高阶色散和指数饱和非线性光纤的调制不稳定性

采用线性稳定性分析法,解析和计算了指数饱和非线性和高阶色散光纤中的调制不稳定条件和增益谱。结果表明:当二阶和四阶色散同为负时,随着参数的不同,增益谱可能只有一个谱区,也可能出现两个分离的谱区;当二阶和四阶色散分别为正和负时,无调制不稳定性;在其它色散区,则只有一个谱区。指数饱和非线性可能使各谱区的谱宽、峰值增益随入纤功率的增大呈现出先增大后减小的特点,即出现两个不同的输入功率对应同一个不稳定增益峰值和谱宽的情形。在其它参数相同时,指数饱和非线性下增益谱的谱宽和峰值增益随入纤功率的变化速度将比传统饱和非线性更快。     

Dynamics of coupled waves in optical waveguides with longitudinally distributed dispersion and nonlinearity parameters

The dynamics of a two-wave pulse in an optical waveguide with longitudinally distributed dispersion and nonlinearity parameters subject to linear and cross-modulation coupling of the waves is studied. The duration of the traveling pulse and the rate of its frequency modulation as functions of the longitudinal coordinates are derived for different nonlinearity and group velocity dispersion profiles.     

Modulation instability of magnetostatic waves in a magnetically coupled two-layer structure

Modulation instability of direct bulk magnetostatic waves in structures consisting of two magnetically coupled planar films separated by a nonmagnetic layer is studied. It is found that, depending on the type of excitation of the waveguide modes, mode coupling can either change the characteristics of the modulation wave instability or ensure their stability with respect to the corresponding perturbations by affecting the dispersion properties of the structure.     

Modulational instability in systems with integrating nonlinearity

A new type of modulational instability for coherent as well as partially coherent light in systems with integrating nonlinearity caused by an irreversible process is investigated both experimentally and theoretically. In such systems plane waves never reach the stationary limit and exhibit a nontrivial time dependence resulting in new features of the modulational instability. For example, the modulational frequency of the nonexponentially increasing perturbation with maximum gain decreases while the wave is propagating. The threshold for vanishing modulational instability due to a finite degree of spatial coherence depends only on system parameters and not on the light intensity.     

Modulation instability in a medium with a nonlocal nonlinearity

The general conditions of appearance of the modulation instability of spatially homogeneous regimes in media with a nonlocal response of nonlinearity are determined. By using, as an example, the nonlocality in the form of the truncated Lennard-Jones potential, which is characteristic of interatomic interaction in Bose-Einstein condensates, the region of stability is found and the character of structures arising upon the loss of stability is discussed.     

饱和非线性正折射异向介质中的调制不稳定性

直接从异向介质中包含饱和非线性、自陡峭和二阶非线性色散效应的非线性扩展传输方程出发,采用线性稳定性分析法,导出了调制不稳定性的色散关系、不稳定条件、无量纲的临界扰动频率和增益谱。计算和讨论了异向介质正折射区无量纲的增益谱随归一化角频率和入射功率密度的变化关系。结果表明,在异向介质正折射区,随归一化角频率和入射功率密度的不同,增益谱将会出现扰动频率大于零、扰动频率大于某个非零临界值、扰动频率大于零而小于某个非零临界值3种形式。在归一化角频率较小时,调制不稳定性可能出现阈值入射功率密度;且在较小的入射功率密度时,调制不稳定性只能出现在大于某个临界频率时。     

Acoustic waves in media with hysteretic nonlinearity and linear dispersion

A hysteresis equation of state is proposed for polycrystalline solids with saturation of nonlinear losses. Effects of amplitude-dependent internal friction and higher harmonic generation that result from propagation of harmonic acoustic waves in rods made of such materials are theoretically and numerically studied.     

Modulation instability of whistler waves

The Karpman and Krushkal criterion has been applied to nonlinear Schrödinger equation derived for whistler waves propagating through magnetoplasma containing parallel electrostatic field. The role of parallel electrostatic field on the frequency spectrum and growth rate of modulational instability has been discussed.     

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.     

Modulation instability of broad optical beams in nonlinear media with general nonlinearity

The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.     

Modulational instability of incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity

The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor to spatial optical soliton formation, modulational instability can be adjusted and controlled by the wavelength combinations of the signal and background beams. We also discuss the dependences of strength of modulational instability on intensities of two signal beams and background beam. These findings make it possible to predict the formation of incoherently coupled soliton pairs in azobenzene-containing polymer.     

