Onset Of Modulational Instability Research Articles

Mitigating mode instabilities by controllable mode beating excitation with a photonic lantern

In this study, a method of stabilizing the output beam of a large-mode-area fiber amplifier operating above the mode instability threshold is demonstrated. A mode control system based on the photonic lantern is used to excite dynamic mode beatings as the seeding stage of a 42/250 µm Yb-doped fiber amplifier. We propose a theoretical explanation for the validity of this method: provided that the mode interference patterns generated by input mode beatings are antisymmetric to those in the main amplifier caused by thermally induced non-linear effects, the refractive index grating will not be formed to indicate the onset of mode instability. Experimentally, significant mode stability and beam quality improvement have been achieved in this system at power levels of up to nearly four times the mode instabilities threshold.

Photonic rogue waves in a strongly dispersive coupled-cavity array involving self-attractive Kerr nonlinearity

Based on the combined Dicke, Bose-Hubbard, and Lipkin-Meshkov-Glick Hamiltonian, we investigate the formation of photonic rogue waves, including their Akhmediev and Kuznetsov-Ma cousins, in the strongly dispersive regime of a generalized atom-cavity array configuration. By means of the multiple-scale approach and mean-field approximation, we unveil that, due to the interplay between the photon hopping-induced tunneling effect and the self-attractive nonlinearity, the photons can redistribute in the whole array, which in turn leads to the redistribution (creation or annihilation) of excited atoms in each cavity and, consequently, the occurrence of Peregrine soliton states in both photonic and atomic fields. This interplay also yields an interesting intensity-clamping effect that the sum of the peak intensities of both rogue waves will be constant, although this quantity varies from site to site. We numerically confirm the analytical predictions, showing that the Peregrine rogue waves generated are stable against perturbations, despite the onset of modulation instability.

Reviving modulational instability with third-order dispersion

It is well-known that third-order dispersion (TOD) plays no role in the onset of modulation instability in the nonlinear Schrödinger (NLS) family of systems. Here we demonstrate that the characteristics of modulational instability can be dramatically altered by the TOD in two different nonlinear systems, namely Wannier exciton mass in a ZnCdSe/ZnSe semiconductor superlattice and nonlinear pulse/beam propagation in a Kerr-like waveguide under non-slowly varying envelope approximation (non-SVEA), with spatial dispersion. Further we reveal the results of numerical simulations suggesting the existence of recently much studied Akhmediev-type breathers and Peregrine-like rogue waves due to the nonlinear development of MI stemming from the TOD.

Mode dynamics in high-power Yb-Raman fiber amplifier.

Yb-Raman fiber amplifier (YRFA) is a compact setup that can be applied to achieve high-power narrow linewidth or special wavelength lasers. In this Letter, we realized a high-power YRFA with seed wavelengths of 1090 nm and 1150 nm, tandem-pumped by a 1018 nm fiber laser. The dynamic of mode interaction has been carefully studied. The beam cleanup effect in the large mode area, step-index fiber has been observed for the first time, to the best of our knowledge, when the pump power ranges from 800 W to 1700 W. A model taking into account the Raman mode interaction is proposed to explain this phenomenon, which agrees well with the experiments. The mode instability (MI) effect is also observed in the amplifier, and the threshold is about 2 kW, which is lower than the conventional Yb-doped fiber amplifier. Stimulated Raman scattering is attributed to the onset of MI. Finally, the 1338 W 1150 nm laser is achieved by this YRFA, which we believe to be the highest power reported at this wavelength.

