Formation of electromagnetic pulses with nonzero electrical area by media with ferromagnetism.

The known rule of conservation of the electrical area of pulses, which plays a decisive role in the effectiveness of the action of extremely short pulses on microobjects, is valid for a wide class of media, including all non-magnetic ones. We show how this rule changes in magnetically ordered media, where pulses can induce magnetization variation. We found that such variations serve as another source of pulse electrical area, in addition to the movement of charges.

Nonconservation of Topological Charge and Cusps in a One-Dimensional Laser Scheme.

An analysis was made of the field structures in a coaxial laser with fast saturable absorption. In such an efficiently one-dimensional scheme, the integer topological index (charge) naturally arises: the phase incursion of the field envelope when bypassing the aperture, divided by 2π. The topological charge is the winding number for the phase curve introduced for the electric field envelope with increase of the coordinate for fixed time.

Control of topology of two-dimensional solitons in a laser with saturable absorption by means of a coherent holding radiation: publisher's note.

This publisher's note contains corrections to Opt. Lett.45, 3284 (2020)OPLEDP0146-959210.

Control of topology of two-dimensional solitons in a laser with saturable absorption by means of a coherent holding radiation.

We propose a simple method to control the topology of laser vortex solitons and their complexes in a wide-aperture laser with saturable absorption by means of weak coherent holding radiation. The holding radiation acting on initial "free" vortex solitons induces the appearance of new peripheral vortices and the splitting of multiple central vortices, as well as reconfiguration of energy flow topology. A wide variety of these stable vortex structures makes the scheme promising for topologically protected information processing.

Asymptotic dynamics of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes.

We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell's equations, taking into account the field inhomogeneity along the nanotube axis beyond the approximation of slowly varying amplitudes and phases. A model is proposed for the analysis of the dynamics of an electromagnetic pulse in the form of an effective equation for the vector potential of the field.

Extreme and Topological Dissipative Solitons with Structured Matter and Structured Light.

Structuring of matter with nanoobjects allows one to generate soliton-like light bundles with extreme characteristics-temporal duration and spatial dimensions. On the other hand, structuring of light gives the possibility to form light bundles with complicated internal structure; their topology could be used for information coding similar to that in self-replicating RNA molecules carrying genetic code. Here we review the both variants of structuring.

Unusual terahertz waveforms from a resonant medium controlled by diffractive optical elements.

Up to now, full tunability of waveforms was possible only in electronics, up to radio-frequencies. Here we propose a new concept of producing few-cycle terahertz (THz) pulses with widely tunable waveforms. It is based on control of the phase delay between different parts of the THz wavefront using linear diffractive optical elements.

Unipolar subcycle pulse-driven nonresonant excitation of quantum systems.

The interaction of subcycle pulses with quantum systems is considered when the pulse duration becomes much smaller than the timescales of electron oscillations. We show analytically that the interaction process in this case is governed by the electric pulse area. The efficient nonresonant excitation of quantum systems by subcycle pulses with a high degree of unipolarity is demonstrated.

Irreversible Hysteresis of Internal Structure of Tangle Dissipative Optical Solitons.

For three-dimensional tangle laser solitons that have a number of unclosed and closed vortex lines and coexist in a range of the scheme parameters, we predict irreversible hysteretic transformation of their internal structure when a system parameter slowly and regularly varies crossing the boundary of the stability of one or another soliton. During the hysteresis cycle, when restoring the initial parameter value, the soliton topology simplifies (decrease of topological indices), its field energy decreases, and the energy of the medium increases. The transient includes a series of elementary reactions: reconnection of vortex lines, separation of closed vortex loops after strong bending of a parent vortex line, and twist of unclosed vortex lines changing topological indices.

Dynamics of nonlinear Schrödinger breathers in a potential trap.

We consider the evolution of the 2-soliton (breather) of the nonlinear Schrödinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard floor. This setting can be implemented in atomic Bose-Einstein condensates, and in a nonlinear planar waveguide in optics. In the absence of the gravity, repulsion of the breather from the floor leads to its splitting into constituent fundamental solitons, if the initial distance from the floor is smaller than a critical value; otherwise, the moving breather persists.

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.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e.

Population density gratings induced by few-cycle optical pulses in a resonant medium.

Creation, erasing and ultrafast control of population density gratings using few-cycle optical pulses coherently interacting with resonant medium is discussed. In contrast to the commonly used schemes, here the pulses do not need to overlap in the medium, interaction between the pulses is mediated by excitation of polarization waves. We investigate the details of the dynamics arising in such ultrashort pulse scheme and develop an analytical theory demonstrating the importance of the phase memory effects in the dynamics.

