Waves In Nonlinear Media Research Articles

Multiple scales analysis of wave–wave interactions in a cubically nonlinear monoatomic chain

The interaction of waves in nonlinear media is of practical interest in the design of acoustic devices such as waveguides and filters. This investigation of the monoatomic mass–spring chain with a cubic nonlinearity demonstrates that the interaction of two waves results in different amplitude and frequency dependent dispersion branches for each wave, as opposed to a single amplitude-dependent branch when only a single wave is present. A theoretical development utilizing multiple time scales results in a set of evolution equations which are validated by numerical simulation. For the specific case where the wavenumber and frequency ratios are both close to 1:3 as in the long wavelength limit, the evolution equations suggest that small amplitude and frequency modulations may be present. Predictable dispersion behavior for weakly nonlinear materials provides additional latitude in tunable metamaterial design. The general results developed herein may be extended to three or more wave–wave interaction problems.

Filamentation processes and dynamical excitation of light condensates in optical media with competing nonlinearities

We analyze both theoretically and by means of numerical simulations the phenomena of filamentation and dynamical formation of self-guided nonlinear waves in media featuring competing cubic and quintic nonlinearities. We provide a theoretical description of recent experiments in terms of a linear stability analysis supported with simulations, showing the possibility of experimental observation of the modulational instability suppression of intense light pulses travelling across such nonlinear media. We also show a novel mechanism of indirect excitation of {\em light condensates} by means of coalescence processes of nonlinear coherent structures produced by managed filamentation of high power laser beams.

Quasi-stationary form of the spectrum of intense seismic waves at the surface of the ground

Transformations of spectra of intense seismic waves propagating in ground columns are studied in numerical experiments. It was found that transformation of spectra to the form E ( f ) ~ f – k in the ground occurs due to nonlinear (hysteresis) energy dissipation and redistribution of the energy of oscillations in the spectrum by means of interaction between waves. Emphasizing the low-frequency components agrees with the Manley‐Row relations of decay instability, according to which energy transport of low-frequency oscillations to high-frequency oscillations is hampered, but decay of high-frequency oscillations and transport of their energy to low-frequency oscillations is facilitated. The authors of papers [1, 2] devoted to accelograms of earthquakes in 1995 in Kobe and 2000 in Tottori (Japan), which were recorded by borehole seismic groups, developed numerical models of the behavior of ground layers in situ; i.e., they estimated the stresses and strains excited by strong motions in the upper ~100 m of the ground. The numerical models describe the behavior of ground layers in ten 1.5-s time intervals during 15 strong motions. The authors of [3] used these models in numerical experiments to study the propagation of intense noise (transverse) waves in the ground layers. The obtained results characterize the statistical phenomena observed during the propagation of intense seismic waves in nonlinear media (the near-surface ground). The interactions between individual spectral components lead to multiplication of spectral lines, nonlinear widening of spectra, and the appearance of a constant component of the seismic field. Figure 1 illustrates transformation of the spectra of intense seismic waves propagating in the ground layers: the results of testing the numerical models are presented for the behavior of the ground in Port Island and the SJK site (a conventional name of the location of vertical groups) during the Kobe earthquake 1995 by the Gaussian white noise (the duration of test signals was chosen to be sufficiently large (~40 min) to obtain smooth spectra; their intensity was chosen so that the stresses and strains excited in the ground coincided on average with the stresses and strains generated during earthquakes to estimate the degree of the response of the ground to earthquakes). The results are presented for five 1.5-s intervals (first, third, …) among ten intervals studied. It is seen in the figure that the spectra of oscillations at the surface take a form close to E ( f ) ~ f – k . In the layers at intermediate depths (16 and 32 m in Port Island; 24.9 m in SJK), the forms of spectra demonstrate a resonance intensification of individual components. Interaction between spectral components takes place along with the resonance intensification. Highand low-frequency combination harmonics are formed. The energy of the propagating seismic waves is redistributed over the spectral band. The spectral peaks are smoothed, and the resulting spectrum of the signal at the surface of the ground tends to obtain the limiting form E ( f ) ~ f – k . Relative deformations in the ground at both points reached ~10 ‐3 in the surface layers and

Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. That is the result of strong transverse selection of spontaneously arising optical fields in optical parametric generator pumped by Bessel beam due to transverse phase-matching of interacting waves in nonlinear medium. A qualitative agreement of theoretical predictions with experimental results is obtained.

