Related papers: Nonlinear solutions for \chi^(2) frequency combs i…
In a one-dimensional periodic nonlinear $\chi^{(2)}$ medium, by choosing a proper material and geometrical parameters of the structure, it is possible to obtain two matching conditions for simultaneous generation of second and third…
A study is made of the nonlinear dynamics of dual pumped microresonator Kerr frequency combs described by a driven and damped nonlinear Schr\"odinger equation, with an additional degree of freedom in the form of the modulation frequency. A…
We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear $\chi^{(2)}$ and $\chi^{(3)}$ frequency conversion processes. In particular, we demonstrate…
The generation of optical frequency combs in microresonators is considered without resorting to the mean-field approximation. New dynamical regimes are found to appear for high intracavity power that cannot be modeled using the…
We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…
Soliton microcombs -- phase-locked microcavity frequency combs -- have become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR, and optical computing. Despite the predicted multimode…
Nonlinear Kerr micro-resonators have enabled fundamental breakthroughs in the understanding of dissipative solitons, as well as in their application to optical frequency comb generation. However, the conversion efficiency of the pump power…
Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems and fall into two separate classes, that of bright solitons, formed in the anomalous group velocity dispersion regime, and `dark solitons' in the…
Dissipative solitons formed in Kerr microresonators may enable chip-scale frequency combs for precision optical metrology. Here we explore the creation of an octave-spanning, 15-GHz repetition-rate microcomb suitable for both f-2f…
Dissipative Kerr-microresonator soliton combs (hereafter called soliton combs) are promising to realize chip scale integration of full soliton comb systems providing high precision, broad spectral coverage and a coherent link to the…
The transition to chaos is ubiquitous in nonlinear systems ranging from fluid dynamics and superconducting circuits to biological organisms. Optical systems driven out of equilibrium such as lasers and supercontinuum generation exhibit…
Rotation symmetry of microresonators supports the generation of phase-locked counter-propagating (CP) solitons that can potentially miniaturize dual-comb systems. Realization of these dual-comb compatible solitons in photonic integrated…
Recently developed techniques for generating precisely equidistant optical frequencies over broad wavelength ranges are revolutionizing precision physical measurement [1-3]. These frequency "combs" are produced primarily using relatively…
Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental…
This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…
We consider the existence and stability of solitons in a $\chi^{(2)}$ coupler. Both the fundamental and second harmonics undergo gain in one of the coupler cores and are absorbed in the other one. The gain and losses are balanced creating a…
We propose a system of coupled microring resonators for the generation frequency combs and dissipative Kerr solitons in silicon at telecommunication frequencies. By taking advantage of structural slow-light, the effective non-linearity of…
Microresonator-based optical frequency combs emitted from high-quality-factor microresonators, also known as microcombs, have opened up new horizons to areas of optical frequency comb technology including frequency metrology, precision…
By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schr\"odinger equation, we unveil the existence condition of the quadratic soliton mode-locked degenerate optical parametric…
Frequency microcombs, successors to mode-locked laser and fiber combs, enable miniature rulers of light for applications including precision metrology, molecular fingerprinting, and exoplanet discoveries. To enable the frequency ruling…