S.A. Darmanyan

Modulational instability in optical fibers with variable dispersion

Abstract We study modulational instability in optical fibres whose dispersion varies with the propagation distance. We distinguish between two cases, viz. periodic and random dispersion variation. In the former case it is found that due to the parametric resonance between the dispersion modulation and the modes of the linearized system new domains of modulational instability arise for anomalous as well as normal average dispersion. In the latter case stochastic parametric resonances again lead to the occurrence of modulational instability for normal dispersion. If the dispersion is anomalous the region of modulational instability increases and the respective gain decreases in comparison with a fibre with constant dispersion.

Modulational instability in optical fibers near the zero dispersion point

Modulational instability (MI) of electromagnetic waves in an optical fiber near the zero dispersion point is investigated both analytical and numerical. The effect of fourth order dispersion is taken into account and a new region with MI is found. The possibility of MI is shown for the case of positive second and fourth order group dispersion. For both positive and negative fourth order dispersion a recurrence phenomenon is observed analogous to the Fermi-Pasta-Ulam problem.

Modulational instability of electromagnetic waves in inhomogeneous and in discrete media

Publisher Summary This chapter discusses the modulational instability (MI) of electromagnetic waves in inhomogeneous and in discrete media. MI exists because of the interplay between the nonlinearity and dispersion/diffraction effects. Important models for investigating MI of electromagnetic waves in nonlinear media represent the scalar and vectorial nonlinear Schrodinger (NLS) equations, the system describing evolution of the envelopes of fundamental and second harmonics waves in quadratically nonlinear media, and sine-Gordon equation. The methods such as periodic solutions of the NLS equation and the coupled-mode theory with three modes are discussed. The chapter discusses the MI of electromagnetic waves in optical media with periodic inhomogeneities. The origin of the random fluctuations of parameters in optical fibers and other nonlinear optical media is described. MI in fibers with random amplification and dispersion and MI in randomly birefringent fibers are discussed. The chapter discusses the MI of electromagnetic waves in nonlinear discrete optical systems such as an array of planar waveguides and fibers. Particular cases of MI in discrete media with cubic nonlinearity and quadratic nonlinearity are investigated.

Evolution of randomly modulated solitons in optical fibers

The influence of initial amplitude and phase random modulation on the soliton propagation in optical fibers is investigated. The soliton amplitude and velocity distribution functions are calculated. It is shown that the amplitude distribution function has a non-Gaussian form whereas the distribution function of the velocity can have either a Gaussian or a non-Gaussian form depending on the statistical properties of the initial noise. The statistical characteristics for the soliton parameters are calculated. The analytical results agree well with previous numerical studies.

Asymmetric dark solitons in nonlinear lattices

New types of stable discrete solitons are discovered. They represent the first example of asymmetric dark solitons and shock waves with a nonzero background. Both types of solutions exhibit a strong intrinsic phase dynamics. Their domains of existence and criteria of stability are identified. Numerical experiments support the analytical findings.

Evolution of spatial solitons in quadratic media with fluctuating nonlinearity

The influence of a fluctuating nonlinearity on the propagation of spatial solitons in quadratic media is studied. We derive mean field evolution equations for both frequency components and show that fluctuations of the nonlinearity induce effective nonlinear losses. The predictions of the mean field theory are in good agreement with numerical simulations of the full stochastic system. We find an approximate analytical expression for the damping rate of spatial solitons and show that the amplitude of the fundamental wave decreases more rapidly than the amplitude of the second harmonic.

Soliton propagation in three coupled nonlinear Schrödinger equations

Abstract Soliton propagation in a system described by three coupled nonlinear Schrodinger equations is investigated. Different initial conditions are considered. The existence of bound states of solitons and soliton separation is demonstrated analytically by perturbation theory and by numerical simulations.

CHAOS IN THE PARAMETRICALLY DRIVEN SINE-GORDON SYSTEM

Abstract The appearance of chaos in the parametrically driven sine-Gordon equation is studied analytically. The chaotic behavior of breathers under the action of the periodic parametrical perturbations is found.

Polariton Effect in Nonlinear Pulse Propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on the propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of the polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside the polariton gap exhibit different velocity and amplitude dependences on their duration.

Stochastic parametric resonance of solitons

Abstract The existence of an analogue of stochastic parametric resonance for solitons in the nonlinear Schrodinger equation and the Kortwweg-de Vries equation is shown. For various types of perturbations the conditions of amplification existence and damping regimes and stationary behavior of solitons have been found.