Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams

We present the first experimental observation of modulation instability of partially spatially incoherent light beams in non-instantaneous nonlinear media. We show that even in such a nonlinear partially coherent system (of weakly-correlated particles) patterns can form spontaneously. Incoherent MI occurs above a specific threshold that depends on the beams' coherence properties (correlation distance), and leads to a periodic train of one-dimensional (1D) filaments. At a higher value of nonlinearity, incoherent MI displays a two-dimensional (2D) instability and leads to self-ordered arrays of light spots.Comment: 16 pages, 4 figure

Incoherent matter-wave solitons

The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a surrounding thermal cloud and by condensate depletion during its evolution. We analyze these aspects of BEC soliton dynamics, using time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The condensate is initially prepared within a harmonic trap at finite temperature, and solitonic behavior is studied by subsequently propagating the TDHFB equations without confinement. Numerical results demonstrate the collapse of the BEC via collisional emission of atom pairs into the thermal cloud, resulting in splitting of the initial density into two solitonic structures with opposite momentum. Each one of these solitary matter waves is a mixture of condensed and noncondensed particles, constituting an analog of optical random-phase solitons.Comment: 4 pages, 2 figures, new TDHFB result

Phase Retrieval with Application to Optical Imaging

This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art in this area, identify challenges, and suggest vision and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large, with applications in a variety of fields ranging from biology and chemistry to physics and engineering

Vector solitons in (2+1) dimensions

We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.Comment: 3 pages, 5 figures, submitted to Opt. Let

On the nature of Coulomb corrections to the e^+e^- pair production in ultrarelativistic heavy-ion collisions

We manifest the origin of the wrong conclusion made by several groups of authors on the absence of Coulomb corrections to the cross section of the e^+e^- pair production in ultrarelativistic heavy-ion collisions. The source of the mistake is connected with an incorrect passage to the limit in the expression for the cross section. When this error is eliminated, the Coulomb corrections do not vanish and agree with the results obtained within the Weizs\"acker-Williams approximation.Comment: 7 pages, LaTe

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Comment: 4 pages, 5 figure

Causality effects on accelerating light pulses

We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in dispersive media. We explore the effects of causality, and find that, whereas decelerating pulses can asymptotically reach zero group velocity, pulses that accelerate towards infinite group velocity inevitably break up, after a specific critical point. The trajectories and the features of causal pulses are analyzed, along with the requirements for the existence of the critical point and experimental schemes for its observation. Finally, we show that causality imposes similar effects on accelerating pulses in the presence of local Kerr-like nonlinearities

Coulomb corrections and multiple e+e- pair production in ultra-relativistic nuclear collisions

We consider the problem of Coulomb corrections to the inclusive cross section. We show that these corrections in the limiting case of small charge number of one of the nuclei coincide with those to the exclusive cross section. Within our approach we also obtain the Coulomb corrections for the case of large charge numbers of both nuclei.Comment: 7 pages, REVTeX

Super-diffusion in optical realizations of Anderson localization

We discuss the dynamics of particles in one dimension in potentials that are random both in space and in time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is suppressed by random fluctuations in the refractive index. If the refractive index fluctuates along the direction of the paraxial propagation of the beam, the localization is destroyed. We analyze this broken localization, in terms of the spectral decomposition of the potential. When the potential has a discrete spectrum, the spread is controlled by the overlap of Chirikov resonances in phase space. As the number of Fourier components is increased, the resonances merge into a continuum, which is described by a Fokker-Planck equation. We express the diffusion coefficient in terms of the spectral intensity of the potential. For a general class of potentials that are commonly used in optics, the solutions of the Fokker-Planck equation exhibit anomalous diffusion in phase space, implying that when Anderson localization is broken by temporal fluctuations of the potential, the result is transport at a rate similar to a ballistic one or even faster. For a class of potentials which arise in some existing realizations of Anderson localization atypical behavior is found.Comment: 11 pages, 2 figure

Soliton dynamics and self-induced transparency in nonlinear nanosuspensions

We study spatial soliton dynamics in nano-particle suspensions. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these systems the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. The possibility of synthesizing artificial nonlinearities using mixtures of nanosuspensions is also considered