Intensity statistics in a long random fiber Raman laser

We study the output emission statistics of a random continuous-wave Raman fiber laser. The signal evolution is governed by a generalized nonlinear Schrödinger equation (NLSE) with inserted gain. The statistics are close to the Rayleigh one, and the deviations are caused by the Kerr nonlinearity. To characterize the deviations, we analytically find the mean of the squared output signal intensity, based on the kinetic theory. We show qualitative agreement with available experimental data and supplement the results with numerical calculations. With the limit of small gain, the kinetic theory gives a finite answer for the mean of squared intensity in the first and the second order with respect to small nonlinearity. The result is consistent with the fact that the NLSE is integrable in the case of zero gain and is applicable to any generalized NLSE if the inserted terms are effectively small.

Effects of thin film and Stokes drift on the generation of vorticity by surface waves

Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [Phys. Rev. Lett. 116, 054501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.054501]. Here we study how a thin (monomolecular) film presented on the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case of liquid with a free surface, and the parameter is the quality factor of surface waves up to numerical factor. We also discuss the PIV experimental scheme intended to observe the generated vorticity and find that Stokes drift influences the measured velocity field. Explicit expression for the vertical vorticity was obtained.

Nonlinear Generation of Vorticity by Surface Waves

We demonstrate that waves excited on a fluid surface produce local surface rotation owing to hydrodynamic nonlinearity. We examine theoretically the effect and obtain an explicit formula for the vertical vorticity in terms of the surface elevation. Our theoretical predictions are confirmed by measurements of surface motion in a cell with water where surface waves are excited by vertical and harmonic shaking the cell. The experimental data are in good agreement with the theoretical predictions. We discuss physical consequences of the effect.

Wave kinetics of random fibre lasers

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example-random fibre laser-we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Wrinkling of vesicles during transient dynamics in elongational flow

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.

Dynamics of nearly spherical vesicles in an external flow

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.

Interaction of solitons through radiation in optical fibers with randomly varying birefringence

Propagation of solitons in optical fibers is studied taking into account the polarization mode dispersion (PMD) effect. We show that the soliton interaction caused by the radiation emitted by solitons due to the PMD disorder leads to soliton jitter, and we find its statistical properties. The theoretical predictions are justified by direct numerical simulations.

Radiation-induced interaction of optical solitons in fibers with randomly varying birefringence

We study propagation of solitons in optical fibers with randomly varying birefringence which results in polarization mode dispersion. Due to the disorder, solitons emit radiation, i.e., the energy of the solitons is partly transferred into the delocalized modes. The radiation serves as a mediator of the intersoliton interaction leading to fluctuations of the soliton separations. We establish statistics of the fluctuations which is found to be sensitive to the phase mismatches and mutual polarizations of the solitons, and independent of the soliton separation. The theoretical results are justified by direct numerical simulations.