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.     

Two-dimensional laser soliton complexes with weak, strong, and mixed coupling

A review is given of features and motion of two-dimensional dissipative solitons in lasers and laser amplifiers with saturable absorption. We present a rich variety of stable complexes with weak, strong, and mixed coupling of individual laser solitons. The type of coupling is determined by the topology of the distribution of energy flows within the complex. We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their centre of mass. This type of motion results from the field distribution asymmetry and is well pronounced for complexes of laser solitons with strong and mixed types of coupling. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons. PACS 42.65.Tg     

Nonstationary multivortex and fissionable soliton-like structures of laser radiation

New types of nonstationary soliton-like structures of laser radiation were found in the mean field approximation by numerical simulation of a class A wide-aperture laser with saturable absorption. In the absence of frequency detunings, multivortex (with several wavefront dislocations distributed over the aperture) asymmetric rotating solitons were revealed, which can be interpreted as strongly coupled states of symmetric laser solitons with topological charges coinciding or differing in sign. In the presence of detunings between the central frequencies of the gain and absorption profiles and the frequency of the cavity mode, “biosoliton” regimes were obtained, which are characterized by the expansion of the initial localized structure and the periodic separation from it of fragments having similar dynamics.     

Incoherent weak coupling of laser solitons

A coupled state of a pair of spatial laser solitons with different topological charges in a wide-aperture class-A laser with saturable absorption was found by numerical simulation. In view of a difference in the frequencies of the individual solitons, periodic (with a period corresponding to the frequency difference) weak pulsations of the shape of the solitons and of the spacing between them take place, but the rotation of the pair and the motion of its center of inertia were not revealed.     

Complexes of moving transversely one-dimensional laser solitons

Complexes of weakly coupled moving solitons are found by numerical solution of the generalized Ginzburg-Landau equation for the transversely one-dimensional scheme of a wide-aperture A-class laser with saturable absorption. As distinct from the case of complexes of motionless solitons, the phase difference between the neighboring moving solitons is close to 7π/2.     

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.     

Bound soliton pulses in a passively mode-locked fibre ring laser

The bound solitons in a passively mode-locked fibre ring laser are observed and their formation mechanism is summarized in this paper. In order to obtain stable bound solitons, a strong CW laser field at the centre of the soliton spectral is necessary to suppress and synchronize the random soliton phase variations.     

Nonlinear interaction of a circularly polarized electromagnetic wave with a dense laser plasma

The interaction of an intense circularly polarized laser pulse with a layer of plasma of supercritical density is studied. The nonlinear skin effect for the electromagnetic field and the coefficient of collisionless absorption of the laser pulse were calculated analytically. It is shown that, in the process of interaction with the plasma, the laser pulse generates solitons propagating through the plasma layer and transferring the radiation through the opaque medium. The coefficient of transparency of the plasma layer for the soliton-like penetration of the laser radiation was calculated. The plasma parameters at which the collisionless absorption is small as compared to the transformation of the laser energy into solitons were found.     

Soliton coupling in birefringent optical fiber with third-order dispersion

Nonlinear coupling of polarized solitons in birefringent optical fiber in the presence of third-order dispersion is considered in the framework of the coupled nonlinear Schrödinger equations. The influence of third-order dispersion on the interaction between solitons is investigated. For sufficiently strong third-order dispersion the interaction may even become repulsive. The stable conditions for solitons of partial pulses are analyzed and amplitude threshold, which decreases with third-order dispersion coefficient decreasing, for the capture of solitons of partial pulses into a coupled two-component pulse is obtained.     

Oblique magneto-acoustic solitons in a rotating plasma

Weakly nonlinear magneto-acoustic waves propagating at an arbitrary angle to the external magnetic field in a rotating plasma are considered. A model equation (Ostrovsky's equation with positive dispersion) is derived from a set of basic magneto-hydrodynamic equations. Stationary solutions of this equation are obtained numerically and analyzed in detail theoretically. These include solitary-type solutions (solitons with monotonic and oscillating tails), complex multisolitons (bound states of coupled single solitons), as well as periodic waves. We emphasize that the positive dispersion, in contrast to the negative one, gives rise to solitary waves within the framework of Ostrovsky's equation.     

Motion of clusters of weakly coupled two-dimensional cavity solitons

An analysis of clusters of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed. The symmetries that control the transverse motion of the clusters are described. Numerical solutions of the governing generalized complex Ginzburg-Landau equation demonstrate the existence of four types of clusters of weakly coupled cavity solitons that correspond to symmetries of transverse intensity distributions and energy flows: (1) stationary (with two mirror symmetry axes), (2) rotating about a stationary center of mass (invariant under rotation), (3) translating without rotation (with a single mirror symmetry axis), and (4) asymmetric ones rotating about a center of mass that moves around a circle (with equal periods of rotation and circular motion).     

