Effective equation of nonlinear pulse evolution in a randomly anisotropic medium

Propagation of a light pulse through a weakly inhomogeneous optical fiber is analyzed. The non-linear envelope equation describing the evolution of polarized pulses is determined by statistical properties of inhomogeneities in the optical fiber. The isotropic Manakov system of equations is shown to be applicable in the presence of high-frequency small-scale defects in the fiber. In the presence of only large-scale inhomogeneities, the signal dynamics are described by an anisotropic system of equations.     

Permittivity of a randomly inhomogeneous medium

A theory of permittivity of suspension-type systems is developed that allows one to calculate such optical parameters of inhomogeneous systems as the length of scattering and the transport length. It is shown that, in the Born approximation, which takes into account two-particle correlations in the arrangement of scattering particles, the theoretical and experimental data are in agreement only to within tens of percent. The contribution of three-particle correlations to the permittivity of a system of solid spheres is determined. It is shown that, in describing the optical properties of suspensions with a large difference between the refractive indices of the medium and the particles, it does not suffice to replace the Rayleigh-Gans form factor by the Mie form factor, even under a restriction to two-particle correlations.     

Beam propagation in a randomly inhomogeneous medium

An integrodifferential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the “3/2 law.”     

Elliptically polarized breather in the nonintegrable problem of laser radiation propagation through an isotropic gyrotropic nonlinear medium

A particular analytical solution to the nonintegrable problem of plane electromagnetic wave propagation through an isotropic gyrotropic nonlinear medium is found in the form of elliptically polarized breather. The intensity ratio for the circularly polarized components of this wave, which remains constant during propagation, can be used to determine the ratio of local and nonlocal nonlinear susceptibilities describing the Kerr nonlinearity and its spatial dispersion.     

Radiative energy transfer in a randomly fluctuating medium

The basic laws of the phenomenological theory of radiative energy transfer are derived, under certain conditions, within the framework of the stochastic scalar wave theory. An equation of radiative energy transfer is derived for wave propagation in a statistically quasihomogeneous medium. Our results relate the extinction and scattering coefficients (which are introduced heuristically in the conventional theory of radiative energy transfer) to the stochastic characteristics of the medium.     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Wave propagation in a one-dimensional randomly perturbed periodic medium

We study the variance of the solution of a periodic randomly perturbed one-dimensional Schrödinger operator after propagation through N periods. It is shown that if the frequency of propagation lies inside the band, then the total variance is proportional to Nσ², where σ is the intensity of the white noise. However, if the wave frequency is close to the band edge (where the transfer matrix has a Jordan block structure), the resulting variance is proportional to Nσ^2/3. Thus, propagation becomes highly sensitive to random perturbations.

Numerical simulations reveal that even low noise in a periodic potential can suppress transmission near the band edges and make it strongly irregular inside the band. Further increase of the noise amplitude leads to intermittent behaviour of the transmission coefficient, and makes transmission possible only for a few random frequencies in the band.     

Elastic wave propagation in a randomly stratified solid medium

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.