Propagation of electromagnetic waves in a medium with nonlinear magnetic susceptibility

The interaction of electromagnetic waves in a medium with nonlinear magnetic susceptibility is investigated. On the basis of Tinkham's measurements an antiferromagnet showing a resonance in the submillimeter region is considered as a nonlinear medium. The solution of both the Landau-Lifshitz and Maxwell equations leads to the RHS wave equation. Its solution with boundary conditions shows that the amplitude of the reflected wave from the nonlinear medium on a combined frequency can be non-zero.     

Traveling waves in a nonlinear medium with cubic nonlinearity

Unlike linear nondispersive media, which allow propagation of wave packets of arbitrary forms, nonlinear media admit only certain profiles of traveling waves. Here we examine media with Duffing oscillators, i.e., with bound electrons for which an equilibrium disturbance causes forces proportional to the first and third powers of deviation. We show that the linearly polarized traveling plane waves such media can transmit have profiles modulated as Jacobi elliptic functions. When discussing propagation across an interface between different media, only incidence from the side of the linear medium is considered. Even in this case, to launch a traveling wave in the nonlinear medium, a severe restriction must be imposed on the incident wave’s amplitude.     

Modulation instability in systems of coupled waves with nonlinearity dispersion

Conditions for the appearance of modulation instability of an optical wave packet formed by one or two unidirectional strongly interacting waves are studied taking into account the influence of the temporal dispersion of a nonlinear response of the medium on this process. The regions of values of the frequency, input radiation intensity, and dispersion parameters in which the wave perturbations are increased are found. It is shown that the initial conditions for excitation of optical fibers of this type significantly affect the dynamics of the modulation instability.     

Multiple fragmentation of wave packets in a nonlinear medium with normal dispersion of the group velocity

The features of the dynamics of the self-ffects of the wave field are considered for the case when the dynamics is described by the nonlinear Schrodinger equation (NSE) with a hyperbolic spatial operator. An analytical investigation of the characteristic regimes of the self-effects is carried out; these regimes are due to the spatial competition of the self-focusing compression of the wave packet in one direction and its defocusing in another. The initial distributions of the wave field are analyzed with the goal of using them in a numerical modeling for illustration of the features of the self-effects. It is shown that three stages can be discerned in the evolution of the localized distributions: self-focusing filamentation of the wave field in the transverse direction, and compression and subsequent fragmentation in the defocusing (longitudinal) direction. The strongest non-uniformities are excited in the self-similar collapse of the wave field to hyperbolas (to the characteristic curves of the hyperbolic operator of the NSE). The stabilization of the development of the fragmentation instability is discussed separately.     

Effects of group-velocity mismatch and cubicquintic nonlinearity on cross-phase modulation instability in optical fibers

The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinearity plays a role similar to the case of neglecting the group-velocity mismatch in modifying the modulation instability, namely, the positive and negative quintic nonlinearities can still enhance and weaken the modulation instability, respectively. The group-velocity mismatch can considerably change the gain spectrum of modulation instability in terms of its shape, peak value, and position. In the normal dispersion regime, with the increase of the group-velocity mismatch parameter,the gain spectrum widens and then narrows, shifts to higher frequencies, and the peak value gets higher before approaching a saturable value. In the abnormal dispersion regime, two separated spectra may occur when the group-velocity mismatch is taken into account. With the increase of the group-velocity mismatch parameter, the peak value of the gain spectrum gets higher and shorter before tending to a saturable value for the first and second spectral regimes, respectively.     

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 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.     

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.     

Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearity

The dynamics of localized waves is analyzed in the framework of a model described by the Korteweg-de Vries (KdV) equation with account made for the cubic positive nonlinearity (the Gardner equation). In particular, the interaction process of two solitons is considered, and the dynamics of a “breathing” wave packet (a breather) is discussed. It is shown that solitons of the same polarity interact as in the case of the Korteweg-de Vries equation or modified Korteweg-de Vries equation, whereas the interaction of solitons of different polarity is qualitatively different from the classical case. An example of “unpredictable” behavior of the breather of the Gardner equation is discussed.     