Experimental study of mode distortion induced by stimulated Raman scattering in high-power fiber amplifiers

The experimental investigation of mode distortion induced by stimulated Raman scattering (SRS) in a high-power fiber amplifier, which includes the evolutions of optical spectra, spatial beam profiles, and time-frequency characteristics, has been carried out in detail. Temporal-frequency characteristics have been studied for the first time, to the best of our knowledge, by using a low-speed camera and high-speed photodiode traces, which revealed that temporal-frequency characteristics of SRS-induced mode distortion are different from traditional dynamic mode instability (MI). The experimental results show that the output beam profile remains stable before the mode distortion occurs and fluctuates obviously after the onset of SRS-induced MI but on a time scale of seconds, which is much lower than that of Yb-gain-induced MI featuring millisecond-level beam profile fluctuation. It also shows that the mode distortion became measurable in company with the onset of inter-mode four-wave mixing (IM-FWM) when the ratio of Raman light reaches 3%; further, the beam quality factor M 2 degrades gradually from 1.4 to 2.1 as the ratio of Raman light increases. The mode distortion is accompanied by an obvious temperature increase of the output passive fiber, which further confirms that the mode distortion originates from SRS. The cause of the mode distortion induced by SRS has been explained in the context of core-pumped SRS effect, and the investigation on the accompanying IM-FWM effect indicates that the main content of the SRS-induced high-order mode is the LP21 mode.

Oscillating two-dimensional Ca2+ waves in cell networks with bidirectional paracrine signaling

Nonlinear excitations of waves are investigated in a two-dimensional cell network with bidirectional paracrine signaling, both in the longitudinal and transversal directions. The semi-discrete approximation is used to show that the dynamics of the intercellular waves can be reduced to complex Ginzburg–Landau equations, depending on the high- or low-frequency regime. The onset of modulational instability is addressed, where the instability features of the low- and high-frequency modes are compared via the instability growth rate. The -expansion method is employed to find analytically spiral-like wave solutions for the two dynamical regimes. Their response to the effect of paracrine coupling is also addressed.

Modulational instability and ion-acoustic envelopes in dense plasmas with trapped/untrapped electrons

The linear and nonlinear properties of ion-acoustic rogons and associated modulational instability (MI) are studied in an unmagnetized dense electron-ion plasma, containing degenerate trapped/untrapped electrons and classical adiabatic ions. Solving the quantum hydrodynamic equations by using the standard multiscale reductive perturbation technique, a nonlinear Schrödinger equation is derived, which admits potential envelopes to be stable (unstable) against the perturbations for PQ < 0 (PQ>0). Here, P and Q are the dispersion and nonlinearity coefficients, respectively. It is numerically shown that for the vanishing ionic temperature ratio (σ=0), the parametric regime at perturbation wavelengths λ≥2.5λeff (λ≤2.5λeff) is always modulationally stable (unstable); here, λeff is the effective screening length. Moreover, the finite ionic temperature (Ti≤10 eV) restores the modulational stability at relatively short wavelengths by confining MI within the perturbation range 4.5λeff≤λ≤1.3λeff. The parameter Θ(=Te/22μ) shows the impact of the untrapped electrons which not only enhances (reduces) the angular frequency (group speed) of the envelope but also piles up the wave crests (energy) to produce the MI. Furthermore, due to degenerate trapped electrons, the instability domain gets widened in the limit PQ > 0 and leads to the onset of MI and unstable excitations. The study has important results for understanding the mechanism of MI and unstable modes in the context of astrophysical environments (white dwarfs, neutron stars, etc.,) and high density experiments.

Dynamic characteristics of stimulated Raman scattering in high power fiber amplifiers in the presence of mode instabilities.

Impact of mode instability on dynamic characteristics of stimulated Raman scattering in high power fiber amplifiers has been studied for the first time, which reveals another characterization of mode instability from the aspect of optical spectrum. It shows that, after the onset of mode instability, the measured light spectrums, especially the Raman light spectrums, are different from those without mode instability, which become burr-like. As mode instability evolves into different stages, the intensity of stimulated Raman scattering effects as laser power increasing also behaves differently. During the transition region, the stimulated Raman scattering effect becomes stronger as the lasing power increases until the mode instability evolves into chaotic regions, where the stimulated Raman scattering effect weakens. The effect of stimulated Raman scattering on mode instability has also been studied. Due to that the stimulated Raman scattering effect is weak and that the fraction of Raman light is only a few percent, the stimulated-Raman-scattering-induced mode instability has not been observed in the experiment, and the observed mode instability is induced by ytterbium ion gain of signal laser. It also revealed that the stimulated Raman scattering has negligible influence on the mode instability induced by ytterbium ion gain.