On weakly nonlinear waves in media exhibiting mixed nonlinearity

We obtain the transport equations governing small amplitude high frequency disturbances, that include both quadratic and cubic nonlinearities inherent in hyperbolic systems of conservation laws. The coefficients of the nonlinear terms in the transport equation are obtained in terms of the Glimm interaction coefficients. For symmetric and isotropic systems the mean curvature of the wave front, which appears as the coefficient of the linear term in the transport equation, is shown to be related to the derivative of the ray tube area along the bicharacteristics; the amplitude of the disturbance is shown to become unbounded in the neighborhood of the point where the ray tube collapses. We also obtain a formula, akin to the one obtained by R. Rosales (1991), for the energy dissipated across shocks.

Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media

It is shown that the Wigner formalism for describing propagation of partially incoherent waves in nonlinear media with slow medium response is equivalent to previously established methods based on coherent density theory, self-consistent multi-mode theory and the mutual coherence function approach.

On the velocity of propagation of a signal in nonlinear optical media

The maximum velocity of propagation of a signal, which is defined as the velocity of propagation of the wave front, is considered for electromagnetic waves in nonlinear media. It is shown that the magnitude of velocity is determined to a considerable extent on the form of the constitutive equation defining the relation between the polarization of the medium with the radiation field strength. In the noninertial nonlinearity model, this velocity may be smaller (in media with self-focusing nonlinearity) or larger (defocusing nonlinearity) than the velocity of light in vacuum. For real nonlinear media, for which the inertia of their response is taken into account, the wave front velocity coincides with the velocity of light in vacuum.

Numerical Treatment of short Laser Pulse Compression in transient stimulated Brillouin Scattering

Results of numerical investigation of the compression process of short pulses during essentially nonstationary SBS are presented, taking into account the diffraction and focusing of the interacting light beams and the finite oscillation period and lifetime of hypersound waves in nonlinear media.

Nonlinear atomic Fabry-Perot interferometer: From the mean-field theory to theatom blockadeeffect

We have investigated nonlinear atom optical effects which arise from atom-atom collisional interactions in a single-mode atomic Fabry-Perot cavity driven by a coherent cw atom laser beam. When the nonlinear interaction energy per single atom is small, the exact numerical solution of the master equation is well reproduced by a mean-field treatment in which quantum fluctuations are included linearizing the stochastic equations of the Positive-P representation. On the other hand, when the damping of the cavity mode is very weak and its wave-function is tightly confined in space, a regime of strong nonlinearity can be achieved. For the specific case of an incident atom laser frequency at resonance with the empty cavity, the numerical calculations predict a sort of atom blockade effect, which is a sort of atom optical analog of the well-known Coulomb blockade effect of electronic transport through microscopic structures: only one atom can occupy the cavity mode at a time and the statistical properties of the transmitted beam, being very similar to the resonance fluorescence from a single two-level system, show definitely nonclassical behaviors such as antibunching. Only at very large incident intensities, more than one atom can be simultaneously forced inside the cavity mode: in this regime, the results of the numerical calculations can be successfully interpreted using a dressed cavity model. From the formal analogy between atomic matter waves and optical light waves in nonlinear media, it follows that the same results hold for photonic systems.

Study of Parallel Pumping of Magnetoelastic Waves in an Antiferromagnetic FeBO3

Parallel pumping of magnetoelastic waves in the sample of FeBO 3 placed in a helix microwave resonator was studied. The resonator is shown to play an important role in the process of parametric excitation of quasiphonon pairs at once above the threshold of pumping. The phenomenon of coupled oscillations of electromagnetic mode of resonator and parametric pair of excited waves is investigated in detail. In order to get correct measurements of absorbed microwave power the equivalent circuit is proposed. We constructed the theory of parametric excitation of waves in nonlinear medium mounted in a resonator and obtained a good agreement with experimental data.

Application of the material-independent PML absorbers to the FDTD analysis of electromagnetic waves in nonlinear media

To more accurately and effectively simulate waves propagating in nonlinear media with the finite-difference time-domain (FDTD) method, a material-independent perfectly matched layer (MIPML) absorber is proposed. Within this absorber, electric displacement D and magnetic field H are directly absorbed, whereas electric field E is simultaneously absorbed through the relation of D and E. It is shown that, with the help of this MIPML absorber, Berenger's PML can be simply and effectively extended to nonlinear media. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 164–168, 1998.

