Victor A. Aleshkevich

Eigenvalue control and switching by fission of multisoliton bound states in planar waveguides

We report the results of numerical studies of the fission of N-soliton bound states at the interface formed by a Kerr nonlinear medium and a linear dielectric in a planar waveguide. A variety of effects are shown to occur, with applications to all-optical eigenvalue soliton control.

Transverse modulational instability of (2 + 1)-dimensional cnoidal waves in media with cubic nonlinearity

We consider transverse modulational instability of (2+1)-dimensional cnoidal waves of cn, dn, and sn, types that are periodic in one direction and are uniform in the other direction. The new method of stability analysis of periodic waves presented here is based on the construction of a translation matrix for a perturbation vector and on the evolution of the eigenvalues of the matrix with changes in modulation frequency and Jacobi parameter that define the degree of energy localization of the corresponding cnoidal waves. We show that the dn wave is subject to the influence of both neck and snake instabilities, the cn wave is affected by neck instability, and the sn wave suffers from snake instability in (2+1) dimensions.

Cnoidal waves compression by means of multisoliton effect

We consider the self-compression of the cnoidal waves of both cn- and dn-types in the materials with focusing Kerr nonlinearity. The dependencies of the compression degree and optimal media length on the parameter describing localisation of the wave energy are presented and the main features of the wave propagation are analysed on the basis of finite number harmonic approximation.

Self-bending of cnoidal waves in photorefractive medium with drift and diffusion nonlinearity

We consider the influence of the nonlocal component of the photorefractive crystal response on the cnoidal waves propagation dynamic and analyze the dependence of the self-bending parameter on the degree of the spatial localization of the wave energy. We have shown that for the case of the cn-wave the role of self-bending effects increases (and for the case of the dn-wave decreases) with growth of spatial localization.

Self-frequency shift of cnoidal waves in a medium with delayed nonlinear response

The influence of a sufficiently nonstationary Raman contribution to nonlinear susceptibility on the dynamics of cnoidal wave propagation in optical fibers is theoretically analyzed. The dependence of the parameter that describes the curvature of the propagation trajectory on the degree of localization of the wave energy is presented.

Diffraction and focusing of extremely short optical pulses: generalization of the Sommerfeld integral

The Sommerfeld diffraction theory is extended to the case of extremely short pulses. We show that in the far field the energy-density distribution of the diffractional pattern is transformed into a Gaussian distribution, when the plane wave with uniform radial amplitude distribution and one oscillation period falls upon the circular aperture. When one focuses the Gaussian beam with one oscillation period, the energy-density distribution in the focal plane differs from the Gaussian distribution.

Self-compression of the cnoidal waves in optical fibers

We consider the self-compression of the cnoidal waves of both cn- and dn-types in the materials with focusing Kerr nonlinearity. The dependencies of the compression degree and optimal media length on the parameter describing localization of the wave energy are presented and the main features of the wave propagation are analyzed on the basis of finite number harmonic approximation.

Nonlinear unidirectional coupler in photorefractive medium with diffusion nonlinearity

We consider switching characteristics of the nonlinear unidirectional coupler embedded in the photorefractive medium with purely diffusion nonlinearity. Transmission characteristics for both two- and three-waveguide couplers are presented. It is shown that the part of energy transmitted into the second waveguide in two-waveguide coupler monotonically decreases with increase of input energy, i.e. no threshold energy value exists. It is also shown that due to the specific character of diffusion nonlinearity transmission characteristics of the three-waveguide coupler strongly depends on the relative disposition of the input waveguide.

On the possibility of suppression of the self-frequency shift of the cnoidal waves in the medium with delayed nonlinear response by bandwidth-limited amplification

We both theoretically and numerically investigate conditions of the stable balance between competing processes of the Raman self-frequency shift and bandwidth-limited amplification of the periodical cnoidal waves. The dependencies of the initial wave form-factor and frequency shift necessary for the stable balance on the parameter describing degree of localisation of the wave energy are presented.

Internal reflection and decay of N-soliton beams at interface with linear dielectric

We report the results of analytical and numerical studies of the reflection of N -soliton bound states at the interface formed by a Kerr nonlinear medium and a linear dielectric. A variety of effects are shown to occur, including bistability and soliton filtering, with applications to all-optical soliton switching concepts.