Impact of gamma-ray radiation-induced photodarkening on mode instability degradation of an ytterbium-doped fiber amplifier

The laser performance of a high-power ytterbium-doped fiber amplifier is mainly hindered by the onset of mode instability. In this work, the slope efficiency and mode instability threshold of the ytterbium-doped fiber under various gamma-ray radiation doses have been measured. Experimental results reveal that gamma-ray radiation-induced photodarkening degrades mode instability severely, and gamma-ray radiation-induced mode instability degradation can be partly bleached by hours of pump-light injection. It is shown that gamma-ray radiation-induced photodarkening results in a steep reduction of slope efficiency and mode instability threshold; moreover, the entire irradiated fiber can be partly bleached by hours of pump-light injection and exhibits both time and gamma-ray radiation-dose saturation properties. The experimental results indicate that mode instability mitigation can be partly realized by pump-light injection and implies photodarkening suppression is beneficial for TMI mitigation, which is very promising for the advancement of high-power fiber lasers.

Power Scaling of Linearly Polarized Random Fiber Laser

The power scaling of linearly polarized random fiber lasers (RFLs) is investigated in detail based on master oscillator power amplifier configuration. A 442-W linearly polarized output with a narrow 3-dB linewidth of 0.28 nm and a 621-W linearly polarized output with a relatively wider 3-dB linewidth of 2.7 nm are realized. Besides, near-diffraction-limited beam quality and high polarization extinction ratio are obtained in both situations, and further power scaling is limited by the onset of mode instability (MI). To the best of our knowledge, these results are highest output powers of linearly polarized RFLs for the time being, in the narrow-linewidth and wide-linewidth situations, respectively. Meanwhile, the differences in the spectral broadening factor and the MI threshold between the narrow-linewidth linearly polarized RFL and the wide-linewidth one are discovered and discussed for the first time. It is experimentally demonstrated that relatively wider linewidth of the RFL seed is in favor of reducing the spectral broadening and increasing the MI threshold, providing significant reference for power scaling of linearly polarized RFL.

Circular dispersive shock waves in colloidal media

A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.

Analytical study of coherence in seeded modulation instability

We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a continuous wave (CW) pump; then, we investigate the effect of adding a deterministic seed to the CW pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when dealing with generation in longer wavelength regions (mid IR). We believe these results to be of relevance when applied to the analysis of the coherence properties of supercontinua generated from CW pumps.

Multi-millijoule few-cycle mid-infrared pulses through nonlinear self-compression in bulk.

The physics of strong-field applications requires driver laser pulses that are both energetic and extremely short. Whereas optical amplifiers, laser and parametric, boost the energy, their gain bandwidth restricts the attainable pulse duration, requiring additional nonlinear spectral broadening to enable few or even single cycle compression and a corresponding peak power increase. Here we demonstrate, in the mid-infrared wavelength range that is important for scaling the ponderomotive energy in strong-field interactions, a simple energy-efficient and scalable soliton-like pulse compression in a mm-long yttrium aluminium garnet crystal with no additional dispersion management. Sub-three-cycle pulses with >0.44 TW peak power are compressed and extracted before the onset of modulation instability and multiple filamentation as a result of a favourable interplay between strong anomalous dispersion and optical nonlinearity around the wavelength of 3.9 μm. As a manifestation of the increased peak power, we show the evidence of mid-infrared pulse filamentation in atmospheric air.

Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave

The conditions for the onset of modulation instability of wave packets in an optical waveguide in the presence of the traveling refractive index wave are investigated. An expression governing the growth rate of a small harmonic perturbation at the early development stage of the modulation instability is obtained. Based on numerical analysis, the behavior of the wave packet at the developed modulation instability stage is studied for different parameters of the waveguide and the refractive index wave.

