Related papers: Nonlinear solutions for \chi^(2) frequency combs i…

We report how a doublet of the symmetric oppositely tilted bistable resonance peaks in a microring resonator with quadratic nonlinearity set for generation of the second harmonic can transform into a Kerr-like peak on one side of the linear…

In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…

Resonator-based optical frequency comb generation is an enabling technology for a myriad of applications ranging from communications to precision spectroscopy. These frequency combs can be generated in nonlinear resonators driven using…

Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for…

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as…

We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms,…

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…

Photonic integrated circuits that exploit nonlinear optics in order to generate and process signals all-optically have achieved performance far superior to that possible electronically - particularly with respect to speed. We review the…

Chi-3 micro resonators have enabled compact and portable frequency comb generation, but require sophisticated dispersion control. Here we demonstrate an alternative approach using a chi-2 sheet cavity, where the dispersion requirement is…

Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and deriving…

Kerr optical frequency combs with multi-gigahertz spacing have previously been demonstrated in chip-scale microresonators, with potential applications in coherent communication, spectroscopy, arbitrary waveform generation, and radio…

Optical frequency combs have revolutionized frequency metrology and timekeeping, and can be used in a wide range of optical technologies. Advances are under way that allow dramatic miniaturization of optical frequency combs using Kerr…

The discovery that externally-driven nonlinear optical resonators can sustain ultrashort pulses corresponding to coherent optical frequency combs has enabled landmark advances in applications from telecommunications to sensing. The main…

Optical-frequency combs enable measurement precision at the 20th digit, and accuracy entirely commensurate with their reference oscillator. A new direction in experiments is the creation of ultracompact frequency combs by way of nonlinear…

We present a model for $\chi^{(2)}$ waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the…

Nonlinear optical effects provide a natural way of light manipulation and interaction, and form the foundation of applied photonics -- from high-speed signal processing and telecommunication, to ultra-high bandwidth interconnects and…

A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. For [$\chi ^{(3)}$] nonlinearity, the model finds two different…

A fully stabilized soliton microcomb is critical for many applications of optical frequency comb based on microresonators. However, the current approaches for full frequency stabilization require either external acousto-optic or…

With demonstrated applications ranging from metrology to telecommunications, soliton microresonator frequency combs have emerged over the past decade as a remarkable new technology. However, standard implementations only allow for the…

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…