Bragg-like microcavity formed by collision of single-cycle self-induced transparency light pulses in a resonant medium.

The coherent interaction of extremely short light pulses with a resonant medium can result in the formation of population difference gratings. Such gratings have been created by pulses that are π/2 or smaller. This paper demonstrates that a microcavity with Bragg-like mirrors can be formed by colliding two single-cycle attosecond self-induced transparency pulses in the center of a two-level medium. The parameters of this structure can be quickly adjusted by increasing the number of collisions, which showcases the ability to control the dynamic properties of the medium on a sub-cycle time scale by using attosecond pulses.

Dissipative three-dimensional topological optical solitons with crossed localization of polarization components.

We present a new, to the best of our knowledge, type of vector three-dimensional dissipative optical solitons with more extended degrees of freedom in a laser or laser medium with saturable absorption. These solitons are reconfigurable, include polarization singularities, and have various mutual orientations of nearly toroidal localization domains of polarization components. Numerical modeling confirms the stability of these solitons and breathers and reveals their symmetry and even "supersymmetry," as well as transformations when parameters leave the stability region. These solitons, which have no scalar analogs, are capable of carrying more than one bit of information. Our results expand the "alphabet" of solitons and can provide a route to breakthroughs in larger-capacity communication and information applications.

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.

Sub-10 fs unipolar pulses of a tailored waveshape from a multilevel resonant medium.

We theoretically demonstrate the possibility to tune the temporal waveform of unipolar pulses of femtosecond duration emitted from a multilevel resonant medium. This is achieved through the control of the medium response by a properly adjusted sequence of half-cycle unipolar or quasi-unipolar driving pulses and the spatial density profile of resonant centers along the medium layer. We show the production of unipolar optical pulses of varying profiles, like rectangular or triangular ones, from an extended layer of a multilevel medium.

Generation of an ultrahigh-repetition-rate optical half-cycle pulse train in the nested quantum wells.

We propose a simple quantum system, namely, a nested quantum-well structure, which is able to generate a train of half-cycle pulses of a few-femtosecond duration when driven by a static electric field. We theoretically investigate the emission of such a structure and its dependence on the parameters of the quantum wells. It is shown that the production of a regular output pulse train with tunable properties and the pulse repetition frequencies of tens of terahertz is possible in certain parameter ranges. We expect the suggested structure can be used as an ultra-compact source of subcycle pulses in the optical range.

Self-Stopping of Light.

Here, we show that light can bring itself to a complete standstill (self-stop) via self-interaction mediated by the resonant nonlinearity in a fully homogeneous medium. An intense few-cycle pulse, entering the medium, may reshape to form a strongly coupled light-matter bundle, in which the energy is transferred from light to the medium and back periodically on the single-cycle scale. Such oscillating structure can decelerate, alter its propagation direction, and even completely stop, depending on the state of its internal degrees of freedom. This phenomenon is expected to occur in the few-cycle strong-field regime when the Rabi oscillation frequency becomes comparable with the frequency of the incoming light.

Frequency locking and alternation of topological indices of vortex laser solitons.

We analyze the effect of frequency locking for polarization components of a semiconductor laser with fast gain, saturating absorption, and weak anisotropy. A mode of alternation of topological indices when leaving the locking area was found.

Tubular laser solitons.

We analyze, to the best of our knowledge, a new type of topological optical solitons in lasers with fast saturable absorption, which is intermediate between 2D and 3D ones. Being generated by 2D laser solitons, such 3D dissipative solitons in a laser cavity of length L have a number of vortex lines, which are straight for under-critical values L and spiral for larger L. For supercritical L, a vortex with multiple topological charges m>1 in generating 2D solitons transforms into m separate vortex lines. Taking into account weak non-paraxiality reveals polarization singularities in the form of lines, on which the elliptical polarization turns into linear in the cross section of the structures.

Temporal differentiation and integration of few-cycle pulses by ultrathin metallic films.

We study theoretically the temporal transformations of few-cycle pulses upon linear interaction with ultrathin metallic films. We show that under certain conditions on the film thickness and the pulse spectrum, one obtains the temporal differentiation of the pulse shape in transmission and the temporal integration in reflection. In contrast to previous studies, these transformations are obtained for the field of few-cycle pulses itself instead of the slowly varying pulse envelope. These results open up new opportunities for the control of the temporal pulse profile in ultrafast optics.

