Related papers: Optical Rogue Waves in Whispering-Gallery-Mode Res…
General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the…
We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
We introduce a new model describing multiple resonances in Kerr optical cavities. It perfectly agrees quantitatively with the Ikeda map and predicts complex phenomena such as super cavity solitons and coexistence of multiple nonlinear…
We construct a specific family of eigenfunctions for a Laplace operator with coefficients having a jump across an interface. These eigenfunctions have an exponential concentration arbitrarily close to the interface, and therefore could be…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
We demonstrate that whispering gallery mode resonators can be utilized to generate optical frequency combs based on four wave mixing process at virtually any frequency that lies in the transparency window of the resonator host material. We…
Optical bistability and oscillating phases exist in a Sagnac interferometer and a single ring resonator made of $\chi^{(3)}$ nonlinear medium where the refractive indices are modulated by the light intensity due to the Kerr nonlinearity. An…
In whispering gallery mode (WGM) resonators light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high…
Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis…
We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop…
A review of hollow core whispering gallery resonators (WGRs)is given. After a short introduction to the topic of whispering gallery resonators we provide a description of whispering gallery modes in hollow or liquid core WGRs. Next,…
We show the existence and investigate the dynamics and statistics of rogue oscillations (standing waves) generated in the frame of the nonlinear quantum harmonic oscillator (NQHO). With this motivation, in this paper, we develop a…
A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schr\"odinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general…
We report the observation of transient nonlinear optical effects in a macroscopic whispering gallery mode resonator made of rutile TiO$_2$, demonstrating strong optical-microwave transduction under laser irradiation. By comparing the…
We report on the first experimental demonstration of terahertz (THz) whispering-gallery modes (WGMs) with an ultra high quality (Q) factor of $1.5 \times {10}^{4}$ at 0.62THz. The WGMs are observed in a high resistivity float zone silicon…
We study the standing periodic waves in the semi-discrete integrable system modelled by the Ablowitz-Ladik equation. We have related the stability spectrum to the Lax spectrum by separating the variables and by finding the characteristic…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
A rogue wave formation mechanism is proposed within the framework of a coupled nonlinear Schrodinger (CNLS) system corresponding to the interaction of two waves propagating in oblique directions in deep water. A rogue condition is…