Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{\"o}dinger equations

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{\"o}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{\"o}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine soliton are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schr{\"o}dinger equation

Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects

The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self-frequency shift- ing solitons and dispersive waves is observed. A mechanism of broadening of the Cherenkov radiation through Hopf instability of the frequency locked solitons is also reported.Comment: 12 pages, 10 figure

Dissipative soliton interaction in Kerr resonators with high-order dispersion

We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato--Lefever equation with fourth order dispersion We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability

Influence of external phase and gain-loss modulation on bound solitons in laser systems

4openopenChang, W.; Akhmediev, N.; Wabnitz, Stefan; Taki, M.W., Chang; N., Akhmediev; Wabnitz, Stefan; M., Tak

Geothermal energy for heating and cooling in agricultural greenhouses

Geothermal source is a perspective technology able to use the ground as a thermal sink or heat source. It is one of the energy resources in Iran that can be used with long-term investment. This study provided a new idea to use of this energy for heating and cooling of buildings. Two wells were used for heating and cooling due to the constant temperature of the water in depth of 12 m underground (approximately is equal  to the annual temperature environment during the year). Water flowed in six speeds: 10, 11.5, 13, 16, 29 and 34 lit/min using a hydraulic pump (12 meters hydraulic height and 2 inch diameter) from first well, and after passing through radiator, discharge to other well. The outdoor temperature was 9oC, 40 °C and 15.5-16 °C for heating, cooling and well water respectively. An axial fan is used to passing the air in six speeds: 0.5, 1.1, 2.2, 3.3, 4.4 and 7.4 m/s through the radiator. The results showed that the use of water from this well can reduce the required power about 25% for heating and increase the air temperature from 9 to 25 °C. Also this system can reduce the required power between 38 to 60% for cooling and decrease the air temperature from 40 to 25 °C

Localized Faraday patterns under heterogeneous parametric excitation

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schr\"odinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.Comment: 10 pages, 9 figures, Accepte

Optical fiber systems are convectively unstable

We theoretically and experimentally evidence that fiber systems are convective systems since their nonlocal inherent properties, such as the dispersion and Raman effects, break the reflection symmetry. Theoretical analysis and numerical simulations carried out for a fiber ring cavity demonstrate that the third-order dispersion term leads to the appearance of convective and absolute instabilities. Their signature is an asymmetry in the output power spectrum. Using this criterion, experimental evidence of convective instabilities is given in a fiber cavity pumped by a pulsed laser

Convection-induced nonlinear-symmetry-breaking in wave mixing

We show that the combined action of diffraction and convection (walk-off) in wave mixing processes leads to a nonlinear-symmetry-breaking in the generated traveling waves. The dynamics near to threshold is reduced to a Ginzburg-Landau model, showing an original dependence of the nonlinear self-coupling term on the convection. Analytical expressions of the intensity and the velocity of traveling waves emphasize the utmost importance of convection in this phenomenon. These predictions are in excellent agreement with the numerical solutions of the full dynamical model.Comment: 5 page

Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger equations

International audienceWe analyze the exact Kuznetsov-Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov-Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kutzetsov-Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov-Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov-Ma soliton by a judicious choice of the amplitude and frequency of the modulation