A. N. Shatsev

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.

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.

Two-dimensional solitons in B-class lasers with saturable absorption

Localized radiation structures under conditions of a semiconductor laser with saturable absorption and a vertical cavity with a large Fresnel number are analyzed numerically and analytically. The boundaries of the region of existence and stability of transversely two-dimensional solitions, the boundary of transition to a moving state, and the boundary of the Andronov-Hopf bifurcation are found. Stable fundamental and vortical (topologically charged) solitons are obtained in a range of relaxation times of the nonlinearities of the media up to 400 lifetimes of a photon in the cavity. These solitons were obtained under the condition that the chosen medium with saturable absorption has a slower response than the active medium of the laser. Otherwise, a rapidly moving solition is formed, which is similar in its properties to a combustion wave. Properties of such a rapid motion along the aperture can be useful for optical data processing.

Discrete dissipative localized modes in nonlinear magnetic metamaterials

We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.

Hysteresis of switching waves and dissipative solitons in nonlinear magnetic metamaterials

Localized structures forming in the bistable regimes in a chain of weakly coupled split ring resonators, which are the building blocks of a nonlinear magnetic metamaterial, where electric current is generated by external electromagnetic radiation, have been studied analytically and numerically. The hysteresis of the velocity of switching waves (fronts) has been revealed and discrete dissipative solitons have been found.

Pulsating solitons in a laser with relaxation of gain and saturable absorption

Results of numerical simulation of the formation of pulsating solitons in a laser with relaxation of gain and saturable absorption are presented. The regions of relaxation parameters are found in which stationary pulsating solitons and solitons with strong modulation of the pulsation amplitude are observed. Examples of multiple subsequent doubling of the oscillation period, caused by changing relaxation parameters, are presented.

Conditions for the existence of laser bullets

Conditions for the existence of completely localized three-dimensional dissipative laser solitons—“laser bullets” in a medium with nonlinear amplification and absorption and frequency dispersion are studied. Solitons with different profiles are considered and the regions of their stable existence are found. The stability of spherical solitons is studied as a function of frequency mismatch of amplification and absorption lines by the method of direct numerical simulation.

Nonstationary multivortex and fissionable soliton-like structures of laser radiation

New types of nonstationary soliton-like structures of laser radiation were found in the mean field approximation by numerical simulation of a class A wide-aperture laser with saturable absorption. In the absence of frequency detunings, multivortex (with several wavefront dislocations distributed over the aperture) asymmetric rotating solitons were revealed, which can be interpreted as strongly coupled states of symmetric laser solitons with topological charges coinciding or differing in sign. In the presence of detunings between the central frequencies of the gain and absorption profiles and the frequency of the cavity mode, “biosoliton” regimes were obtained, which are characterized by the expansion of the initial localized structure and the periodic separation from it of fragments having similar dynamics.

Simulation of Interaction of Oriented J Aggregates with Resonance Laser Radiation

The interaction of laser radiation with single J aggregates of cyanine dyes is theoretically analyzed and numerically simulated. The quantum-mechanical calculations of the equilibrium geometry and the energies and intensities of the lowest singlet electronic transitions in pseudoisocyanine chloride and its linear (chain) oligomers are fulfilled. The data of these calculations can serve as parameters of the analyzed model of interaction of J aggregates with radiation in the one-particle density matrix approximation. This model takes into account relaxation processes, the annihilation of excitations at neighboring molecules, and inhomogeneous broadening. Assuming that the inhomogeneous broadening is absent, calculations demonstrate the existence of spatial bistability, molecular switching waves, and dissipative solitons. The effect of the inhomogeneous broadening and the radiation intensity on the effective coherence length in linear (chain) J aggregates is analyzed.

Incoherent weak coupling of laser solitons

A coupled state of a pair of spatial laser solitons with different topological charges in a wide-aperture class-A laser with saturable absorption was found by numerical simulation. In view of a difference in the frequencies of the individual solitons, periodic (with a period corresponding to the frequency difference) weak pulsations of the shape of the solitons and of the spacing between them take place, but the rotation of the pair and the motion of its center of inertia were not revealed.