Regime of wave-packet self-action in a medium with normal dispersion of the group velocity

Peculiar features of the self-action of non-one-dimensional wave packets described by the nonlinear Schrodinger equation with a hyperbolic spatial operator were studied analytically and numerically. It was shown that the self-action dynamics is determined by the consequence of the processes of transverse self-focusing filamentation and longitudinal splitting. Splitting scenarios were classified. It is shown that the strongest inhomogeneities are excited along "hyperbolas" in the self-similar collapse process.     

On the collapse of wave packets in a medium with normal group velocity dispersion

A solution to the problem of realizing the collapse of three-dimensional wave packets in nonlinear media with normal group velocity dispersion is proposed. Wave packets with pronounced hyperbolic topology are shown to collapse; i.e., the field increases infinitely near the system axis. In particular, wave collapse of the tubular axisymmetric packets occurs through the concentration of the compressed ring field distribution at the axis. The collapse is shown to stabilize due to the saturation of nonlinearity or nonlinear dissipation, which restrict the field increase and lead to the packet splitting in the transverse direction.     

Radiation of slow electromagnetic waves in an isotropic medium with spatial dispersion

This paper discusses the distinctive features of radiation of electromagnetic waves with anomalously large values of the wave vector and small phase velocity that exist near narrow absorption lines. The distribution of radiated energy with respect to angle and frequency is calculated for Čerenkov radiation and bremsstrahlung of the slow waves. It is shown that the angular distribution of the slow-wave bremsstrahlung exhibits a characteristic maximum in the direction perpendicular to the plane of motion of the particles. Zh. éksp. Teor. Fiz. 112, 1557–1562 (November 1997)     

Compton散射对五阶非线性下零色散附近调制不稳定性的影响

应用多光子非线性Compton散射模型和非线性薛定谔方程,研究了Compton散射对五阶非线性零色散附近调制不稳定性的影响.将入射光和Compton散射光作为产生调制不稳定性的机制,分析了光纤损耗、四阶色散和五阶非线性对增益谱的影响.结果表明:散射下的正或负五阶非线性分别使零色散附近的增益谱宽和峰值比散射前增大得更大或...     

Nonlinear equations for quasi-monochromatic waves near a caustic in a dispersive dissipative medium with cubic or quadratic nonlinearity

The behavior of a quasi-monochromatic nonlinear wave near a caustic is considered. Nonlinear ordinary differential equations for a dispersive dissipative medium with a cubic or quadratic nonlinearity are derived. For the latter medium, nonstationary equations describing it near the caustic are presented with allowance for the dissipative dispersive terms. These equations yield ordinary ones for quasi-monochromatic waves. The amplitude of the second harmonic is expressed in terms of the squared amplitude of the first harmonic. The amplitude of the second harmonic, as well as the solution as a whole, increases near the caustic.     

Amplification of solitary optical waves in fibers with positive group velocity dispersion

Solitary optical waves with characteristic red frequency shift have been numerically identified in fibers with positive group velocity dispersion in the presence of amplification by semiconductor amplifiers. Influence of the Henry factor, the net gain, gain saturation characteristics, and frequency modulation on the frequency shift of the observed solitary optical waves has been examined. Normalized pulse energy as a function of the gain saturation characteristics has been studied.      

Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity

We derive model equations for the propagation of ultrashort pulses in materials with resonant linear and quadratic nonlinear responses and find approximate soliton solutions describing all-bright and dark-bright polaritons. We report the specific phase matching condition for efficient 2nd harmonic generation, which involves detuning from the resonance. We also demonstrate that the 2nd harmonic emission by the polaritonic pulses can lead to reduction of their group velocity, having zero as a theoretical limit. Our analytical results are supported by numerical simulations.     

Molecules with a permanent dipole moment in a periodic medium with quadratic nonlinearity

Nonlinear optical effects in a one-dimensional periodic medium containing spatially oriented molecules of J aggregates of a dye and silver nanoparticles are studied. It is shown that, in such composite medium, the presence of a permanent dipole moment of an exciton transition of molecules of J aggregates results in the appearance of new nonlinear optical properties.