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Optical frequency combs emit narrow pulses of light with a stable repetition rate. Equivalently, the generated light spectrum consists of many discrete frequencies spaced by this same repetition rate. These precision light sources have…
The dark solitons observed in a large variety of nonlinear media are unstable against the modulational (snake) instabilities and can break in vortex streets. This behavior has been investigated in nonlinear optical crystals and ultracold…
Robust control and stabilization of optical frequency combs enables an extraordinary range of scientific and technological applications, including frequency metrology at extreme levels of precision, novel spectroscopy of quantum gases and…
Optical frequency combs are utilized in a wide range of optical applications, including atomic clocks, interferometers, and various sensing technologies. They are often generated via four-wave mixing in chip-integrated microring resonators,…
Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially…
Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical…
We theoretically study the generation of optical frequency combs and corresponding pulse trains in doubly resonant intracavity second-harmonic generation (SHG). We find that, despite the large temporal walk-off characteristic of realistic…
We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to…
A study is made of frequency comb generation described by the driven and damped nonlinear Schr\"odinger equation on a finite interval. It is shown that frequency comb generation can be interpreted as a modulational instability of the…
Optical frequency combs are crucial for both fundamental science and applications demanding wide frequency spanning and ultra-precision resolutions. Recent advancements of nonlinear Kerr effect based optical frequency combs in microcavities…
Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we…
Optical frequency combs based on mode-locked lasers have proven to be invaluable tools for a wide range of applications in precision spectroscopy and metrology. A novel principle of optical frequency comb generation in whispering-gallery…
We investigate theoretically frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that…
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…
Optical frequency combs, coherent light sources that connect optical frequencies with microwave oscillations, have become the enabling tool for precision spectroscopy, optical clockwork and attosecond physics over the past decades. Current…
Optical frequency combs allow for precise measurement of optical frequencies and are used in a growing number of applications beyond spectroscopy and optical frequency metrology. A class of compact microresonator based frequency comb…
Dissipative Kerr solitons are localized structures that exist in optical microresonators. They lead to the formation of microcombs --- chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by…
Continuously pumped passive nonlinear cavities can be harnessed for the creation of novel optical frequency combs. While most research has focused on third-order "Kerr" nonlinear interactions, recent studies have shown that frequency comb…
We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of…
We demonstrate a new technique for the experimental measurement of the spectral coherence of microresonator optical frequency combs. Specifically, we use a spectral interference method, typically used in the context of supercontinuum…