One-dimensional Modulation Instability Research Articles

One-Dimensional Modulational Instability of Broad Optical Beams In Photorefractive Crystals with Both Linear and Quadratic Electro-Optic Effects

One-Dimensional Modulational Instability of Broad Optical Beams In Photorefractive Crystals with Both Linear and Quadratic Electro-Optic Effects

Evolution of Water Wave Groups in the Forced Benney–Roskes System

For weakly nonlinear waves in one space dimension, the nonlinear Schrödinger Equation is widely accepted as a canonical model for the evolution of wave groups described by modulation instability and its soliton and breather solutions. When there is forcing such as that due to wind blowing over the water surface, this can be supplemented with a linear growth term representing linear instability leading to the forced nonlinear Schrödinger Equation. For water waves in two horizontal space dimensions, this is replaced by a forced Benney–Roskes system. This is a two-dimensional nonlinear Schrödinger Equation with a nonlocal nonlinear term. In deep water, this becomes a local nonlinear term, and it reduces to a two-dimensional nonlinear Schrödinger Equation. In this paper, we numerically explore the evolution of wave groups in the forced Benney–Roskes system using four cases of initial conditions. In the one-dimensional unforced nonlinear Schrödinger equa tion, the first case would lead to a Peregrine breather and the second case to a line soliton; the third case is a long-wave perturbation, and the fourth case is designed to stimulate modulation instability. In deep water and for finite depth, when there is modulation instability in the one-dimensional nonlinear Schdrödinger Equation, the two-dimensional simulations show a similar pattern. However, in shallow water where there is no one-dimensional modulation instability, the extra horizontal dimension is significant in producing wave growth through modulation instability.

Three-dimensional modulational instability of the electrostatic waves in e–p–i magnetoplasmas having superthermal particles

The three-dimensional (3D) modulational instability (MI) of the nonlinear ion-acoustic wave propagating in a non-Maxwellian electron-positron-ion magnetoplasma is investigated. The plasma electrons and positrons obey the Kappa distribution function, which has been proved to be appropriate for modeling the nonthermal features of different plasma environments. The derivative expansion method is carried out to derive the three-dimensional nonlinear Schrodinger equation governing the modulation of the ion-acoustic wavepacket. Criteria under which the MI occurs are discussed in detail. It is found that the conditions, which indicate where the 3D MI sets in, are totally different from the one-dimensional MI. The impact of the relevant plasma parameters, particularly, superthermal parameters, on the MI of the ion-acoustic envelope wavepacket is discussed, and a comparison with previous results is presented. It is noticed that the spectrum of MI in the non-Maxwellian (superthermal) plasma is significantly differe...

Одномерные модели модуляционной неустойчивости интенсивных ленгмюровских колебаний в плазме на основе уравнений Захарова и Силина

Одномерные модели модуляционной неустойчивости интенсивных ленгмюровских колебаний в плазме на основе уравнений Захарова и Силина, Загородний А.Г., Киричок А.В., Куклин В.М.

Modulational instability of incoherently coupled beams in biased photorefractive crystals

We study the one-dimensional modulational instability of incoherently coupled beams in biased photorefractive crystals under steady-state conditions. By globally treating the space-charge equation and only considering the local space-charge effect, i.e., neglecting the higher-order terms in the space-charge equation, we obtain the global and local one-dimensional modulational instability growth rates of incoherently coupled beams in biased photorefractive crystals. Our results show that both the modulational instability growth rates can be adjusted and controlled by external bias field and the intensities of background beam and incoherently coupled signal beams.

Temperature dependency of modulation instability in photorefractive crystals

We provide a theoretical investigation of temperature effects on one-dimensional modulation instability of broad optical beams in photorefractive crystals. Those physical factors related to the temperature effect, i.e., the dielectric constant, diffusion process and the dark irradiance, are considered. Our results show that, for non-centrosymmetric crystals, the dark irradiance dominates the temperature dependence of modulation instability; however, the dielectric constant temperature-dependence dominates the process in centrosymmetric photorefractive crystals. Relevant examples are provided.

