Stability of vortex solitons in the cubic-quintic model

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, gives rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s=2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities.

We show that small negative fourth-order dispersion can arrest spatiotemporal collapse of ultrashort pulses with anomalous dispersion in a planar waveguide with pure Kerr nonlinearity, resulting in (2 + 1)D optical bullets. Similarly to solitons, these bullets undergo elastic collisions. Since these bullets can self-trap from noisy Gaussian input beams and propagate without any power losses, this result may be used to realize experimentally stable, nondissipative optical bullets.

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Optical light bullets in a pure Kerr medium.

Free-space propagation of ultrashort pulses is investigated. Space-time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.

Bessel pulse beams and focus wave modes.

We study two- and three-dimensional latticesnodes of which take three states: rest, eccited, andrefractory, and deterministically update their states indiscrete time depending on the number of excited closest neighbors. Every resting node isexcited if exactly 2 of its 8 (in two-dimensionallattice) or exactly 4 of its 26 (in three-dimensionallattice) closest neighbors are excited. A node changesits excited state into the refractory state and itsrefractory state into the rest state unconditionally. Weprove that such lattices are the minimal models oflattice excitation that exhibit bounded movable patterns of self-localized excitation(particle-like waves). The minimal, compact, stable,indivisible, and capable of nonstop movementparticle-like waves represent quanta of information.Exploring all possible binary collisions betweenparticle-like waves, we construct the catalogue of thelogical gates that are realized in the excitablelattices. The space and time complexity of the logicaloperations is evaluated and the possible realizations ofthe registers, counters, and reflectors are discussed.The place of the excitable lattices in the hierarchy ofcomputation universal models and their high affinity to real-life analogues affirm that excitablelattices may be the minimal models of real-likedynamical universal computation.

Universal Dynamical Computation in Multidimensional Excitable Lattices

The conditions for the formation of a light bullet pulse, propagating with nearly constant spatial and temporal parameters in a bulk nonlinear medium, are obtained. A pump and probe pulse configuration using an induced phase modulation (IPM) is used. The IPM effect provides a well-controllable spatial and temporal trapping of the probe pulse. The authors derive analytical expressions for the critical parameters of the system, incorporating input power, pulse duration, pump and probe beam radii, medium parameters, etc. The system parameters analyzed are rather general and include varying pump and probe pulse durations and delay. The constant parameters of the light formation are shown to be limited by the walk-off effect. An analytical balance condition is obtained for the spatial and temporal soliton-like formation. >

Light bullets formation in a bulk media

A method for pulse compression to the subpicosecond range in the VUV and the XUV is investigated theoretically. The induced phase modulation on a signal by a pump pulse near two-photon resonance in inert gases is analyzed, including group-velocity dispersion, pulse walk-off, initial delay, shift of the signal peak, and linear and nonlinear chirp rates for Gaussian and hyperbolic secant pulses. A reasonable agreement is found with the theoretical and experimental results of other authors.

A. B. Blagoeva

Papers

Light bullets formation in a bulk media

Modeling the subpicosecond pulse compression in the vacuum ultraviolet and the extreme ultraviolet