Generation of unipolar half-cycle pulses via unusual reflection of a single-cycle pulse from an optically thin metallic or dielectric layer.

We propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse from a thin flat metallic or dielectric layer. Unipolar pulses in reflection arise due to specifics of one-dimensional pulse propagation. Namely, we show that the field emitted by the layer is proportional to the velocity of the oscillating charges in the medium, instead of their acceleration.

Ultrafast creation and control of population density gratings via ultraslow polarization waves.

In the regime of resonant coherent light-matter interaction, light pulses may interact with each other indirectly via a polarization wave created by the other pulse. We show that such interaction allows fast creation and erasing of high-contrast dynamic population density gratings, as well as control of their period in a few-cycle regime. Our scheme uses counter-propagating optical pulses, which do not cross each other in the medium.

Self-induced transparency mode locking, and area theorem.

Self-induced transparency mode locking (or coherent mode locking, CML), which is based on intracavity self-induced transparency soliton dynamics, potentially allows achievement of nearly single-cycle intracavity pulse durations, much below the phase relaxation time T in a laser which, despite having great promise, has not yet been realized experimentally. We develop a diagram technique which allows us to predict the main features of CML regimes in a generic two-section laser far from the single-cycle limit. We show that CML can arise directly at the first laser threshold if the phase relaxation time is large enough.

Spatial and temporal structures in cavities with oscillating boundaries.

We review the general features of particles, waves and solitons in dynamical cavities formed by oscillating cavity mirrors. Considered are the dynamics of classical particles in one-dimensional geometry of a dynamical billiard, taking into account the non-elastic collisions of particles with mirrors, the (quasi-energy) states of a single quantum particle in a potential well with periodically oscillating wells, and nonlinear structures, including nonlinear Rabi oscillations, cavity optical solitons and solitons of Bose-Einstein condensates, in dynamical cavities or traps.

Knotted solitons in nonlinear magnetic metamaterials.

We demonstrate that nonlinear magnetic metamaterials comprised of a lattice of weakly coupled split-ring resonators driven by an external electromagnetic field may support entirely new classes of spatially localized modes--knotted solitons, which are stable self-localized dissipative structures in the form of closed knotted chains. We demonstrate different topological types of stable knots for the subcritical coupling between resonators and instability-induced breaking of the chains for the supercritical coupling.

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.

Vortex solitons in lasers with feedback.

We report on the existence, stability and dynamical properties of two-dimensional self-localized vortices with azimuthal numbers up to 4 in a simple model for lasers with frequency-selective feedback.We build the full bifurcation diagram for vortex solutions and characterize the different dynamical regimes. The mathematical model used, which consists of a laser rate equation coupled to a linear equation for the feedback field, can describe the spatiotemporal dynamics of broad area vertical cavity surface emitting lasers with external frequency selective feedback in the limit of zero delay.

Interaction of dissipative Bragg solitons in active nonlinear fibers.

We investigate numerically and analytically interaction of dissipative optical solitons in active nonlinear fibers with Bragg grating. In the framework of the coupled mode theory, we analyze the effect of initial separation and phase difference between the pulses on the final solitons' characteristics. Beyond the framework of this approach, a number of new phenomena are studied, including location of centers of motionless solitons near the maxima of refractive index grating, the discreteness of moving solitons velocity and the existence of a motionless weakly coupled two-soliton structure.

Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling.

We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption.

Damping of persistent oscillations of quadratic optical solitons.

We investigate the dynamics of optical soliton formation in media with quadratic nonlinearity under conditions of long-living oscillations produced by the soliton's internal modes. We compare the predictions of the second-order perturbation approach, combining it with the energy conservation law, with the direct numerical simulations using the transparent boundary conditions. We demonstrate that these two approaches correlate well and describe the nonlinear radiation damping of the internal modes.

Polarization state of quadratic spatial optical solitons.

We derive governing equations that determine a full polarization state of transversely two-dimensional spatial solitons in a bulk anisotropic medium with the second-order nonlinearity. Based on nonlinear vectorial Maxwell's equations and approximation of slowly varying envelopes, our approach describes also lowest-order nonparaxial effects, however the most important factor governing radiation polarization is the medium anisotropy. This factor results in mixing of orthogonal components of electric field of quadratic soliton that consists of coupled beams at the fundamental frequency and its second harmonics.