Bright and dark solitons in the systems with strong light-matter coupling: Exact solutions and numerical simulations.

We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons including bright solitons on zero and nonzero background and dark-gray and gray-gray solitons. The solutions are found in the analytical form by reducing the two-component problem to a single stationary equation with cubic-quintic nonlinearity. All found solutions coexist under the same set of the model parameters, but, in a properly defined linear limit, approach different branches of the polariton dispersion relation for linear waves. Bright solitons with zero background feature an oscillatory-instability threshold which can be associated with a resonance between the edges of the continuous spectrum branches. "Half-topological" dark-gray and nontopological gray-gray solitons are stable in wide parametric ranges below the modulational instability threshold, while bright solitons on the constant-amplitude pedestal are unstable.

PROJECTING OF COMPLEX HEALTH TRAINING FOR MATURE MEN WITH METABOLIC SYNDROME.

OBJECTIVE: The aim: To identify risk factors for metabolic syndrome; to model, justify and experimentally test the effectiveness of a program of complex health training for mature men with MS. PATIENTS AND METHODS: Materials and methods: Theoretical - analysis, generalization, pedagogical observation, modelling; empirical - methods of implementation of the results in practice (pedagogical experiment involving 50 mature menwho had no contraindications to training), methods of monitoring and measuring of physical evolvement, body systems functional status (samples: Rufier, Stange), general performance level (Harvard step test), medical indicators (blood glucose level, arterial tension). RESULTS: Results: A complex organized health training program (graduated, systematic, all-round motor activity managed by an instructor) showed better results (24,5 %) compared an independent health training system(15,2 %). Both types of activity contributed to weight loss(CG2 - 10,1 %; EG2 - 15,5 %) and reduction of body parts overall size; functional improvement of cardiovascular and respiratory systems of the male body, in particular in the indicators of the Stange test (CG2 - 29,8 %,EG2 - 33,9 %), Ruffier index (CG2 - 5,8 %, EG2 - 23,0 %) and step test (CG2 - 15,8 %, EG2 - 26,9 %); positive changes in blood glucose levels (CG2 - 20,7 %, EG2 - 31,5 %) andarterial tension (CG2 - 6,2 %, EG2 - 9,8 %); development of different muscle groupsstrength endurance. CONCLUSION: Сonclusions: Positive changes according to the studied indicators show the decrease in risk factors for mature men metabolic syndrome and thereby preventingcomplications.

CURRENT ASPECTS OF DELIVERY IN HEALTHY WOMEN IN ACCORDANCE WITH THE DATA OF RETROSPECTIVE ANALYSIS.

OBJECTIVE: The aim: to study the current aspects of the course of labor in healthy women using retrospective indicators. PATIENTS AND METHODS: Materials and methods: To study this topic, an analysis of 1,078 births on the basis of the maternity ward for pregnant women with obstetric pathology of the State Institution «IPAG. acad. O.M. Lukyanova National Academy of Medical Sciences of Ukraine¼. It was found that among all births, the share of first-borns was 602 (55.8 %) women, of whom 451 (41.8 %) were pregnant for the first time, and only 86 (8 %) were healthy pregnant women. RESULTS: Results: It was found that among 86 births the frequency of physiological births was 64%, of which in 47.7% of cases the birth was complicated, and pathological - 36%. The most common complications during childbirth were: premature rupture of membranes (PRPO), episio- and perineotomy, trauma to the birth canal. The main causes of pathological childbirth: abnormalities of labor, fetal distress, defect of the placenta and membranes, clinically narrow pelvis, malposition of the fetus and early postpartum hemorrhage. All children were born alive. It should be noted that all births where the Apgar score was ≤ 6 had no partner support, and the women themselves did not receive any preparation for childbirth. CONCLUSION: Conclusions: According to our data, in almost healthy women who gave birth for the first time and had no perinatal loss in the anamnesis, did not undergo prenatal training and did not have partner support during childbirth, the number of complications during childbirth is increasing. Therefore, this group of healthy pregnant women needs more detailed study and analysis, development of prenatal training algorithms to improve perinatal indicators.

Ultrafast-nonlinear ultraviolet pulse modulation in an AlInGaN polariton waveguide operating up to room temperature.

Ultrafast nonlinear photonics enables a host of applications in advanced on-chip spectroscopy and information processing. These rely on a strong intensity dependent (nonlinear) refractive index capable of modulating optical pulses on sub-picosecond timescales and on length scales suitable for integrated photonics. Currently there is no platform that can provide this for the UV spectral range where broadband spectra generated by nonlinear modulation can pave the way to new on-chip ultrafast (bio-) chemical spectroscopy devices. We demonstrate the giant nonlinearity of UV hybrid light-matter states (exciton-polaritons) up to room temperature in an AlInGaN waveguide. We experimentally measure ultrafast nonlinear spectral broadening of UV pulses in a compact 100 µm long device and deduce a nonlinearity 1000 times that in common UV nonlinear materials and comparable to non-UV polariton devices. Our demonstration promises to underpin a new generation of integrated UV nonlinear light sources for advanced spectroscopy and measurement.

