combs—optical fields that repeat themselves once per cavity round trip. Here we show that the same instability may also result in self-starting harmonic frequency combs—waveforms that repeat themselves multiple times per round trip, akin to perfect soliton crystals in ring Kerr microresonators. We can tailor the intermode spacing of harmonic frequency combs by placing two minute defects with a well-defined separation between them along the ring waveguide. On-demand excitation of frequency comb states with few powerful modes spaced by hundreds of gigahertz may find their use in future sub-terahertz generators. 

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