Related papers: Closed-form solutions and scaling laws for Kerr fr…
There is considerable fundamental and applicative interest in obtaining non-diffractive and non-dispersive spatio-temporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the…
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…
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…
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…
We demonstrate a new mechanism for coherent comb generation in both radiation and matter domains, which is by using strong-field quantum electrodynamics processes. Specifically, we demonstrate this for nonlinear Compton scattering which has…
An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular…
In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schr$\ddot{\mbox{o}}$dinger equation with variable coefficients. This equation appears in literature describing the…
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser within an optical microresonator. It has been observed that…
The nonlinear interaction of a microresonator pumped by a laser has revealed complex dynamics including soliton formation and chaos. Initial studies of coupled-resonator systems reveal even more complicated dynamics that can lead to…
The Kerr microcomb has a huge potential advantage as a quantum computing platform because of its large-scale and globally coherent optical modes. The micro-comb has always faced a primary problem is how to increase the controllability of…
Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a…
We introduce a new, reduced nonlinear oscillator model governing the spontaneous creation of sharp pulses in a damped, driven, cubic nonlinear Schroedinger equation. The reduced model embodies the fundamental connection between mode…
Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven, damped nonlinear Schr\"odinger equation. We find that the ordinary differential equations, which…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
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…
Kerr frequency combs from microresonators are now extensively investigated as a potentially portable technology for a variety of applications. Most studies employ anomalous dispersion microresonators that support modulational instability…
The two-dimensional cubic nonlinear Schr\"{o}dinger equation is used to describe the propagation of an intense laser beam through a medium with Kerr nonlinearity. The coupled two-dimensional cubic nonlinear Schr\"{o}dinger equations are…
Frequency combs are light sources with coherent evenly-spaced lines. It has been observed that in certain laser systems, combs can form whose output is frequency-modulated (FM) in time. In this state, they produce an output whose frequency…
For more than 20 years, optical microresonators have served as the backbone of integrated nonlinear photonics, exploiting Kerr nonlinearity to generate octave-spanning frequency combs, enable quantum effects, and drive optical parametric…
We present a cardinal solution for the long-standing and fundamental problem associated with the adiabatic, reversible, and controlled excitation of both dark and bright solitons in Kerr micro-resonators with normal group velocity…