Related papers: Nonlinear solutions for \chi^(2) frequency combs i…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
Chip-scale optical frequency combs based on microresonators (microcombs) enable GHz-THz repetition rates, broad bandwidth, compactness, and compatibility with wafer-scale manufacturing. Silicon nitride photonic integrated circuits have…
Microresonator based optical frequency combs (MFC) have demonstrated promise in extending the capabilities of optical frequency combs. Here we demonstrate all optical stabilization of a low noise temporal soliton based MFC in a crystalline…
The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…
We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or $\chi^{(2)}$ ] periodic optical media. We derive a novel physical model for gap solitons in…
Microresonator-based optical frequency combs, or "microcombs", have attracted lots of attention in the last few years thanks to their promising applications in telecommunications, spectroscopy and optical clocks. The process of comb…
In nonlinear optics $2\pi$-periodic solutions $a\in C^2([0,2\pi];\mathbb{C})$ of the stationary Lugiato-Lefever equation $-d a"= ({\rm i} -\zeta)a +|a|^2a-{\rm i} f$ serve as a model for frequency combs, which are optical signals consisting…
Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The requirement on external driving lasers has been…
Microcombs -- optical frequency combs generated in coherently-driven nonlinear microresonators -- have attracted significant attention over the last decade. The ability to generate two such combs in a single resonator device has in…
Microcombs, optical frequency combs generated by nonlinear integrated micro-cavity resonators, have the potential to offer the full capability of their benchtop comb based counterparts, but in an integrated footprint. They have enabled…
We prove the existence of travelling-wave solutions for a system of coupled nonlinear Schr\"{o}dinger equations arising in nonlinear optics. Such a system describes second-harmonic generation in optical materials with $\chi^{(2)}$…
Optical frequency combs are broadband sources that offer mutually-coherent, equidistant spectral lines with unprecedented precision in frequency and timing for an array of applications. Kerr frequency combs in microresonators require a…
Recent investigations of microcavity frequency combs based on cascaded four-wave mixing have revealed a link between the evolution of the optical spectrum and the observed temporal coherence. Here we study a silicon nitride microresonator…
Optical solitons are waveforms that preserve their shape while propagating, relying on a balance of dispersion and nonlinearity. Soliton-based data transmission schemes were investigated in the 1980s, promising to overcome the limitations…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we…
The ability to detect and identify molecules at high sensitivity without the use of labels or capture agents is important for medical diagnostics, threat identification, environmental monitoring, and basic science. Microtoroid optical…
Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the…
Optical frequency combs based on mode-locked lasers have revolutionized many areas of science and technology, such as precision metrology, optical frequency synthesis or telecommunications. In recent years, a particular kind of frequency…
The drive to miniaturize optical frequency combs for practical deployment has spotlighted microresonator solitons as a promising chip-scale candidate. However, these soliton microcombs could be very power-hungry when their span increases,…