Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber.

Passively mode-locked lasers with intracavity weakly birefringent fiber are theoretically analyzed based on two coupled complex one-dimensional Ginzburg-Landau equations. The model includes fiber birefringence, spectral filtering, saturable gain, and saturable loss. Phase-locked soliton solutions are found for small amounts of birefringence and several types of soliton with periodic polarization evolution for higher amounts of birefringence.

Ultrashort pulses generated by mode-locked lasers with either a slow or a fast saturable-absorber response.

We present a new exact solution for ultrashort pulses generated by passively mode-locked lasers, taking into account the slow and the fast parts of the semiconductor saturable-absorber response in the nonsaturated limit.

Multiport soliton devices with controllable transmission.

We describe new planar multiport devices written by spatial solitons that are composed of several nonlinearly coupled components in Kerr-type media. Such devices have no radiation losses at a given wavelength. We demonstrate that, for the same relative angle between the input soliton-induced channels, one can vary the transmission coefficients into the output channels by adjusting the polarizations of multicomponent solitons.

Asymmetric partially coherent solitons in saturable nonlinear media.

We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart.

Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions.

We carry out a theoretical investigation of the properties of partially coherent solitons for media which have a slow Kerr-like nonlinearity. We find exact solutions of the Nth-order Manakov equations in a general form. These describe partially coherent solitons (PCSs) and their collisions.

Soliton interactions in perturbed nonlinear Schrödinger equations.

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schrödinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the soliton amplitudes remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula.

Multisoliton complexes on a background.

We obtain solutions of M coupled nonlinear Schrodinger equations that describe multisoliton complexes (MCs) on a background. We present explicit multiparameter families of solutions and numerical simulations, demonstrating specific features of MCs and their collisions. It is shown, in particular, that a MC on a background can have a complicated intensity profile due to a nonlinear superposition of pairs of bright and dark single solitons.

Modes of periodic waveguides.

We calculate exactly the two bound Floquet modes of a periodic linear waveguide induced in a medium by a second-order soliton of the nonlinear Schrödinger equation. The modes are degenerate at the writing frequency, having the same quasi-propagation constant, which suggests applications of our method to spectral filtering.

Optical conveyor belts: a new scheme for fiber communications.

A scheme is proposed for high-bandwidth, robust data transmission in silica fibers in the normal-dispersion regime. The scheme uses a uniform periodic train of dark solitons to eliminate completely the dispersion of a data stream encoded in linear pulses of small but otherwise arbitrary amplitude in the orthogonal polarization. Data pulses carried by dark solitons of differing contrast do not interfere with one another when the solitons collide.

Modulation instability of the ground state of the nonlinear wave equation: optical machine gun.

The nonstationary (time-dependent) problem of longitudinal modulation instability of a self-focusing beam in a nonlinear medium with and without saturation is solved for the first time, to our knowledge, by using numerical methods. We present the dependence of instability growth rates on the modulation frequency for different saturation parameters. The radial profile of the complex perturbation function is also calculated.

Information erasing in the phenomenon of long-lived photon echo.

The possibility of erasing information in an arbitrary cell of an optical memory device based on the phenomenon of long-lived photon echo is theoretically considered. Optimal conditions for a maximal number of write-erase cycles in a given cell are obtained, and an experimental setup for observing this effect is proposed.