Complementary optical rogue waves in parametric three-wave mixing.

We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.

Effects of next-nearest-neighbor interactions on discrete multibreathers corresponding to Davydov model with saturable nonlinearities

The influence of next-nearest-neighbor interactions (next-NNI) of dipole–dipole type is analyzed in Davydov model with saturable nonlinearities. We analytically study the regions of discrete modulational instability (MI) of plane carrier waves and it appears that this region decreases as the number of nearest neighbors, m, increases. We also show via the instability growth rate (gain) that when m increases, bandwidth of instability decreases. Otherwise, it is noted that the saturation also has an antagonistic effect on the gain. Numerical simulations indicate that the presence of next-NNI induced downward corrections of the time of onset of MI. After having sought Discrete Soliton (DS) and Discrete Multihump soliton (DMHS) numerically with m=1; 2; 3, the next-nearest neighbor dependence of the width and height of these solutions is discussed. A study of mobility is achieved and it results that next-NNI increase the speed of DMHS. Furthermore, the collisions of two DMHS are performed and it emerges mainly that next-NNI lead to the formation of large stationary solitons.

13 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities

We report on the high power amplification of 1064nm linearly-polarized laser in all-fiber polarization-maintained MOPA, which can operate at output power level of 1.3kW. The main amplifier was pumped with six 915nm laser diodes, and the slope efficiency is 65.3%. The beam quality (M2) was measured to be <1.2 at full power operation. The polarization extinction rate of the fiber amplifier was measured to be above 94% before mode instabilities (MI) sets in, which reduced to about 90% after the onset of MI. Power scaling capability of strategies for suppressing MI is analyzed based on a novel semi-analytical model, the theoretical results of which agree with the experimental results. It shows that mitigating MI by coiling the gain fiber is an effective and practical way in standard double-cladding large mode area fiber, and, by tight coiling of the gain fiber to the radius of 5.5cm, the MI threshold can be increased to 3 times higher than that without coiling or loose coiling. Experimental study has been carried out to verify the idea, which has proved that MI was suppressed successfully in the amplifier by tight coiling.

Breathers and ‘black’ rogue waves of coupled nonlinear Schrödinger equations with dispersion and nonlinearity of opposite signs

Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a ‘black’ rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.

Dispersive shock waves in colloids with temperature dependent compressibility

The formation of a dispersive shock wave in a colloidal medium, due to an initial jump in the light intensity, is studied. The compressibility of the colloidal particles is modeled using a series in the particle density, or packing fraction, where the virial coefficients depend on the particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results for the second virial coefficient show that it is temperature dependent and that the particle interactions can be either repulsive or attractive. These effects are modeled using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump is resolved via a dispersive shock wave which forms before the onset of modulational instability. A semi-analytical solution is developed for the one-dimensional line bore case which predicts the amplitude of the solitary waves which form in the dispersive shock wave. The solitary wave amplitude versus jump height diagrams can exhibit three different kinds of behaviors. A unique solution, an S-shaped solution curve and multiple solution branches where the upper branch has separated from the lower branches. A bifurcation from the low to the high power branch can occur for many parameter choices as the amplitude of the initial jump increases. The effect of temperature on the evolution of the bore, the amplitude of the solitary waves and the bifurcation patterns are all discussed and the semi-analytical solutions are found to be very accurate.

Nonlinear nanoantenna with self-tunable scattering pattern

A new concept of a nonlinear plasmonic nanoantenna with self-tunable scattering pattern (indicatrix) is suggested. It is shown that the onset of modulational instability in a nanoantenna consisting of two identical nonlinear metallic nanoparticles results in dynamic energy exchange between the eigenmodes of the nanodimer, accompanied by periodic rotation and switching of the scattering pattern. Such a nanoantenna features a wide scanning sector, a relatively low working threshold, and a short response time. This makes it attractive for applications in nanophotonics and biology.