Energy quantization of twin-pulse solitons in a passively mode-locked fiber ring laser

A novel twin-pulse form of solitary wave was recently revealed in a passively mode-locked fiber ring laser. In this paper we report on the energy quantization feature of the twin-pulse solitons in the laser. We show that, as in the case of single-pulse solitons, multiple twin-pulse solitons can coexist in the laser cavity, and, in particular, that all of them have exactly the same pulse energy and twin-pulse separation. The pump-power hysteresis effect previously reported for the single-pulse soliton operation is also observed for the twin-pulse soliton operation of the laser. PACS 42.81.Dp; 42.55.Wd; 42.60.Fc     

Incoherently coupled two component screening photovoltaic solitons in two-photon photorefractive materials under the action of external field

The existence of incoherently coupled two-component steady state photovoltaic solitons in biased two-photon photorefractive materials due to two-photon photorefractive effect has been investigated. In the steady state regime, these incoherently coupled solitons can propagate in bright–bright, dark–dark and bright–dark configurations. The most important finding is that, with the application of electric field, it is possible to generate solitons and control them in those media where soliton formation was hitherto prohibited. Dynamic evolution of these solitons has been examined using numerical simulations, which show that these solitons are stable.     

Chaotic dynamics of a passively mode-locked soliton fiber ring laser

We report on the experimental and numerical studies of the chaotic dynamics of a soliton fiber ring laser passively mode-locked by using the nonlinear polarization rotation (NPR) technique. Period-doubling route to chaos on the soliton repetition rate of either the single pulse soliton or the bound solitons of the laser was experimentally observed. Based on a coupled complex Ginzburg-Landau equation model and also taking into account the laser cavity effect, we further show numerically that the period-doubling bifurcations and route to chaos are intrinsic properties of the laser, whose appearance is independent of the details of the laser cavity design and the laser soliton operation. Property of the solitons under the dynamical bifurcations is also numerically investigated.     

Interaction of ultrashort light pulses with carbon nanotubes

The possibility of existence of electromagnetic solitons in carbon nanotubes is investigated on the basis of the coupled equations for the classical distribution function of electrons in such nanotubes and the Maxwell equations for electromagnetic fields. Solitons arise due to the matched change in the classical distribution function and the electric field formed by nonequilibrium electrons of a carbon nanotube. The data of numerical calculations, indicative of the existence of solitons, are reported.     

Electromagnetic solitons in bundles of zigzag carbon nanotubes

The possibility of forming solitons in zigzag carbon nanotubes is investigated using the coupled equations for the classical function of the electron distribution and the Maxwell equations for an electromagnetic field. It is demonstrated that the solitons are generated as a result of correlated changes in the classical distribution function and the electric field induced by nonequilibrium electrons of a carbon nanotube. The effective equation describing the dynamics of the electromagnetic field is derived. The existence of solitons is confirmed by the results of numerical calculations. The characteristics of solitons are investigated as a function of the diameter of zigzag carbon nanotubes.     

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学.从Maxwell方程出发,利用多重尺度法,导出了光学整流场与两个基频电场包络的非线性耦合模方程组,给出了耦合模方程组的孤子解.结果表明,由于二阶非线性导致的光学整流场对基频电场有调制作用,使得两个基频电场分量可以呈现为亮孤子亮孤子、暗孤子暗孤子及亮孤子-暗孤子对 当两个基频电场的振动频率趋于光子晶体频带的带边频率时,光学整流场消失     

Collisions of complexes of weakly coupled laser solitons

Different scenarios of collisions of complexes of weakly coupled solitons moving in antiparallel directions in a wide-aperture class-A laser with saturable absorption are found by numerical simulation. Depending on the impact parameter and the phase difference of the initial complexes, they can adhere to each other or form new complexes composed of both initial complexes, while the number of solitons can change from their total disappearance to the extension of the region of generation over the whole transverse cross section of the laser.     

Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing

We study breathers and solitons on different backgrounds in optical fiber system, which is governed by generalized coupled Hirota equations with four wave mixing effect. On plane wave background, a transformation between different types of solitons is discovered. Then, on periodic wave background, we find breather-like nonlinear localized waves of which formation mechanism are related to the energy conversion between two components. The energy conversion results from four wave mixing. Furthermore, we prove that this energy conversion is controlled by amplitude and period of backgrounds. Finally, solitons on periodic wave background are also exhibited. These results would enrich our knowledge of nonlinear localized waves' excitation in coupled system with four wave mixing effect.     

Interaction between multiple spatial solitons in the diffraction catastrophe region upon focusing a high-power laser beam in a nonlinear medium

When a high-power laser beam is focused in a nonlinear Kerr medium, beam self-diffraction by induced inhomogeneities of the refractive index is observed. A method for calculating the field amplitude and phase in the focal region with regard for self-diffraction by self-induced inhomogeneities is developed. Computer analysis of saturable Kerr media showed that the optical-field region with the least cross section of the focal pattern is followed by that of chaotically radiating “splashes” and long filaments. The latter radiate outward from the region of the caustic waist over long distances. They represent bright spatial solitons, which channel a significant portion of the primary beam energy. No less than 8–12 clear-cut solitons traveling in the positive z direction and moving apart in the transverse (x, y) plane are observed in the cross section. The field amplitude oscillates along each of the solitons. Various parameters of the saturable Kerr medium are taken into account.