Controllable soliton emission from a Bose-Einstein condensate

We demonstrate, through numerical simulations, the controllable emission of matter-wave bursts from a Bose-Einstein Condensate in a shallow optical dipole trap. The process is triggered by spatial variations of the scattering length along the trapping axis. In our approach, the outcoupling mechanism are atom-atom interactions and thus, the trap remains unaltered. Once emitted, the matter wave forms a robust soliton. We calculate analytically the parameters for the experimental implementation of this atomic soliton machine gun.Comment: 4 pages, 5 figure

Linear and nonlinear waveguiding of few-cycle optical solitons in a planar geometry

We consider the guiding of a few-cycle optical soliton by total internal reflexion, in a planar geometry. By means of numerical solution of a cubic generalized Kadomtsev-Petviashvili equation, we show that, for intensities high enough to induce soliton formation, the nonlinear effects considerably widen the guided mode and can even prevent guiding for the shortest pulses and the narrowest waveguides. However, waveguiding can be achieved by means of a steep variation of the nonlinear coefficients, e.g., by using a higher nonlinear coefficient in the cladding than that in the waveguide core. We further propose an analytical approach for extremely narrow guides, which allows us to derive a modified Korteweg–de Vries-type model for the propagation of few-cycle optical solitons in the planar waveguide

Few-optical-cycle dissipative solitons

By using a powerful reductive perturbation technique, or multiscale analysis, a generalized modified Korteweg–de Vries partial differential equation is derived, which describes the physics of few-optical-cycle dissipative solitons beyond the slowly varying envelope approximation. Numerical simulations of the formation of stable dissipative solitons from arbitrary breather-like few-cycle pulses are also given

Optical solitons in the few-cycle regime: Recent theoretical results

We provide a brief overview of recent theoretical studies of several models used for the adequate description of both temporal and spatiotemporal dynamics of few-cycle optical pulses in both cubic and quadratic nonlinear media beyond the framework of slowly varying envelope approximation

Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials

Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 are unstable, splitting into tripoles. Stability regions for the dipoles and tripoles are identified too. The periodic potential cannot stabilize CSVs with S>=2 either; instead, families of stable compact square-shaped quadrupoles are found

Models of few optical cycle solitons beyond the slowly varying envelope approximation

In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing field of the so-called extreme nonlinear optics. This review concentrates on theoretical studies performed in the past decade concerning the description of few optical cycle solitons beyond the slowly varying envelope approximation (SVEA). Here we systematically use the powerful reductive expansion method (alias multiscale analysis) in order to derive simple integrable and nonintegrable evolution models describing both nonlinear wave propagation and interaction of ultrashort (femtosecond) pulses. To this aim we perform the multiple scale analysis on the Maxwell–Bloch equations and the corresponding Schrödinger–von Neumann equation for the density matrix of two-level atoms. We analyze in detail both long-wave and short-wave propagation models. The propagation of ultrashort few-optical-cycle solitons in quadratic and cubic nonlinear media are adequately described by generic integrable and nonintegrable nonlinear evolution equations such as the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the complex modified Korteweg–de Vries equation, the sine–Gordon equation, the cubic generalized Kadomtsev–Petviashvili equation, and the two-dimensional sine–Gordon equation. Moreover, we consider the propagation of few-cycle optical solitons in both (1 + 1)- and (2 + 1)-dimensional physical settings. A generalized modified Korteweg–de Vries equation is introduced in order to describe robust few-optical-cycle dissipative solitons. We investigate in detail the existence and robustness of both linearly polarized and circularly polarized few-cycle solitons, that is, we also take into account the effect of the vectorial nature of the electric field. Some of these results concerning the systematic use of the reductive expansion method beyond the SVEA can be relatively easily extended to few-cycle solitons in the general case of multilevel atoms. Prospects of the studies overviewed in this work are given in the conclusions

Spatiotemporal optical solitons in carbon nanotube arrays

We consider the formation of ultrashort spatiotemporal optical waveforms in arrays of carbon nanotubes. We use a short-wave approximation to derive a generic two-dimensional sine-Gordon equation, describing ultrashort soliton evolution in such nanomaterials. This model was derived by using a rigorous application of the reductive perturbation formalism (multiscale analysis) for the Maxwell equations and for the corresponding Boltzmann kinetic equation for the distribution function of electrons in carbon nanotubes. We show numerically diffractionless and dispersionless robust propagation over large distances (with respect to the wavelength) of few-cycle (2+1)-dimensional spatiotemporal solitons in the form of optical breathers