Rodislav Driben

Inversion and tight focusing of Airy pulses under the action of third-order dispersion.

By means of direct simulations and theoretical analysis, we study the nonlinear propagation of truncated Airy pulses in an optical fiber exhibiting both anomalous second-order and strong positive third-order dispersions (TOD). It is found that the Airy pulse first reaches a finite-size focal area as determined by the relative strength of the two dispersion terms, and then undergoes an inversion transformation such that it continues to travel with an opposite acceleration. The system notably features tight focusing if the TOD is a dominant factor. These effects are partially reduced by Kerr nonlinearity.

Instabilities, solitons and rogue waves in -coupled nonlinear waveguides

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity?time (𝒫𝒯)-symmetric system of linearly coupled nonlinear Schr?dinger equations, which describes a Kerr-nonlinear optical coupler with mutually balanced gain and loss in its cores. Besides the linear coupling, the overlapping cores are coupled through the cross-phase-modulation term too. While the rogue waves, built according to the pattern of the Peregrine soliton, are (quite naturally) unstable, we demonstrate that the focusing cross-phase-modulation interaction results in their partial stabilization. For 𝒫𝒯-symmetric and antisymmetric bright solitons, the stability region is found too, in an exact analytical form, and verified by means of direct simulations.

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.

Newton's cradles in optics: From N-soliton fission to soliton chains

A mechanism for creating a Newton’s cradle (NC) in nonlinear light wave trains under the action of the third-order dispersion (TOD) is demonstrated. The formation of the NC structure plays an important role in the process of fission of higher-order (N ) solitons in optical fibers. After the splitting of the initial N soliton into a nonuniform chain of fundamental quasisolitons, the tallest one travels along the entire chain, through consecutive collisions with other solitons, and then escapes, while the remaining chain of pulses stays as a bound state, due to the radiation-mediated interaction between them. Increasing the initial soliton’s order, N , leads to the transmission through, and release of additional solitons with enhanced power, along with the emission of radiation, which may demonstrate a broadband supercontinuum spectrum. The NC dynamical regime remains robust in the presence of extra perturbations, such as the Raman and self-steepening effects, and dispersion terms above the third order. It is demonstrated that essentially the same NC mechanism is induced by the TOD in finite segments of periodic wave trains (in particular, soliton chains). A difference from the mechanical NC is that the TOD-driven pulse passing through the soliton array collects energy and momentum from other solitons. Thus, uniform and nonuniform arrays of nonlinear wave pulses offer an essential extension of the mechanical NC, in which the quasiparticles, unlike mechanical beads, interact inelastically, exchanging energy and generating radiation. Nevertheless, the characteristic phenomenology of NC chains may be clearly identified in these nonlinear-wave settings too.

Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic-crystal fibers.

Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between copropagating solitons with small temporal and wavelength separation. We show that the mechanism of acceleration of a trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic-crystal fibers. As a result of fusion, large-intensity robust light structures arise and propagate over significant distances. In the presence of small random noise the delicate condition for the effective fusion between solitons can easily be broken, making the fusion-induced giant waves a rare statistical event. Thus oblong-shaped giant accelerated waves become excellent candidates for optical rogue waves.

Coupled Airy breathers

The dynamics of two component-coupled vectorial Airy beams is investigated. In the linear propagation regime, a complete analytic solution describes the breather-like propagation of two components that feature nondiffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility of designing more complex nondiffracting propagation scenarios. In the strongly nonlinear regime, the dynamics remain qualitatively robust as is revealed by direct numerical simulations. Because of the Kerr effect, the two beams emit solitonic breathers whose coupling period is compatible with the remaining Airy-like beams. The results of this study are relevant for the description of photonic and plasmonic beams that propagate in coupled planar waveguides, as well as for birefrigent or multiwavelength beams.

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 systems 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.

Split-step solitons in long fiber links

Abstract We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton (localized pulse) through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the systems stepsize (cells size) L comparable to the pulses dispersion length z D , SSM supports stable propagation of pulses which almost exactly coincide with fundamental solitons of the corresponding averaged nonlinear Schrodinger (NLS) equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly relaxes to it, emitting some radiation. A pulse whose initial amplitude is too large splits into two solitons; however, splitting can be suppressed by appropriately chirping the initial pulse. On the other hand, if the initial amplitude is too small, the pulse turns into a breather, and, below a certain threshold, it quickly decays into radiation. If L is essentially larger than z D , the input soliton rapidly rearranges itself into another soliton, with nearly the same area but smaller energy. At L still larger, the pulse becomes unstable, with a complex system of stability windows found inside the unstable region. Moving solitons are generated by lending them a frequency shift, which makes it possible to consider collisions between solitons. Except for a case when the phase difference between colliding solitons is ≲0.05π, the interaction between them is repulsive. We also simulate collisions between solitons in two-channel SSM, concluding that the collisions are strongly inelastic: even if the solitons pass through each other, they suffer a large reduction of the amplitude.

Transition to miscibility in a binary Bose–Einstein condensate induced by linear coupling

A one-dimensional mean-field model of a two-component condensate in the parabolic trap is considered, with the components corresponding to different spin states of the same atom. We demonstrate that the linear coupling (interconversion) between them, induced by a resonant electromagnetic wave, can drive the immiscible binary condensate into a miscible state. This transition is predicted in an analytical form by means of a variational approximation (for an infinitely long system), and is confirmed by direct numerical solutions of the symmetric and asymmetric models (the asymmetry accounts for a possible difference in the chemical potential between the components). We define an order parameter of the system as an off-centre shift of the centre of mass of each component. A numerically found dependence of the order parameter on the linear-coupling strength reveals a second-kind phase transition (in an effectively finite system). The phase transition looks very similar in two different regimes, namely, with a fixed number of atoms, or a fixed chemical potential. An additional transition is possible between double- and single-humped density distributions in the weak component of a strongly asymmetric system. We also briefly consider dynamical states, with the two components oscillating relative to each other. In this case, the components periodically separate even if they should be mixed in the static configuration.

Bistable guided solitons in the cubic-quintic medium

We consider spatial solitons in a channel waveguide with uniform cubic–quintic nonlinearity. By means of the variational approximation and numerical methods, two branches of the soliton solutions are found, which are in contrast to their free-space counterparts; the bistability occurs exactly at those values of the propagation constant where the free-space solitons do not exist. The Vakhitov–Kolokolov criterion formally predicts that one branch should be unstable; however, direct numerical tests disprove this expectation, showing that all the solitons are completely stable. Besides the bistability, another feature of the solitons which is promising for applications is that their edges can be made much sharper than in the free-space solitons. Systematic simulations of the evolution of an initial Gaussian beam are also performed, showing that it quickly self-traps into a soliton of either type, or into a breather, but never decays into radiation.