N. V. Vysotina

Formation of soliton-like light beams in an aqueous suspension of polystyrene particles

A Kerr nonlinear medium consisting of an aqueous suspension of dielectric nanoparticles is used for the observation of continuous self-focusing of laser light. The minimum width of the soliton-like beam is measured in relation to the radiation power and the particle concentration. The possibilities of maximum narrowing of the beam in such a medium are discussed.

Extremely short dissipative solitons in an active nonlinear medium with quantum dots

A medium consisting of quartz with embedded active (amplifying) or passive (absorbing) impurities, i.e., quantum dots, is proposed for producing extremely short dissipative solitons on the basis of the effect of enhanced self-induced transparency. The calculations show that, in such a medium, the initial standard femtosecond pulses can be transformed into extremely short dissipative solitons with a peak intensity of ∼1011 W/sm2, with a duration corresponding to the inverse frequency of transitions in impurities, and with the coherent spectral supercontinuum covering almost the entire transmission region of quartz.

Extremely short pulses of amplified self-induced transparency

The propagation of optical pulses in a waveguide containing atoms with resonant amplification and absorption has been analyzed. The possibility of amplification-based realization of a pulse compression regime similar to self-induced transparency has been demonstrated up to a duration comparable with the inverse frequency of the atomic transition (several femtoseconds) with a simultaneous increase in the peak amplitude.

Forward light reflection from a moving inhomogeneity

The reflection of monochromatic and quasi-monochromatic pulsed light incident on a moving inhomogeneity in the optical characteristics of a medium having plasma-type dispersion has been analyzed. The velocity V of the inhomogeneity, induced in the medium by an intense laser pulse, has been changed by varying its carrier frequency. It has been shown that the usual back-reflection mode, when the reflected radiation pulse moves in the direction opposite the direction of incident radiation, is implemented only if the velocity V is less than the critical value Vmin, which depends on the carrier frequency of the incident radiation pulse. It has been found that reflected radiation moves in the same direction as the incident radiation in a certain range of the velocity Vmin < V < Vmax (forward reflection). In this case, the reflected radiation pulse begins to lag behind a fast-moving inhomogeneity. When Vmax < V < c, where c is the speed of light in vacuum, the group velocity of the incident radiation pulse is less than the speed of inhomogeneity, and there is no reflection. Analytical treatment is supported by numerical simulation.

Dissipative extremely short localized structures of radiation

Sets of steady-state localized temporal structures of radiation with a duration comparable with the period corresponding to the frequency of atomic transitions are found for a medium consisting of active (with a pump) and passive (without a pump) atoms with homogeneous broadening. The velocity of motion of these structures takes discrete values depending on the number of field spikes and the number of oscillations of the polarization of the active and passive atoms within the intervals between the field spikes.

Soliton in stationary and dynamical traps

Soliton dynamics in a one-dimensional trap with immobile and oscillating walls has been analyzed by the example of an atomic Bose-Einstein condensate. Agreement between the consequences of a simplified Newton’s equation describing the interaction of a soliton with its antiphase mirror reflections and the initial Gross-Pitaevskii equation has been demonstrated. Comparison with the dynamics of a classical point particle in the Fermi-Ulam problem has been carried out.

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 reflection from a moving Bragg lattice formed by a train of pulses in a nonlinear medium

Reflection of a weak (probe) radiation pulse from a refractive index lattice that is induced in a non-linear medium by intense pulses and that moves in it is simulated numerically. The possibility of a significant increase in the reflection coefficient (as compared to the case of single inhomogeneity of the refractive index) under the conditions of the Bragg resonance is verified.

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.