arXiv subjects

Avner Peleg

Publications and source records attributed to Avner Peleg.

29 records · Page 2Linked to original sources

arXiv2010

Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission

We study the deterministic effects of Raman-induced crosstalk in amplified wavelength division multiplexing (WDM) optical fiber transmission lines. We show that the dynamics of pulse amplitudes in an N-channel transmission system is described by an N-dimensional predator-prey model. We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. The stability is independent of the exact details of the approximation for the Raman gain curve. Furthermore, we investigate the impact of cross phase modulation and Raman self and cross frequency shifts on the dynamics and establish the stability of the equilibrium state with respect to these perturbations. Our results provide a quantitative explanation for the robustness of differential-phase-shift-keyed WDM transmission against Raman crosstalk effects.

physics.optics↗

arXiv2009

Diverging probability density functions for flat-top solitary waves

We investigate the statistics of flat-top solitary wave parameters in the presence of weak multiplicative dissipative disorder. We consider first propagation of solitary waves of the cubic-quintic nonlinear Schrödinger equation (CQNLSE) in the presence of disorder in the cubic nonlinear gain. We show by a perturbative analytic calculation and by Monte Carlo simulations that the probability density function (PDF) of the amplitude $η$ exhibits loglognormal divergence near the maximum possible amplitude $η_{m}$, a behavior that is similar to the one observed earlier for disorder in the linear gain [A. Peleg et al., Phys. Rev. E {\bf 72}, 027203 (2005)]. We relate the loglognormal divergence of the amplitude PDF to the super-exponential approach of $η$ to $η_{m}$ in the corresponding deterministic model with linear/nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSE with weak disorder in the linear gain both the amplitude and the group velocity $β$ become random. We therefore study analytically and by Monte Carlo simulations the PDF of the parameter $p$, where $p=η/(1-\varepsilon_sβ/2)$ and $\varepsilon_s$ is the self-steepening coefficient. Our analytic calculations and numerical simulations show that the PDF of $p$ is loglognormally divergent near the maximum $p$-value.

nlin.PS↗

arXiv2009

Energy exchange in fast optical soliton collisions as a random cascade model

We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the τ_{q} exponents from multifractal theory and by the Cramér function S(x). We find that the n-th moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of τ_{q} or S(x).

nlin.PS↗

arXiv2007

Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems

We study the combined effect of delayed Raman response and bit pattern randomness on pulse propagation in massive multichannel optical fiber communication systems. The propagation is described by a perturbed stochastic nonlinear Schrödinger equation, which takes into account changes in pulse amplitude and frequency as well as emission of continuous radiation. We perform extensive numerical simulations with the model, and analyze the dynamics of the frequency moments, the bit-error-rate, and the mutual distribution of amplitude and position. The results of our numerical simulations are in good agreement with theoretical predictions based on the adiabatic perturbation approach.

nlin.PS↗

arXiv2006

Scintillation reduction by use of multiple Gaussian laser beams with different wavelengths

We study the scintillation index of N partially overlapping collimated lowest order Gaussian laser beams with different wavelengths in weak atmospheric turbulence. Using the Rytov approximation we calculate the initial beam separation that minimizes the longitudinal scintillation. Further reduction of the longitudinal scintillation is obtained by optimizing with respect to both beam separation and spot size. The longitudinal scintillation of the optimal N-beam configurations is inversely proportional to N, resulting in a 92% reduction for a 9-beam system compared with the single beam value. The radial scintillation values for the optimal N-beam configurations are significantly smaller than the corresponding single beam values.

physics.optics↗

arXiv2006

Scintillation index for two Gaussian laser beams with different wavelengths in weak atmospheric turbulence

We study propagation of two lowest order Gaussian laser beams with different wavelengths in weak atmospheric turbulence. Using the Rytov approximation and assuming a slow detector we calculate the longitudinal and radial components of the scintillation index for a typical free space laser communication setup. We find the optimal configuration of the two laser beams with respect to the longitudinal scintillation index. We show that the value of the longitudinal scintillation for the optimal two-beam configuration is smaller by more than 50% compared with the value for a single lowest order Gaussian beam with the same total power. Furthermore, the radial scintillation for the optimal two-beam system is smaller by 35%-40% compared with the radial scintillation in the single beam case. Further insight into the reduction of intensity fluctuations is gained by analyzing the self- and cross-intensity contributions to the scintillation index.

physics.optics↗

arXiv2006

Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems

We investigate the effects of delayed Raman response on pulse dynamics in massive multichannel optical fiber communication systems. Taking into account the stochastic nature of pulse sequences in different frequency channels and the Raman induced energy exchange in pulse collisions we show that the pulse parameters exhibit intermittent dynamic behavior, and that the pulse amplitudes exhibit relatively strong and long-range correlations. Moreover, we find that the Raman-induced cross frequency shift is the main intermittency-related mechanism leading to bit pattern deterioration and evaluate the bit-error-rate of the system.

physics.optics↗

arXiv2002

Phase ordering with a global conservation law: Ostwald ripening and coalescence

Globally conserved phase ordering dynamics is investigated in systems with short range correlations in the initial condition. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are found under which the sharp-interface limit of this equation is reducible to the area-preserving motion by curvature. Numerical simulations show that, for both critical and off-critical quench, the equal time pair correlation function exhibits dynamic scaling, and the characteristic coarsening length obeys a power law in time with a 1/2 exponent. For the critical quench, our results are in excellent agreement with earlier results. For off-critical quench (Ostwald ripening) we investigate the dynamics of the size distribution function of the minority phase domains. The simulations show that, at large times, this distribution function has a self-similar form with growth exponent 1/2. The scaled distribution, however, strongly differs from the classical Wagner distribution. We attribute this difference to coalescence of domains. A new theory of Ostwald ripening is developed that takes into account binary coalescence events. The theoretical scaled distribution function agrees very well with that obtained in the simulations.

cond-mat.stat-mech↗

arXiv2001

Area-preserving dynamics of a long slender finger by curvature: a test case for the globally conserved phase ordering

A long and slender finger can serve as a simple ``test bed'' for different phase ordering models. In this work, the globally-conserved, interface-controlled dynamics of a long finger is investigated, analytically and numerically, in two dimensions. An important limit is considered when the finger dynamics are reducible to the area-preserving motion by curvature. A free boundary problem for the finger shape is formulated. An asymptotic perturbation theory is developed that uses the finger aspect ratio as a small parameter. The leading-order approximation is a modification of ``the Mullins finger" (a well-known analytic solution) which width is allowed to slowly vary with time. This time dependence is described, in the leading order, by an exponential law with the characteristic time proportional to the (constant) finger area. The subleading terms of the asymptotic theory are also calculated. Finally, the finger dynamics is investigated numerically, employing the Ginzburg-Landau equation with a global conservation law. The theory is in a very good agreement with the numerical solution.

cond-mat.dis-nn↗

arXiv2000

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.

cond-mat.dis-nn↗

arXiv2000

Dynamics of fractal dimension during phase ordering of a geometrical multifractal

A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at $t=0$ represents a non-uniform recursive fractal set, and that this set is a geometrical multifractal characterized by a $f(α)$-curve. It is assumed that the droplets shrink according to their size and preserving their ordering. It is shown that at early times the Hausdorff dimension does not change with time, whereas at late times its dynamics follow the $f(α)$ curve. This is illustrated by a special case of a two-scale Cantor dust. The results are then generalized to a wider range of coarsening mechanisms.

cond-mat.dis-nn↗