Solitons In Optical Media Research Articles

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities.

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, gives rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s=2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

Subwavelength spatial solitons in optical media with non-Kerr nonlinearities

We consider very narrow time-independent spatially localized solutions (spatial solitons), whose width may be comparable to or smaller than the carrier wavelength, in two-and three-dimensional waveguides with the cubic-quintic or saturable nonlinearity. Equations describing the shape of the solitons are derived directly from the Maxwell equations, taking into account terms which are neglected in the usual paraxial (nonlinear Schrodinger) approximation, which is valid for solitons whose width is much larger than the wavelength. We consider both transverse electric and transverse magnetic solitons, and show that, in all cases, there is a finite minimum value of the soliton's width, which is attained at a certain value of the propagation constant (an internal parameter of the family of soliton solutions), and the width diverges at some larger value of the propagation constant, which is an existence border for the soliton family. The full similarity of the results obtained for both the cubic-quintic and saturable nonlinearities suggests that the same general conclusions apply to narrow bright solitons in any model featuring nonlinearity saturation in some form.

Damping of internal soliton modes in media with quadratic nonlinearity

Optical solitons in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Internal soliton modes and the rate of their radiative damping as a function of detuning from the phase-matching condition and the nonlinear shift of phase velocity for different soliton dimensions (d=1, 2, 3) are found. The length of a nonlinear medium required to form a stationary soliton is determined.

Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity

We study spatiotemporal three-dimensional bright solitons in optical media whose non-linear response includes third- and fifth-order terms. By means of numerical simulations, lower and upper stability and existence borders for the solitons without the internal ``spin'' are identified. Using the variational method based on two different trial functions and collating the results, we obtain approximate solutions for spinning (vortex) solitons. The presence of the lower stability border for both the zero-spin and spinning solitons is a drastic difference of the three-dimensional solitons from those in one and two dimensions. The results show that the corresponding stability and existence borders are chiefly determined by the spatial dimension, quite weakly depending on the soliton's ``spin.'' However, the energy of the spinning soliton is much larger than that of the zero-spin one.

The effect of ground vias on changing signal layers in a multilayered PCB

generation TDBPMSHG , which is an extension of the linear TDBPM. It involves solving the coupled parabolic nonlinear equations using the explicit finite-difference technique, where all spatial and time variations were retained in the analysis. The technique was also applied to model pulsed optical beams in a dielectric waveguide containing secondorder nonlinear effects. It is concluded that the method is very efficient and simple to implement. The TDBPMSHG is well suited for the study of the unidirectional propagation of compact temporal pulses over long distances in a guidedwave environment. In addition, the method should find application in the study of spatiotemporal optical solitons in media with quadratic nonlinearity 17 .

Bright and dark spatial solitons in non-Kerr media

An overview of the theory of self-guided optical beams, spatial optical solitons supported by non-Kerr non-linearities, is presented. This includes bright and dark solitons in optical media with intensity-dependent non-linear response as well as two-component solitary waves supported by parametric wave mixing in quadratic or cubic media. The properties of non-linear spatially localized waves are discussed for qualitatively different types of soliton bearing non-integrable non-linear models, including the scalar model described by a generalized non-linear Schrodinger equation and the models of the second- and third-harmonic generation. Special attention is paid to the recent advances of the theory of soliton stability and soliton internal modes.

Stochastic instability of chirped optical solitons in media with periodic amplification

A variational method is used to study propagation of chirped optical pulses in media with periodic amplification. A nonlinear resonance and chaos in oscillations of the pulse duration are considered. A stochastic instability of evolution of the pulse duration and also pulse decay under the influence of periodic amplification are predicted. A calculation is reported of the stochastic pulse-decay length and a comparison is made with the results of a numerical simulation. The applications of the results to long-haul optical communication lines with amplifiers and to optical fibres with a periodically modulated core diameter are considered.

Optical Solitons in Media with Combined Resonant and Non-resonant (Cubic) Nonlinearities in the Presence of Perturbations

Abstract Optical solitons in a medium with both resonant and non-resonant (Kerr-type) nonlinearities have earlier been shown to exist only under a definite relationship between the parameters of medium and radiation. In this paper, we study the influence of a small deviation from this relationship on the distortion of the soliton propagation. Our approach is realized via an algebraic version of the soliton perturbation theory formulated by means of the Riemann boundary problem. Corrections for the soliton parameters are calculated and an expression is obtained which describes the soliton shape deformation. Conditions of the soliton tail appearance are also analysed.

Optical Solitons in Media with Resonant and Non-resonant Self-focusing Nonlinearities

Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.