Dynamics Of Modulation Instability Research Articles

Spatiotemporal dynamics of modulation instability in Kerr nonlinear media with pure-quartic dispersion

We present the analytical and numerical analysis on spatiotemporal dynamics of modulation instability (MI) in Kerr nonlinear media with pure-quartic dispersion. We apply a linear stability method to arrive at a universal expression for pure-quartic instability gain, which can simultaneously describe the temporal, spatial, and spatiotemporal cases. The results show that the condition of such three fundamental instability occurrence in pure-quartic dispersion media (PDM) is the same as that in conventional quadratic dispersion media (QDM). Another interesting observation is that the maximum gain is also the same in both cases. For temporal instability, there exists a critical power below which the instability bandwidth becomes wider than the corresponding case in QDM or otherwise. For spatiotemporal instability, the instability region depending on critical frequencies is found to show some remarkable difference when compared with the latter case. The analytical prediction resulting from linear stability analysis is confirmed by the numerical method.

Modulation instability with high-order dispersion: fundamental limitations of pattern formation.

We theoretically and numerically investigate modulation instability in the presence of even, high-order dispersion, focusing on general trends rather than on specific results for a particular dispersion order. We show that high-order dispersion leads to increasingly poor phase matching between the three central waves (i.e. the pump and the ±1 sidebands) and the higher sideband orders, inhibiting in effect four-wave mixing frequency generation. For sufficiently large dispersion orders, the problem in effect can reduce to a three-wave system. Our predictions are in excellent agreement with numerical simulations and show that high-order dispersion imposes a fundamental limit on modulation instability dynamics.

Analysis of interaction dynamics and rogue wave localization in modulation instability using data-driven dominant balance

We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schrödinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which particular physical processes drive propagation in different regimes, a task usually performed using intuition and comparison with asymptotic limits. We first apply the method to interpret known analytic results describing Akhmediev breather, Kuznetsov-Ma, and Peregrine soliton (rogue wave) structures, and show how we can automatically distinguish regions of dominant nonlinear propagation from regions where nonlinearity and dispersion combine to drive the observed spatio-temporal localization. Using numerical simulations, we then apply the technique to the more complex case of noise-driven spontaneous modulation instability, and show that we can readily isolate different regimes of dominant physical interactions, even within the dynamics of chaotic propagation.

Stabilization of modulation instability by control field in semiconductor quantum wells

This article explores the modulation instability of a continuous or quasi-continuous weak probe pulse in a three-level asymmetric double quantum wells under an electromagnetically induced transparency regime, controlled by a strong laser beam. The dynamics of modulation instability reveals that the instability gain as well as its bandwidth is greatly influenced by control field Rabi frequency. The probe pulse is found to be almost stable against modulation instability for higher values of control field Rabi frequency. The results of this investigation may potentially apply for oscillation free generation of supercontinuum in quantum well nanostructures.

Omnipresent instability criterion of birefringent Kundu-Eckhaus model with nonic nonlinearity

This paper intends to present an investigation of the ultra shortpulse propagation under the nonlinear birefringent Kundu-Eckhaus (KE) model. The dynamics of modulational instability(MI) is revealed with the linear stability analysis of the KE equation with higher-order, the cubic, and nonic nonlinearity effects. The role of cubic-nonic nonlinearity on MI gain spectra in KE fiber system with self and cross phase modulation is studied for the first time. The impact of nonic nonlinearity is shown to be much more prominent over its cubic-quintic counterpart. The presence of cubic-nonic combo nonlinearity lets the MI gain profile to be adjusted with the rate of self-phase modulation (SPM). This new MI gain growth dynamics controlled by the SPM parameter will be useful on soliton generation in birefringent KE fiber media.