Nonlinear Control of Electromagnetic Topological Edge States.

Topological photonics has emerged recently as a smart approach for realizing robust optical circuitry, and the study of nonlinear effects is expected to open the door for tunability of photonic topological states. Here we realize experimentally nonlinearity-induced spectral tuning of electromagnetic topological edge states in arrays of coupled nonlinear resonators in the pump-probe regime. When nonlinearity is weak, we observe that the frequencies of the resonators exhibit spectral shifts concentrated mainly at the edge mode and affecting only weakly the bulk modes. For a strong pumping, we describe several scenarios of the transformation of the edge states and their hybridization with bulk modes, and also predict a parametrically driven transition from topological stationary to unstable dynamic regimes.

Nonlinearity-induced localization in a periodically driven semidiscrete system.

We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a system which is discrete in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic modulation of the gradient strength along the discrete axis leads to the usual rapid spread of an initially confined wave packet. Addition of the cubic nonlinearity makes the dynamics drastically different, inducing robust localization of moving wave packets. Similar nonlinearity-induced effects are also produced in the presence of a combination of static and oscillating linear potentials. The predicted dynamical localization in the nonlinear medium can be realized in photonic lattices and Bose-Einstein condensates.

Bloch oscillations sustained by nonlinearity.

We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields of physics such as optics and Bose-Einstein condensates. We demonstrate that designing an optimal relation between the nonlinearity and the linear gradient strength provides extremely long-lived Bloch oscillations with little degradation. Such robust oscillations can be observed for a broad range of parameters and even for moderate nonlinearities and large enough values of linear potential. We also present an approximate analytical description of the wave packet's evolution featuring a hybrid Bloch oscillating wave-soliton behavior that excellently corresponds to the direct numerical simulations.

Self-adjusted all-dielectric metasurfaces for deep ultraviolet femtosecond pulse generation.

The advantage of metasurfaces and nanostructures with a high nonlinear response is that they do not require phase matching, and the generated pulses are short in the time domain without additional pulse compression. However, the fabrication of large-scale planar structures by lithography-based methods is expensive, time consuming, and requires complicated preliminary simulations to obtain the most optimized geometry. Here, we propose a novel strategy for the self-assembled fabrication of large-scale resonant metasurfaces, where incident femtosecond laser pulses adjust the initial silicon films via specific surface deformation to be as resonant as possible for a given wavelength. The self-adjusting approach eliminates the necessity of multistep lithography and designing, because interference between the incident and the scattered parts of each laser pulse "imprints" resonant field distribution within the film. The self-adjusted metasurfaces demonstrate a high damage threshold (≈1012 W cm-2) and efficient frequency conversion from near-IR to deep UV. The conversion efficiency is up to 30-fold higher compared with nonresonant smooth Si films. The resulting metasurfaces allow for the generation of UV femtosecond laser pulses at a wavelength of 270 nm with a high peak and average power (≈105 W and ≈1.5 µW, respectively). The results pave the way to the creation of ultrathin nonlinear metadevices working at high laser intensities for efficient deep UV generation at the nanoscale.

Motion of dissipative optical fronts under the action of an oscillating pump.

The dynamics of domain walls in optical bistable systems with pump and loss is considered. It is shown that an oscillating component of the pump affects the average drift velocity of the domain walls. The cases of harmonic and biharmonic pumps are considered. It is demonstrated that in the case of biharmonic pulse the velocity of the domain wall can be controlled by the mutual phase of the harmonics. The analogy between this phenomenon and the ratchet effect is drawn. Synchronization of the moving domain walls by the oscillating pump in discrete systems is studied and discussed.

Emulation of Fabry-Perot and Bragg resonators with temporal optical solitons.

The scattering of weak dispersive waves (DWs) on several equally spaced temporal solitons is studied. It is shown by systematic numerical simulations that the reflection of the DWs from the soliton trains strongly depends on the distance between the solitons. The dependence of the reflection and transmission coefficients on the inter-soliton distance and the frequency of the incident waves are studied in detail, revealing fascinating quasi-periodic behavior. The analogy between the observed nonlinear phenomena in the temporal domain and the usual Fabry-Perot and Bragg resonators is discussed.

Interaction of high-order solitons with external dispersive waves.