Modulational instability of matter waves under strong nonlinearity management

We study modulational instability of matter-waves in Bose-Einstein condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an optical lattice and homogeneous BEC are considered in the framework of the Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in an optical lattice, it is shown that the loop formed on a dispersion curve undergoes transformation due to the nonlinearity-management. A critical strength for the nonlinearity-management strength is obtained that changes the character of instability of an attractive condensate. MI is shown to occur below (above) the threshold for the positive (negative) effective mass. The enhancement of number of atoms in the nonlinearity-managed gap soliton is revealed.     

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.     

Modulation instability of femtosecond pulses in fibres with slowly decreasing dispersion

In this paper,we investigate the modulation instability for generating femtosecond pulses in fibres with slowly decreasing dispersion.Higher-order dispersion and higher-order nonlinear effects are taken into account when the continuous wave or quasi-continuous wave evolves into sub-picosecond and femtosecond pulses by modulation instability in the optical fibres.Our research results show that the gain spectrum of the dispersion-decreasing fibres is much wider than that in conventional fibres.The third-order dispersion effect has no contribution to gain spectrum,while the self-steepening effect reduces the maximum value and gain bandwidth,and the Raman self-scattering effect widens the extent to which the modulation instability occurs.     

Modulation instability in negative refractive metamaterials with exponential saturable nonlinearity and self-steepening effects

Modulation instability (MI) in negative refractive metamaterials with exponential saturable nonlinearity and the self-steeping effect is investigated by using the standard linear stability analysis and the Drude electromagnetic model. The dispersion relation, instability condition, cut-off frequency, gain spectrum, and their corresponding dimensionless expressions are analytically deduced and then calculated. The results show that, the self-steepening effect will suppress MI by decreasing the cut-off frequency and the maximum gain. And the larger the power density ratio is, more slowly the cut-off frequency and the maximum gain decrease with increase of the self-steepening parameter. Although the sign of the self-steepening parameter does not influence MI but its absolute value must be smaller than a certain value. Depending on different self-steepening parameters, the cut-off frequency and maximum gain may decrease or increase before decrease with increase of the power density ratio. In particular, for large self-steepening parameters, the power density ratio may have a threshold value. When the power density ratio is under this threshold, MI will disappear.     

Cross-phase modulational instability in an elliptical birefringent fiber with higher order nonlinearity and dispersion

We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.     

Modulation instability of ion-acoustic waves in a multi-ion plasma

A nonlinear Schrödinger equation for ion-acoustic waves in a collision-free plasma, consisting of a mixture of two cold ion species and hot isothermal electrons is derived using the KBM method. It is used to discuss the modulation instability in which the effect of the light-on concentration is analysed. We find that the unstable region depends sensitively upon the fraction of light-ion concentration (α) and the ion-mass ratio. An approximate relation for α_critical is derived for a given ion species in terms of the ion-mass ratio, which governs the minimum wave number, below which the carrier wave is stable against the modulational instability.     

Effect of the group velocity mismatch and dispersion of nonlinear susceptibility on the modulation instability of electromagnetic waves in a medium with quadratic nonlinearity

Modulation instability of continuous plane waves of the pump beams and the second harmonic that are described by the set of equations for the process of second-harmonic generation with allowance made for the dispersion of nonlinear susceptibility is considered. The case of type I phase matching is analyzed. In the regions of anomalous and normal group velocity dispersion, the instability increments are determined as functions of the frequency and the wave numbers of perturbations. It was found that the difference in the group velocities of the interacting waves exerts the most substantial effect on the evolution of the modulation instability.     

Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion

Modulational instability (MI) of electromagnetic waves in a birefringent fiber with a periodic dispersion (two-step dispersion management scheme) is investigated. The properties of new sidebands are studied. The strong variation of dispersion leads to the decreasing of the main MI region and the suppression of additional resonance. In the random dispersion case the MI of all frequencies of modulation in the normal dispersion region is predicted. In the anomalous dispersion case the decreasing of the main MI peak is calculated and changes in the spectral bandwidth of MI gain are found. The analytical predictions are confirmed by the numerical simulations of the full coupled nonlinear Schr?dinger equations with periodic coefficients.