Hidden Akhmediev breathers and vector modulation instability in the defocusing regime

We study the dynamics of modulation instability (MI) of the vector nonlinear Schrödinger equations (the Manakov system) in the defocusing regime. A general family of exact Akhmediev breather (AB) solutions of intricate structures is presented. The physical spectra with infinite number of sidebands that describe the asymmetric expansion–contraction cycle are calculated analytically. In contrast to the MI dynamics in the focusing regime, an unusual phenomenon in the defocusing regime—hidden ABs with initial modulation frequency is revealed during nonlinear evolution of higher-order MI. Such a phenomenon is universal when the MI starts from simple periodic modulation with equal phase in the low-frequency region. We present the existence diagram of such excitations. A simple way to restore the hidden ABs is to consider the initial modulation with π phase difference. We substantiate all these findings by constructing exact multi-AB solutions with free parameters. It is shown that the hidden dark ABs appear as a result of nonlinear supposition between multi-dark-ABs.

Modulation instability in higher-order nonlinear Schrödinger equations.

We investigate the dynamics of modulation instability (MI) and the corresponding breather solutions to the extended nonlinear Schrödinger equation that describes the full scale growth-decay cycle of MI. As an example, we study modulation instability in connection with the fourth-order equation in detail. The higher-order equations have free parameters that can be used to control the growth-decay cycle of the MI; that is, the growth rate curves, the time of evolution, the maximal amplitude, and the spectral content of the Akhmediev Breather strongly depend on these coefficients.

Modulation instability in quasi-two-dimensional spin–orbit coupled Bose–Einstein condensates

We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin–orbit coupled Bose–Einstein condensates (BECs) with Rabi coupling. The analysis is performed for equal densities of pseudo-spin components. Different combination of the signs of intra- and intercomponent interaction strengths are considered, with a particular emphasis on repulsive interactions. We observe that the unstable modulation builds from originally miscible condensates, depending on the combination of the signs of the intra- and intercomponent interaction strengths. The repulsive intra- and intercomponent interactions admit instability and the MI immiscibility condition is no longer significant. The influence of interaction parameters such as spin–orbit and Rabi coupling on MI are also investigated. The spin–orbit coupling (SOC) inevitably contributes to instability regardless of the nature of the interaction. In the case of attractive interaction, SOC manifests in enhancing the MI. Thus, a comprehensive study of MI in two-dimensional spin–orbit coupled BECs of pseudo-spin components is presented.

Modulation instability dynamics of coupling pulses with different powers in nonlinear fibers

In the paper, the modulation instability (MI) of the pulses with different powers is studied based on the modified coupled nonlinear Schrödinger equations in nonlinear fiber. By analyzing MI gain spectrum with different power ratios, it shows that the increase of power ratio leads to the diminution in the range of strongly unstable frequency and the decrease in the gain of MI spectra. With a fixed power ratio, the increased relaxation time is equally suppressing overall MI.

Instability of wave packets in nonlinear inhomogeneous waveguides

Conditions for modulation instability of a wave packet to occur in cubically nonlinear single- and double-mode waveguides with various distributions of dispersion parameters over the waveguide length are investigated. Analytical expressions are obtained for the integral gain increment and other characteristics governing the modulation instability dynamics. Features of the dynamics are revealed using numerical simulation.

Spectral dynamics of modulation instability described using Akhmediev breather theory

The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi-Pasta-Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss, and Raman scattering are used to identify that the primary physical factors that preclude perfect recurrence are related to imperfect initial conditions.

Nonlinear dynamics of modulation instability in distributed resonators under external harmonic driving

We study the regimes of complex field dynamics upon modulation instability in distributed nonlinear resonators under external harmonic driving. Two regimes are considered: the regime of a nonlinear ring cavity, described by nonlinear Schrodinger equation (NLS) with a delayed boundary condition, and the regime of a one-dimensional Fabri-Perot cavity, described by a system of coupled NLS for the forward and backward waves. Theoretical stability analysis of stationary forced oscillations is carried out. The results of numerical simulation of transition to chaos with increasing input intensity are presented.

Full-time dynamics of modulational instability in spinor Bose-Einstein condensates

We describe the full-time dynamics of modulational instability in $F=1$ spinor Bose-Einstein condensates for the case of the integrable three-component model associated with the matrix nonlinear Schr\"odinger equation. We obtain an exact homoclinic solution of this model by employing the dressing method which we generalize to the case of the higher-rank projectors. This homoclinic solution describes the development of modulational instability beyond the linear regime, and we show that the modulational instability demonstrates the reversal property when the growth of the modulated amplitude is changed by its exponential decay.