One-dimensional modulation instability in biased two-photon photorefractive–photovoltaic crystals

The one-dimensional modulation instability of broad optical beams in biased two-photon photorefractive–photovoltaic crystals is investigated under steady-state conditions. Our analysis indicates that the modulation instability growth rate depends on the external bias field, the bulk photovoltaic effect and the ratio of the intensity of the incident beam to that of the dark irradiance. Moreover, our results show that this modulation instability growth rate is the same as that in two-photon photorefractive–photovoltaic crystals under open circuit conditions in the absence of an external bias field, and the modulation instability growth rate in two-photon biased photorefractive–nonphotovoltaic crystals can be predicted when the bulk photovoltaic effect is neglected.

External electric field induced modulation instability of an electromagnetic beam in two-photon photorefractive materials

The modulation instability of a broad electromagnetic beam in a biased two-photon photovoltaic photorefractive material, due to two-photon-photorefractive effect has been investigated. The one-dimensional modulation instability growth rate has been estimated under the linear stability framework. The behavior of the gain spectrum is different in low and high power regions. It has been predicted that, with the application of external electric field, it is possible to initiate and control growth of the instability in those media, where modulation instability was hitherto prohibited. The influence of different system parameters on the instability growth rate has been examined.

One-dimensional modulational instability of broad optical beams in biased centrosymmetric photorefractive crystals

We study the one-dimensional modulational instability of broad optical beams in biased centrosymmetric photorefractive crystals under steady-state conditions. The one-dimensional modulational instability growth rates are obtained by globally and locally treating the space-charge field, which depend on the external bias field and the ratio of the intensity of optical beam to that of the dark irradiance. Our analysis indicates that the modulational instability growth rate in local effects can be determined from that in nonlocal effects.

Interplay between nonlocality and nonlinearity in nematic liquid crystals

Spatial nonlocality has a crucial role in the optical response of bulk liquid crystals. With specific reference to one-dimensional modulation instability, we demonstrate the tuning of transverse nonlocality in the nonlinear response of nematics.

One-dimensional modulation instability of broad optical beams in biased photorefractive–photovoltaic crystals under steady-state conditions

We present a comprehensive study of the one-dimensional modulation instability of broad optical beams in biased photorefractive–photovoltaic crystals under steady-state conditions. We obtain the one-dimensional modulation instability growth rate by globally treating the space-charge field and by considering distinction between values of E0 in nonlocal effects and local effects in the space-charge field, where E0 is the field constant correlated with terms in the space-charge field, which depends on the external bias field, the bulk photovoltaic effect, and the ratio of the optical beam’s intensity to that of the dark irradiance. The one-dimensional modulation instability growth rate in local effects can be determined from that in nonlocal effects. When the bulk photovoltaic effect is neglectable, irrespective of distinction between values of E0 in nonlocal effects and local effects in the space-charge field, the one-dimensional modulation instability growth rates in nonlocal effects and local effects are those of broad optical beams studied previously in biased photorefractive–nonphotovoltaic crystals. When the external bias field is absent, the one-dimensional modulation instability growth rates in nonlocal effects and local effects predict those of broad optical beams in open- and closed-circuit photorefractive–photovoltaic crystals.

One-dimensional transverse modulational instability in nonlocal media with a reorientational nonlinearity

Transverse modulational instability is investigated in undoped nematic liquid crystals, a highly nonlocal material system encompassing a reorientational nonlinear response. Using an elliptic Gaussian excitation, we observe the one-dimensional development of transverse patterns eventually leading to beam breakup, filamentation, and spatial solitons, both in the cases of spatially coherent and partially incoherent excitations.

(1+1)-Dimensional modulation instability of spatially incoherent light

We present a comprehensive study of the one-dimensional modulation instability of partially spatially incoherent light in noninstantaneous self-focusing media. For this instability to occur, the nonlinearity has to exceed a specific threshold that depends on the coherence properties of the beam. Above this threshold a uniform-intensity partially spatially coherent wave front becomes unstable and breaks up into periodic trains of one-dimensional stripes.

