N. A. Veretenov

Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber

We present results of a semianalytical and numerical study of transverse two-dimensional stationary and oscillating solitons in a wide-aperture laser with a saturable absorber and fast nonlinearity of both gain and absorption. We determine the stability conditions and bifurcations of axially symmetric solitons with screw wavefront dislocations of different order. We demonstrate the existence of asymmetric rotating laser solitons with different numbers of intensity maxima.

Oscillons of Bose–Einstein condensate (A review)

The dynamics of localized structures of atomic Bose–Einstein condensate in traps with oscillating walls has been analyzed. The properties of these oscillons localized in the longitudinal and transverse directions with respect to the trap axis are compared with the properties of conservative and dissipative solitons.

Light-induced “plasmonic” properties of organic materials: Surface polaritons and switching waves in bistable organic thin films

Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated, and the propagation of surface polaritons at the material/air interface was demonstrated. Here, we develop a theory of nonlinear light-induced “plasmonic” properties of organic materials. We predict the generation of switching waves or kinks in the bistable organic thin films that enable us to observe a bistable behaviour of the surface polaritons at the organic thin film/dielectric interface under laser irradiation. We present the alternating-sign dependence of the switching wave velocity on pump intensity and discuss a possibility of controlling the polariton propagation by switching waves.

Soliton of Bose–Einstein condensate in a trap with rapidly oscillating walls: II. Analysis of the soliton behavior upon a decrease in the wall oscillation frequency

This work is a continuation of our study [1], in which a two-scale analytical approach to the investigation of a soliton oscillon in a trap with rapidly oscillating walls has been developed. In terms of this approach, the solution to the equation of motion of the soliton center is sought as a series expansion in powers of a small parameter, which is a ratio of the intrinsic frequency of slow soliton oscillations to the frequency of fast trap wall oscillations. In [1], we have examined the case ε ≪ 1, in which, to describe the motion of the soliton, it is sufficient to restrict the consideration to the zero approximation of the sought solution. However, when the frequency of wall oscillations begins to decrease, while the parameter begins to increase, it is necessary to take into account corrections to the zero approximation. In this work, we have calculated corrections of the first and second orders in to this approximation. We have shown that, with an increase in, the role played by the corrections related to fast oscillations of the trap walls increases, which results in a complex shape of the envelope of oscillations of the soliton center. It follows from our calculations that, if the difference between the amplitudes of wall oscillations is not too large, the analytical solution of the equation of motion of the soliton center will coincide very well with the numerical solution. However, with an increase in this difference, as well as with a decrease in the wall oscillation frequency, the discrepancy between the numerical and analytical solutions generally begins to increase. Regimes of irregular oscillations of the soliton center arise. With a decrease in the frequency of wall oscillations, the instability boundary shows a tendency toward a smaller difference between the wall oscillation amplitudes. In general, this leads to enlargement of the range of irregular regimes. However, at the same time, stability windows can arise in this range in which the analytical and numerical solutions correlate rather well with each other. Our comparative analysis of the analytical and numerical solutions has allowed us not only to study their properties in detail, but also to draw conclusions on the limits of applicability of the analytical approach.

Soliton of Bose–Einstein condensate in a trap with rapidly oscillating walls: I. Multiscale method and analysis of soliton motion in the limit of extremely fast wall oscillations

Motion of a soliton of Bose–Einstein condensate of atoms captured by a trap with rapidly oscillating walls has been studied. This motion can be described using both the Gross–Pitaevskii equation for a condensate wave function and an approximate equation in the form of the Newton equation for the soliton center coordinate. An analytical approach for solving the Newton equation has been developed. This approach is based on the multiscale method where the solution is sought for in the form of small-parameter expansion. This parameter is a ratio of the frequency of intrinsic slow soliton oscillations around the equilibrium position to the frequency of fast oscillations of the trap walls. In the first part of the study, an approach based on two time scales is described and the case of extremely fast wall oscillations is investigated. The calculation performed within the zero approximation shows a very good coincidence with the numerical solution of the Newton equation with respect to all parameters. A good agreement with the numerical solutions of the Gross–Pitaevskii equation is also demonstrated for calculations of the parameters such as oscillation frequency and shift of the soliton equilibrium position under the action of the wall motion. In the second part, the role of corrections to the obtained solution is analyzed for a decreasing wall-oscillation frequency and the range of applicability of the used analytical approach is discussed.

Topological three-dimensional dissipative optical solitons

This article presents a review of recent investigations of topological three-dimensional (3D) dissipative optical solitons in homogeneous laser media with fast nonlinearity of amplification and absorption. The solitons are found numerically, with their formation, by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around a vortex straight line with their simultaneous twist. After a transient, the ‘hula-hoop’ solitons can form with a number of closed and unclosed infinite vortex lines, i.e. the solitons are tangles in topological notation. They are attractors and are characterized by extreme stability. The solitons presented here can be realized in lasers with fast saturable absorption and are promising for information applications. The tangle solitons of the type described present an example of self-organization that can be found not only in optics but also in various distributed dissipative systems of different types. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

Structure of Energy Fluxes in Topological Three-Dimensional Dissipative Solitons

The internal structure of dissipative topological solitons has been revealed by example of three-dimensional dissipative optical solitons with one open and one closed dislocation lines of a wavefront. This structure is manifested in the existence of critical points, lines, and surfaces in the field of electromagnetic energy fluxes (Poynting vector). The conservation of the topological characteristics of such solitons, which can be formed in a homogeneous laser medium with saturated amplification and absorption or in lasers with quite large longitudinal and transverse dimensions, provides additional capabilities for information applications.

Investigation of oscillations of a soliton of a bose condensate of atoms in a trap in the limit of small oscillations of its walls

The motion of the center of a soliton in a trap with oscillating walls is studied analytically and numerically for the case in which the intrinsic frequency of small soliton oscillations in the equilibrium state considerably exceeds the frequency of wall oscillations. this problem can be solved either by applying the gross–pitaevskii equation, which most exactly describes the behavior of the soliton in the trap, or by using the approximate, “mechanical,” equation of motion of the newtonian type for the center of the soliton. an approximate analytical solution of the mechanical equation is obtained and is compared with the numerical solution of the newton equation, while the latter solution is compared with the numerical solution of the gross–pitaevskii equation. good agreement between the first two solutions is revealed. it is also shown that there is a range of parameters in which the numerical solutions of the newton and gross–pitaevskii equations are closest to each other. the frequency-sweeping effect of soliton center oscillations is revealed. an approximate analytical formula for the limiting frequency of these oscillations is obtained and the numerical analysis of this phenomenon is performed.

Motion of dissipative soliton complexes in a nonlinear interferometer with driving radiation

A numerical analysis has been made of the motion of spatial dissipative soliton complexes in a wide-aperture interferometer with the Kerr nonlinearity, which is excited by continuous coherent driving radiation. It has been demonstrated that, depending on the symmetry of the radiation intensity distribution, the complex can exhibit four variants of dynamics, including the curvilinear motion of its center. The results obtained have been compared with the case of laser soliton complexes (without coherent driving radiation) and with the predictions made from the phenomenological model of the motion of soliton complexes.

Modulation instability and decay of atomic Bose-Einstein condensates into solitonic trains

The dynamics of free and optically induced decay of quasi-one-dimensional atomic Bose-Einstein condensates (BECs) is considered. The main characteristics of BEC modulation instability were found and compared for the cases of local and non-local interatomic interaction potential. The dynamics of BEC decay was studied numerically for the cases of positive and negative scattering length, absence or presence of optical standing wave, and for different shapes of initial BEC density distribution.