Effect of Nonlinear Gradient Terms on the Dynamics of Solitons in the Cubic-Quintic Complex Ginzburg-Landau Equation

The modulational instability of the one-dimensional cubic-quintic complex Ginzburg-Landau equation with the nonlinear gradient terms is investigated. The presence of the nonlinear gradient terms modifies the modulational instability gain spectrum. We numerically investigate the dynamics of modulational instability in the presence of the nonlinear gradient terms. It is found that they introduce more interactions (both elastic and inelastic) dynamics to the solitons generated by the modulational instability. The signs of the gradient terms determine the propagation direction of the soliton. - PACS numbers: 42.65.Tg, 42.81Dp, 42.65.Sf.

Nonlinear Pulse Propagation and Modulation Instability in Periodic Media with and without Defects

The nonlinear propagation of EMW in periodic media is of great interest due to the possibility to accumulate energy in periodic media within the stop band and, therefore, the input intensity levels for observation of nonlinear phenomena are quite low [1]. For resonant interactions, also it is possible to realize matching conditions, which are not possible in uniform media. Both resonant multiwave interactions and selfaction of EMW in nonlinear periodic media have been analyzed [1, 2]. Also, a method based on a slow variation in time was proposed, which seems more adequate than others based on coupled equations [3]. The presence of defects in periodic structure leads to narrow regions of transmission within the stop-band. In this case, the application of coupled equations for counter propagating waves becomes doubtful, and a more general approach is needed [3]. Also, the influence of defects on the dynamics of modulation instability of long pulses is of a great interest. The present paper considers numerical simulations of the pointed above phenomena. For a correct description of the nonlinear dynamics, it is necessary also to take into account the wave dissipation and possible transverse diffraction. The results of simulations demonstrated the essential influence of defects within the periodic structure on the nonlinear propagation of EM pulses, even if the carrier frequency is chosen within the stop band of the structure with a defect. This fact can be explained by a quite wide spectrum of the input pulse, and the “tail” of such a spectrum is within the transmission region due to the defect. This situation is analogous to the nonlinear propagation of short spin-dipole waves in the vicinity of the cut-off frequency [4]. The dynamics of modulation instability also changes in the presence of the defect. The diffraction can affect essentially the modulation instability dynamics.

Nonlinear Diffraction of Magnetostatic Waves in Ferrite Films

Two-dimensional nonlinear diffraction of magnetostatic waves (MSW) in ferrite films is studied numerically using the model of nonlinear parabolic equation. This equation is derived by a new method from a bilinear relation similar to the Lorentz lemma. It is shown, that in the framework of this model the evolution of two-dimensional backward volume MSW pulse leads to a collapse in the case of an infinite film, while in a film waveguide of a finite width the collapse can be avoided, and the pulse amplitude can be stabilized. Dynamics of modulation instability of both backward volume and forward volume MSW under continuous excitation is also investigated.

Role of nonlinear dispersion in the dynamics of induced modulational instability in Kerr media

We show that even small, but not negligible, nonlinear dispersion can affect the dynamics of modulational instability in Kerr media. Time and frequency asymmetries are observed both in the numerical solutions and in a three-wave simplified analytical model, and they closely match available experimental data. Variations of the spatial period, which are due to those asymmetries, are also predicted and observed.

Modulational instability, periodic waves and black and white vector solitons in birefringent Kerr media

We analyze the dynamics of modulational instability and periodic waves in the coupled nonlinear Schrödinger equations describing light propagation in birefringent dispersive Kerr media. New stationary periodic solutions are found for these equations. Our analysis reveals the fundamental link which exists between the phenomenon of polarization modulational instability and the so-called black and white vector soliton.

Modulational instability dynamics in a spatial focusing and temporal defocusing medium.

The modulational instability of a wave in media where the nonlinearity has a focusing-in-space and defocusing-in-time character is investigated. An approximate self-similar solution of the nonlinear Schr\"odinger equation is derived for this nonlinearity and is used as background envelope of the wave. We show that this background wave envelope can initially enhance exponential growth of a transverse spatial modulation. The analysis is extended to the case of a modulation in both time and space, and it is found that such a spatiotemporal modulation can be unstable as well.