We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The D
M map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal light bullets, stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstrate that stability of the 3D spatiotemporal solitons is determined by the usual DM-strength parameter, $S$: they are quasi-stable at $ S<S_{0}approx 0.93$, and completely stable at $S>S_{0}$. Stable vortex solitons are constructed too. We also consider collisions between the 3D solitons, in both axial and transverse directions. The interactions are quasi-elastic, including periodic collisions between solitons which perform shuttle motion in the transverse plane.
We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transver
se trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number $n=1$, while vortices with $n=2$ are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.
We introduce a system of two component two-dimensional (2D) complex Ginzburg-Landau equations (CGLEs) with spin-orbit-coupling (SOC) describing a wide-aperture microcavity laser with saturable gain and absorption. We report families of two-component
self-trapped dissipative laser solitons in this system. The SOC terms are represented by the second-order differential operators, which sets the difference, $|Delta S|=2$, between the vorticities of the two components. We have found stable solitons of two types: vortex-antivortex (VAV) and semi-vortex (SV) bound states, featuring vorticities $left( -1,+1right) $ and $left( 0,2right) $, respectively. In previous works, 2D localized states of these types were found only in models including a trapping potential, while we are dealing with the self-trapping effect in the latteraly unconfined (free-space) model. The SV states are stable in a narrow interval of values of the gain coefficients. The stability interval is broader for VAV states, and it may be expanded by making SOC stronger (although the system without SOC features a stability interval too). We have found three branches of stationary solutions of both VAV and SV types, two unstable and one stable. The latter one is an attractor, as the unstable states spontaneously transform into the stable one, while retaining vorticities of their components. Unlike previously known 2D localized states, maintained by the combination of the trapping potential and SOC, in the present system the VAV and SV complexes are stable in the absence of diffusion. In contrast with the bright solitons in conservative models, chemical potentials of the dissipative solitons reported here are positive.
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing nonlinearity. We dem
onstrated that the commonly known background instability driven by the linear gain can be suppressed by a combination of a harmonic-oscillator trapping potential and effective diffusion. Systematic numerical analysis of one- and two-dimensional (1D and 2
We employ the generic three-wave system, with the $chi ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave solitons in a
setting which is not available in other nonlinear systems. The advantage is that the single-wave TAWs, carried by either one of the FF component, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transforms them into a set of solitons, the number of which decreases with the increase of the total power. The TAW absorbs an incident small-power soliton, and a high-power soliton absorbs the TAW. Between these limits, the collision with an incident soliton converts the TAW into two solitons, with a remnant of the TAW attached to one of them, or leads to formation of a complex TAW-soliton bound state. At large velocities, the collisions become quasi-elastic.
Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric $chi^{2}$ solitons is considered in the 2D system with the quadratic nonlinearity. The spontaneous conversion is driven by the parametric instabi
lity of the SH wave. The input in the form of the AW vortex is considered too. As a result, one, two, or three stable solitons emerge in a well-defined form, unlike the recently studied 1D setting, where the picture is obscured by radiation jets. Shares of the total power captured by the emerging solitons and conversion efficiency are found as functions of parameters of the AW input.
Spontaneous creation of solitons in quadratic media by the downconversion, i.e., parametric instability against the generation of fundamental-frequency excitations, from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. P
arameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude jets. Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.
We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr nonlinearity. T
he asymmetry is defined by a difference between bandgap widths in the two BGs. In the linear system, exact defect modes (DMs) are found. Composite gap solitons pinned to the central layer are found too, in analytical and numerical forms, in the nonlinear model. In the asymmetric system, existence boundaries for the DMs and gap solitons, due to the competition between attraction to the gapless layer and repulsion from the reflectivity step, are obtained analytically. Stability boundaries for solitons in the asymmetric system are identified by means of direct simulations. Collisions of moving BG solitons with the gapless layer are studied too.
We introduce the simplest one-dimensional nonlinear model with the parity-time (PT) symmetry, which makes it possible to find exact analytical solutions for localized modes (solitons). The PT-symmetric element is represented by a point-like (delta-fu
nctional) gain-loss dipole {delta}^{prime}(x), combined with the usual attractive potential {delta}(x). The nonlinearity is represented by self-focusing (SF) or self-defocusing (SDF) Kerr terms, both spatially uniform and localized ones. The system can be implemented in planar optical waveguides. For the sake of comparison, also introduced is a model with separated {delta}-functional gain and loss, embedded into the linear medium and combined with the {delta}-localized Kerr nonlinearity and attractive potential. Full analytical solutions for pinned modes are found in both models. The exact solutions are compared with numerical counterparts, which are obtained in the gain-loss-dipole model with the {delta}^{prime}- and {delta}- functions replaced by their Lorentzian regularization. With the increase of the dipoles strength, {gamma}, the single-peak shape of the numerically found mode, supported by the uniform SF nonlinearity, transforms into a double-peak one. This transition coincides with the onset of the escape instability of the pinned soliton. In the case of the SDF uniform nonlinearity, the pinned modes are stable, keeping the single-peak shape.
We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schrodinger equations, coupled by repulsive XPM (cross-phase-modulation) terms, in the absence of the SPM (self-phase-modulation) nonlinearity. T
he equations include a periodic potential acting on both components, thus giving rise to GSs of the symbiotic type, which exist solely due to the repulsive interaction between the two components. The model may be implemented for holographic solitons in optics, and in binary bosonic or fermionic gases trapped in the optical lattice. Fundamental symbiotic GSs are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. Symmetric solitons are destabilized, including their entire family in the second bandgap, by symmetry-breaking perturbations above a critical value of the total power. Asymmetric solitons of intra-gap and inter-gap types are studied too, with the propagation constants of the two components falling into the same or different bandgaps, respectively. The increase of the asymmetry between the components leads to shrinkage of the stability areas of the GSs. Inter-gap GSs are stable only in a strongly asymmetric form, in which the first-bandgap component is a dominating one. Intra-gap solitons are unstable in the second bandgap. Unstable two-component GSs are transformed into persistent breathers. In addition to systematic numerical considerations, analytical results are obtained by means of an extended (tailed) Thomas-Fermi approximation (TFA).
