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. In the framework of the generalized Ginzburg-Landau equation, shown are finite numbers of plane-wave modes, stable with respect to weak perturbations, and solitonlike modes with inhomogeneous intensity distributions and different topological charge. It was found that the topological charge could change during transient to steady state. The events of these changes alternate with formation of cusps of the phase curve occurring when extrema of the field intensity and phase coincide.

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)OPLEDP0146-959210.1364/OL.394727.

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.

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. Suitable subcycle THz wavefronts can be generated via coherent excitation of nonlinear low-frequency oscillators by few-cycle optical pulses. Using this approach it is possible to shape the electric field rather than the slow pulse envelope, obtaining, for instance, rectangular or triangular waveforms in the THz range. The method is upscalable to the optical range if the attosecond pump pulses are used.

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. The results are confirmed by direct numerical solution of multilevel Bloch equations.

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. During the transient, new (metastable) types of localized topological structures arise. It is shown that the tangent energy flow along closed vortex lines is unidirectional or direction alternating.

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)'.

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. In the presence of gravity, the breather always splits into a pair of "co-hopping" fundamental solitons, which may be frequency locked in the form of a quasi-breather, or unlocked, forming an incoherent pseudo-breather. Some essential results are obtained in an analytical form, in addition to the systematic numerical investigation.

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. Besides, the oscillation velocity of the charges can be forced to keep a constant sign throughout the pulse duration. That is, reflection of ultrashort pulses from broad-area layers with nanometer-scale thickness can be very different from the common reflection in the case of longer pulses and thicker layers. This suggests a possibility of unusual transformations of few-cycle light pulses in completely linear optical systems.

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., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.

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. The mechanism is able to work with pulse durations up to the single-cycle limit. Somewhat surprisingly, ultrafast grating wave vector control requires the generation of polarization waves with the phase velocity much smaller than that of light.

Rotating and Precessing Dissipative-Optical-Topological-3D Solitons.

We predict and study a new type of three-dimensional soliton: asymmetric rotating and precessing stable topological-dissipative-optical localized structures in homogeneous media with saturable amplification and absorption. The crucial factor determining their dynamics is the ratio of the diffusion coefficients characterizing the frequency dispersion and angular selectivity (dichroism) of the scheme. These vortex solitons exist and are stable for overcritical values of the selectivity coefficients and can be realized in lasers of large sizes with saturable absorption.

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 T2 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. Furthermore, we discuss the stability of the corresponding mapping. We also predict the existence of "super-CML regimes," with a pulse coupled to several Rabi oscillations in the nonlinear medium.

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.

Effects of spatial inhomogeneities on the dynamics of cavity solitons in quadratically nonlinear media.

We study the dynamics of cavity solitons under the influence of spatial inhomogeneities and derive generalized equations of motions. For perturbations large compared to the soliton size we find the modulus of the soliton velocity to be proportional to the gradient of the respective perturbation and that the proportionality coefficient changes sign when the soliton peak power drives the cavity beyond the resonance. For short scale perturbations solitons may be trapped at the extrema of the inhomogeneities. Shape and stability of these trapped solitons can be quasianalytically described by means of a perturbation theory. If both types of perturbations act solitons are either trapped or move depending on the strength of the respective perturbation. In the framework of a quasiparticle approach this dynamics is governed by a differential equation that holds for particle motion in a strongly viscous fluid under the action of a constant and harmonically varying force. We also show that in addition to acquiring a velocity the very existence conditions of the solitons (hysteresis curve) are affected by both kinds of perturbations. We find good quantitative agreement between our analytical results and numerical findings, which were obtained for a two wave interaction in a cavity filled with a quadratically nonlinear material.

Stable bound states of one-dimensional autosolitons in a bistable laser.

Differential equations describing the interaction of two weakly overlapping autosolitons in the transverse section of a wide-aperture laser with a saturable absorber are derived and analyzed. The existence of in-phase and out-of-phase stable bound autosoliton states is predicted analytically and confirmed numerically.

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. For the case of weak anisotropy we determine the soliton polarization state by a perturbation method; it turns out that it is elliptical and changing over the soliton transverse section. The approach allows generalization to the case of optical parametric oscillators.

Study of the early somatosympathetic reflex response.

Using anesthetized cats, we studied the early components of the somatosympathetic reflex in the white rami communicantes of segments T(3) and L(2) in response to stimulation of the corresponding segmental somatic nerves. The results show that the early somatosympathetic reflex is a complex and highly organized response consisting of three typical waves. The shortest latency wave of this reflex was investigated in detail and evidence of its monosynaptic nature was obtained. Calculations showed that the efferent part of this reflex component may be formed by sympathetic preganglionic neurons with axonal conduction velocities of about 10 m/sec or more.