One-dimensional modulation instability of wave packets in media with resonant dispersion

Modulation instability of small-amplitude quasimonochromatic wave packets in media containing compact oscillators is analysed in the one-dimensional case. Conservative media with quadratic nonlinearity and linear nondamped oscillators are considered. Frequency range of unstable wave-packet propagation is found. It is shown that instability results from resonant long-wave-short-wave interaction.

One-dimensional modulational instability in a crossed-field gap.

Cycloidal electron flows in a gap with crossed electric and magnetic fields are found to be violently unstable when a small ac voltage is imposed across the gap. This instability is electrostatic and one dimensional. It occurs over a wide band of frequencies and is insensitive to the precise level of the injected current density. The physical origin of this instability is the formation of a virtual cathode right in front of the cathode. An analytic theory is presented which accurately predicts the onset of the instability in the low-frequency limit.

Vlasov simulation of modulational instability and Langmuir collapse

Vlasov simulations are developed to study the one-dimensional modulational instability and Langmuir collapse in a plasma driven by an external field. Both electrons and ions in the plasma are described by the Vlasov equations. The external driving field energy density is ∼10−3 times the initial electron thermal energy density. The plasma has a mass ratio of mi/me=1836, and a temperature ratio of Ti/Te=0.1 or 1.0, where mi, me, Ti, and Te are the ion mass, electron mass, ion temperature, and electron temperature. The modulational instability is saturated by the formation of Langmuir cavitons which later collapse and burn out due to the strong wave–particle interactions. The particle heating during a single Langmuir collapse is small under this weak driving field. The accelerated electron and ion jet-like streams in phase space as well as the nucleation of cavitons are observed during the evolution. Zakharov equations with the same parameters and similar initial conditions are also simulated, and the results are compared with those of the Vlasov simulations. The two models agree with each other quantitatively up to the first collapse following the saturation of exponential growth; dynamic differences appear after the first collapse.

Dispersive effects on the main-wave modulational instability in free-electron lasers.

The main-wave one-dimensional modulational instability due to the dispersive terms of the wave equation in a free-electron laser is introduced and analyzed. We derive the appropriate dispersion relation and compare its associated growth rate with one due to wave-particle energy exchange alone, as obtained by Davidson and Wurtele under the deep trapping assumption [Phys. Fluids 30, 557 (1987)]. It is found that, depending basically on the relation between some characteristic pa­ rameters, the modulational instability may be governed by wave dispersion. We also discuss the effects of waveguides on these instabilities and the behavior of the unstable modes as a function of the mentioned characteristic parameters. It is known that the initial parametric instability in free-electron lasers (FEL) saturates when particles begin to be trapped in the ponderomotive wells formed by the beatiny of the main electromagnetic wave and the wiggler field. 1• As was discussed by Davidson and Wurtele,2 one essential point is to understand the stability of such a state because, in general, the space-time variation of the main signal may affect its monochromaticity degrading FEL efficiency (of course, we are not talking about a proper tapering of FEL's parameters, which may enhance its gain 3 - 5 ). In the present work, we reconsider the problem of the main-wave stability in the sense defined by Davidson and Wurtele.2 In other words, given an initial steady-state wave, we wish to know if slow perturbations on the phase and amplitude of this wave are unstable functions of time. An important difference, however, will be introduced. Davidson and Wurtele2 discarded ali the slow second derivatives in Maxwell's equations for the main wave based on the reasonable (but not always correct) supposi­ tion that their effect is smaller than the one due to the first derivatives. In their case, the modulational instabili­ ty (MI) was originated by energy exchange between wave and particles. In our treatment we will keep these second derivatives. Putting in another way, we may say that our interest will be the analysis of the instabilities that come out as a combined result of these second derivatives and the already mentioned wave-particle energy exchange. The resultant instability will be called modulational insta­ bility due to kinetic effects (MIK) when the second derivatives are not important. On the opposite limit, when they are decisive in determining the signal of the perturbation squared frequency, the instability will be re­ ferred as due to dispersive effects (MID). Modulational instability due to dispersive effects has been discussed by many authors in many contexts, 6• 7 and here we intend to show under which conditions it may dominate the insta­ bility processes. By definition, two electromagnetic waves A and Aw are present in our system. They are described by the fol­ lowing functions: