Related papers: Nonlinear solutions for \chi^(2) frequency combs i…
We present an analytical and numerical investigation into the phenomenon of filter-induced modulation instability in passive hybrid optical resonators exhibiting quadratic and cubic nonlinearity. We show that asymmetric spectral losses,…
Recent developments demonstrate that parametric four-wave mixing (FWM) in high-Q microresonators is a highly promising and effective approach for optical frequency comb generation, with applications including spectroscopy, optical clocks,…
We report on the experimental observation of coherent cavity soliton frequency combs in silica microspheres. Specifically, we demonstrate that careful alignment of the microsphere relative to the coupling fiber taper allows for the…
Simultaneous Kerr comb formation and second-harmonic generation with on-chip microresonators can greatly facilitate comb self-referencing for optical clocks and frequency metrology. Moreover, the presence of both second- and third-order…
Optical atomic clocks deliver unrivaled precision, yet their size and complexity still confine them to specialized laboratories. Frequency combs provide the crucial optical-to-microwave division needed for clock readout, but conventional…
Electro-optic modulation is an attractive approach for generating flat, stable, and low-noise optical frequency combs with relatively high power per comb line. However, a key limitation of electro-optic combs is the restricted number of…
We consider the Lugiato-Lefever (LL) model of optical fibers. We construct a two parameter family of steady state solutions, i.e. Kerr frequency combs, for small pumping parameter $h>0$ and the correspondingly (and necessarily) small…
This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a…
We present a novel compact dual-comb source based on a monolithic optical crystalline MgF$_2$ multi-resonator stack. The coherent soliton combs generated in two microresonators of the stack with the repetition rate of 12.1 GHz and…
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…
Temporal cavity solitons in ring microresonators provide broad and controllable generation of frequency combs with applications in frequency standards and precise atomic clocks. Three level media in the {\Lambda} configuration inside…
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
We propose that stable boson stars generically fall within an infinite-parameter family of solutions that oscillate on any number of non-commensurate frequencies. We numerically construct two-frequency solutions and explore their parameter…
We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation…
In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of…
The two-frequency problem of synchronization of the pulse train of a passively mode locked soliton laser to an externally injected pulse train is solved in the weak injection regime. The source and target frequency combs are distinguished…
Optical frequency comb based on microresonator (microcomb) is an integrated coherent light source and has the potential to promise a high-precision frequency standard, and self-reference and long-term stable microcomb is the key to this…
The frequency and orbital angular momentum (OAM) are independent physical properties of light that both offer unbounded degrees of freedom. However, creating, processing, and detecting high-dimensional OAM states have been a pivot and…