Statistical Theory for Incoherent Light Propagation in Nonlinear Media

A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip

Instabilities and Bifurcations of Nonlinear Impurity Modes

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres

Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR

Laser-assisted guiding of electric discharges around objects

Electric breakdown in air occurs for electric fields exceeding 34 kV/cm and results in a large current surge that propagates along unpredictable trajectories. Guiding such currents across specific paths in a controllable manner could allow protection against lightning strikes and high-voltage capacitor discharges. Such capabilities can be used for delivering charge to specific targets, for electronic jamming, or for applications associated with electric welding and machining. We show that judiciously shaped laser radiation can be effectively used to manipulate the discharge along a complex path and to produce electric discharges that unfold along a predefined trajectory. Remarkably, such laser-induced arcing can even circumvent an object that completely occludes the line of sight

New features of modulational instability of partially coherent light; importance of the incoherence spectrum

It is shown that the properties of the modulational instability of partially coherent waves propagating in a nonlinear Kerr medium depend crucially on the profile of the incoherent field spectrum. Under certain conditions, the incoherence may even enhance, rather than suppress, the instability. In particular, it is found that the range of modulationally unstable wave numbers does not necessarily decrease monotonously with increasing degree of incoherence and that the modulational instability may still exist even when long wavelength perturbations are stable.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Experimental observation of a photonic hook

Applied Physics Letters journal paper entitled "Experimental observation of a photonic hook".Other funders supporting this work in addition to EC Grant 737164: Russian Science Foundation, Project No. 17-79-20346. , Ser Cymru National Research Network (NRNF66), Tomsk Polytechnic University Competitiveness Enhancement Program

Statistical Effects in the Multistream Model for Quantum Plasmas

A statistical multistream description of quantum plasmas is formulated, using the Wigner-Poisson system as dynamical equations. A linear stability analysis of this system is carried out, and it is shown that a Landau-like damping of plane wave perturbations occurs due to the broadening of the background Wigner function that arises as a consequence of statistical variations of the wave function phase. The Landau-like damping is shown to suppress instabilities of the one- and two-stream type.Comment: 5 page

Solitary wave solution to the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability

We present a solitary wave solution of the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability using a scaling transformation and coupled amplitude-phase formulation. We have considered the third-order dispersion effect (TOD) into our model and show that soliton shift may be suppressed in a negative index material by a judicious choice of the TOD and self-steepening parameter.Comment: 6 page

Computing Naturally in the Billiard Ball Model

Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental models of collision-based computing, and it is essentially based on elastic collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are brought into the model to deflect balls to complete the computation. However, the use of fixed mirrors is "physically unrealistic" and makes the BBM not perfectly momentum conserving from a physical point of view, and it imposes an external architecture onto the computing substrate which is not consistent with the concept of "architectureless" in collision-based computing. In our initial attempt to reduce mirrors in the BBM, we present a class of gates: the m-counting gate, and show that certain circuits can be realized with few mirrors using this gate. We envisage that our findings can be useful in future research of collision-based computing in novel chemical and optical computing substrates.Comment: 10 pages, 7 figure

Two-soliton collisions in a near-integrable lattice system

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.Comment: Phys. Rev. E, in pres