Single-cycle pulse compression in dense resonant media.

We propose here a new approach for compression and frequency up-conversion of short optical pulses in the regime of extreme nonlinear optics in optically dense absorbing media, providing an alternative route to attosecond-scale pulses at high frequencies. This method is based on dynamics of self-induced transparency (SIT) pulses of nearly single cycle duration, leading to single-cycle-scale Rabi oscillations in the medium. The sub-cycle components of an incident pulse behave as separate SIT-pulses, approaching each other and self-compressing, resulting in the threefold compression in time and frequency up-conversion by the same factor. As we show, the scheme can be cascaded, staying at the subsequent stage with nearly the same compression and up-conversion ratio. In this way, as our simulations show, after only few micrometers of propagation, a 700 nm wavelength single cycle pulse can be compressed to a pulse of 200 attoseconds duration located in XUV frequency range.

Population difference gratings created on vibrational transitions by nonoverlapping subcycle THz pulses.

We study theoretically a possibility of creation and ultrafast control (erasing, spatial frequency multiplication) of population density gratings in a multi-level resonant medium having a resonance transition frequency in the THz range. These gratings are produced by subcycle THz pulses coherently interacting with a nonlinear medium, without any need for pulses to overlap, thereby utilizing an indirect pulse interaction via an induced coherent polarization grating. High values of dipole moments of the transitions in the THz range facilitate low field strength of the needed THz excitation. Our results clearly show this possibility in multi-level resonant media. Our theoretical approach is based on an approximate analytical solution of time-dependent Schrödinger equation (TDSE) using perturbation theory. Remarkably, as we show here, quasi-unipolar subcycle pulses allow more efficient excitation of higher quantum levels, leading to gratings with a stronger modulation depth. Numerical simulations, performed for THz resonances of the [Formula: see text] molecule using Bloch equations for density matrix elements, are in agreement with analytical results in the perturbative regime. In the strong-field non-perturbative regime, the spatial shape of the gratings becomes non-harmonic. A possibility of THz radiation control using such gratings is discussed. The predicted phenomena open novel avenues in THz spectroscopy of molecules with unipolar and quasi-unipolar THz light bursts and allow for better control of ultra-short THz pulses.

Stable coherent mode-locking based on [Formula: see text] pulse formation in single-section lasers.

Here we consider coherent mode-locking (CML) regimes in single-section cavity lasers, taking place for pulse durations less than atomic population and phase relaxation times, which arise due to coherent Rabi oscillations of the atomic inversion. Typically, CML is introduced for lasers with two sections, the gain and absorber ones. Here we show that, for certain combination of the cavity length and relaxation parameters, a very stable CML in a laser, containing only gain section, may arise. The mode-locking is unconditionally self-starting and appears due to balance of intra-pulse de-excitation and slow interpulse-scale pump-induced relaxation processes. We also discuss the scaling of the system to shorter pulse durations, showing a possibility of mode-locking for few-cycle pulses.

Selective ultrafast control of multi-level quantum systems by subcycle and unipolar pulses.

The most typical way to optically control population of atomic and molecular systems is to illuminate them with radiation, resonant to the relevant transitions. Here we consider a possibility to control populations with the subcycle and even unipolar pulses, containing less than one oscillation of electric field. Despite the spectrum of such pulses covers several levels at once, we show that it is possible to selectively excite the levels of our choice by varying the driving pulse shape, duration or time delay between consecutive pulses. The pulses which are not unipolar, but have a peak of electric field of one polarity much higher (and shorter) than of the opposite one, are also capable for such control.

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. Our numerical analysis demonstrates the possibility of a satisfactory description of the evolution of the pulse field at large times by means of a three-dimensional generalization of the sine-Gordon and double sine-Gordon equations.

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. In the first variant, we consider a linear molecular chain and organic film interacting resonantly with laser radiation. Demonstrated are optical bistability, switching waves, and dissipative solitons, whose sizes for molecular J-aggregates can reach the nanometer range. We also discuss some theoretical approaches to take into account multi-particle interaction and correlations between molecules. In the second variant, light structuring in large-size laser medium with saturable amplification and absorption is achieved by preparation of the initial field distribution with a number of closed and unclosed vortex lines where the field vanishes. Various types of topological solitons, parameter domains of their stability, and transformation of the solitons with slow variation of the scheme parameters are presented.

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. 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.

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. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.

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.