Application of the material‐independent PML absorbers to the FDTD analysis of electromagnetic waves in nonlinear media

Application of the material‐independent PML absorbers to the FDTD analysis of electromagnetic waves in nonlinear media

Direct and inverse scattering for transient electromagnetic waves in nonlinear media

Nonlinear propagation of electromagnetic waves is an important problem in optics. Often the properties of the nonlinear media are not fully understood. The solution of an inverse problem can provide an aid to that understanding. An inverse transmission problem is posed; it is one of reconstructing the medium parameters, by measurement of a wave that has been propagated through the nonlinear medium. The nonlinear medium is assumed to be homogeneous and isotropic. The methods have application to nonlinear optics, and the numerical results for both the direct and inverse problems presented are based on the nonlinear Kerr effect, which is observed in the optical wavelength band. However, the mathematical techniques that are developed are applicable to any set of nonlinear first-order equations. The method is therefore model independent.

Self-focusing dynamics of nonlinear waves in media with parabolic-type inhomogeneities

The possibility of accelerating the self-focusing dynamics of light beams in nonlinear and dispersive media with either a constant or a weakly oscillating parabolic density profile is investigated. It is shown that the self-compression of wave packets, that freely self-focus in homogeneous media, can be enhanced by the action of appropriate parabolic inhomogeneities, whose lensing influence shortens the focal time of the wave. A similar property also occurs when the scalar envelope of a nonlinear waveform interacts with a uniform external magnetic field. The motion of light beamlets, originating from the filamentation instability of an incident beam, is analytically described for inhomogeneous media with focusing and defocusing density profiles.

Defocusing regimes of nonlinear waves in media with negative dispersion.

Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schr{umlt o}dinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called {ital critical} dimension cannot collapse in finite time in the sense that their transverse (anomalously dispersing) and longitudinal (normally dispersing) extensions never vanish. Solutions defined at the {ital supercritical} dimension are proved to exhibit a nonvanishing mean longitudinal size, and cannot transversally collapse if they are assumed to shrink along each spatial direction. {copyright} {ital 1996 The American Physical Society.}

Transverse instability of counterpropagating waves in photorefractive media.

The transverse instability of counterpropagating waves in nonlinear media with a photorefractive or Kerr-type nonlinearity is studied. The problem is formulated for a sluggish nonlinear medium that responds much slower than the optical frequency. In this limit, a general dispersion relation, valid for arbitrary longitudinal variation of the optical intensities, is obtained and solved numerically for several representative cases. It is found that, while photorefractive media provide sufficient nonlinear coupling for the observation of transverse instabilities, such observations may be difficult due to the presence of strong amplified incoherent scattering (fanning) in photorefractive media.

Time-domain Fourier transform holography and possible applications in signal processing

The principles of holographic storage and the reconstruction of short light pulses based on spatial spectral decomposition of radiation are described. This method may be designated as time-domain Fourier transform holography or spectral holography. Also described are various transformations of optical time signals based on holographic spectral filtering and dynamic interaction of spectral decomposition waves in nonlinear media. A system of methods of time signal processing based on spectral holography is proposed. Among these methods are shaping optical pulses, space-time conversions of signals, matched filtering, and recognition oftime optical signals. In addition, the possibilities for realizing time-division multiplexing of data streams using dynamic spectral holography are shown.

The effect of acoustic diffraction and acoustic attenuation on the dynamic range of acoustooptic Bragg cells

A three-dimensional model for the propagation of finite acoustic waves in nonlinear media is developed. This model implicitly includes the effects of acoustic attenuation and divergence due to diffraction. The generation of intermodulation products in the case of a two-tone input signal is numerically analyzed. It is found that acoustic diffraction can have a significant effect on the dynamic range of a Bragg cell if the acoustic field extends well into the Fraunhofer region. Inclusion of the effect of diffraction in the model predicts a dynamic range that can be considerably larger than the value obtained by using the infinite plane wave assumption. It is shown that acoustic attenuation significantly reduces the level of the acoustic intermodulation products relative to the level of the fundamental modes. This also increases the dynamic range. The influence of these effects on design considerations for Bragg cells is discussed.

Instability of almost opposite mutually noncoherent waves in nonlinear media with a local transient response

The instability thresholds were found for almost opposite waves whose interference pattern could not be recorded by a medium utilizing a transient optical nonlinearity of the local type. Pairs of waves with an angular shift relative to the direction opposite to the pump radiation were generated.

Solitary waves in nonlinear media with gain and loss

Evolution of solitary waves in nonlinear media that include gain and two-photon absorption is investigated. Stationary propagation of solitary waves is shown to be possible in the media for any gain and loss; nevertheless, it is limited within a finite distance due to the intrinsic characteristic of instability of the waves.