The effect of mutual interaction between second-order soliton and dispersive waves (DWs) is investigated. It is predicted analytically and confirmed numerically that DWs (both transmitted and reflected components) become polychromatic after interaction with the soliton. Collision with DWs of considerable intensity can lead to acceleration/deceleration and central frequency shift of the soliton, while still preserving the soliton's oscillating structure. Two second-order solitons with resonant DWs trapped between them can form an effective solitonic cavity with "flat" or "concave mirrors," depending on the intensity of the input.

Weak and strong interactions between dark solitons and dispersive waves.

The effect of mutual interactions between dark solitons and dispersive waves is investigated numerically and analytically. The condition of the resonant scattering of dispersive waves on dark solitons is derived and compared against the results of the numerical simulations. It is shown that the interaction with intense dispersive waves affects the dynamics of the solitons by accelerating, decelerating, or destroying them. It is also demonstrated that two dark solitons can form a cavity for dispersive waves bouncing between the two dark solitons. The differences of the resonant scattering of the dispersive waves on dark and bright solitons are discussed. In particular, we demonstrate that two dark solitons and a dispersive wave bouncing in between them create a solitonic cavity with convex "mirrors," unlike the concave "mirror" in the case of bright solitons.

Resonant radiation from oscillating higher order solitons.

We present radiation mechanism exhibited by a higher order soliton. In a course of its evolution the higher-order soliton emits polychromatic radiation resulting in formation of multipeak frequency comb-like spectral band. The shape and spectral position of this band can be effectively controlled by the relative strength of the third order dispersion. An analytical description is corroborated by numerical simulations. It is shown that for longer pulses the described effect persists also under the action of higher order perturbations such as Raman and self-steepening.

Tuning resonant interaction of orthogonally polarized solitons and dispersive waves with the soliton power.

We demonstrate that the relatively small power induced changes in the soliton wavenumber comparable with splitting of the effective indexes of the orthogonally polarized waveguide modes result in significant changes of the efficiency of the interaction between solitons and dispersive waves and can be used to control energy transfer between the soliton and newly generated waves and to delay or accelerate solitons.

Conservative and PT-symmetric compactons in waveguide networks.

Stable discrete compactons in interconnected three-line waveguide arrays are found in linear and nonlinear limits in conservative and in parity-time (PT)-symmetric models. The compactons result from the interference of the fields in the two lines of waveguides ensuring that the third (middle) line caries no energy. PT-symmetric compactons require not only the presence of gain and losses in the two lines of the waveguides but also complex coupling, i.e., gain and losses in the coupling between the lines carrying the energy and the third line with zero field. The obtained compactons can be stable and their branches can cross the branches of the dissipative solitons. Unusual bifurcations of branches of solitons from linear compactons are described.

Trapping of light in solitonic cavities and its role in the supercontinuum generation.

We demonstrate that the fission of higher-order N-solitons with a subsequent ejection of fundamental quasi-solitons creates cavities formed by a pair of solitary waves with dispersive light trapped between them. As a result of multiple reflections of the trapped light from the bounding solitons which act as mirrors, they bend their trajectories and collide. In the spectral domain, the two solitons receive blue and red wavelength shifts, and the spectrum of the trapped light alters as well. This phenomenon strongly affects spectral characteristics of the generated supercontinuum. Consideration of the system's parameters which affect the creation of the cavity reveals possibilities of predicting and controlling soliton-soliton collisions induced by multiple reflections of the trapped light.

Soliton interaction mediated by cascaded four wave mixing with dispersive waves.

We demonstrate that trapping of dispersive waves between two optical solitons takes place when resonant scattering of the waves on the solitons leads to nearly perfect reflections. The momentum transfer from the radiation to solitons results in their mutual attraction and a subsequent collision. The spectrum of the trapped radiation can either expand or shrink in the course of the propagation, which is controlled by arranging either collision or separation of the solitons.

Two-dimensional superfluid flows in inhomogeneous Bose-Einstein condensates.

We report an algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevskii equation to the one-dimensional nonlinear Schrödinger equation, the latter allowing for exact solutions, with the conformal mapping of the given domain, where the flow is considered, to a half space. The stability of the obtained flows is addressed. A number of stable and physically relevant examples are described.

Generation of spatial solitons by a localized active cluster.

The formation, stability, and dynamics of solitons are considered in an optical system with focusing nonlinearity and active clusters. It is shown that stochastic generation of solitons is possible in such a system provided the cluster properties are properly designed.

Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials.

Exact solutions for the generalized nonlinear Schrödinger equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic modulations in the space of complex potentials and nonlinearity coefficients. Examples of stable and unstable solutions are given. We also demonstrated numerically the existence of stable dissipative breathers in the presence of an additional parabolic trap.