Dissipative solitons in pattern-forming nonlinear optical systems : cavity solitons and feedback solitons

Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, theory, experimental status, and potential application of such solitons is reviewed

Surface morphological evolutions on single crystal films by strong anisotropic drift-diffusion under the capillary and electromigration forces

The morphological evolution of voids at the unpassivated surfaces and the sidewalls of the single crystal metallic films are investigated via computer simulations by using the novel mathematical model developed by Ogurtani relying on the fundamental postulates of irreversible thermodynamics. The effects of the drift-diffusion anisotropy on the development of the surface morphological scenarios are fully explored under the action of the electromigration (EM) and capillary forces (CF), utilizing numerous combination of the surface textures and the directions of the applied electric field. The interconnect failure time due to the EM induced wedge shape internal voids and the incubation time of the oscillatory surface waves, under the severe instability regimes, are deduced by the novel renormalization procedures applied on the outputs of the computer simulation experiments.Comment: 41 pages, 18 figures. related simulation movies utilizing numerous combination of the surface texture, see http://www.csl.mete.metu.edu.tr/aytac/thesis/movies/index.ht

Asymptotics of the trap-dominated Gunn effect in p-type Ge

We present an asymptotic analysis of the Gunn effect in a drift-diffusion model---including electric-field-dependent generation-recombination processes---for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and annihilation of solitary waves. Each stage may be described by one evolution equation for only one degree of freedom (the current density), except for the generation of each new wave. The wave generation is a faster process that may be described by solving a semiinfinite canonical problem. As a result of our study we have found that (depending on the boundary condition) one or several solitary waves may be shed during each period of the oscillation. Examples of numerical simulations validating our analysis are included.Comment: Revtex, 25 pag., 5 fig., to appear Physica

Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems

Motionless domains walls representing heteroclinic temporal or spatial orbits typically exist only for very specific parameters. This report introduces a novel mechanism for stabilizing temporal domain walls away from the Maxwell point opening up new possibilities to encode information in dynamical systems. It is based on anti-periodic regimes in a delayed system close to a bistable situation, leading to a cancellation of the average drift velocity. The results are demonstrated in a normal form model and experimentally in a laser with optical injection and delayed feedback.Comment: 6 pages, 5 figures, resubmitted manuscrip

Fundamentals and applications of spatial dissipative solitons in photonic devices : [Chapter 6]

We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines

Dissipative phase solitons in semiconductor lasers

We experimentally demonstrate the existence of non dispersive solitary waves associated with a 2$\pi$ phase rotation in a strongly multimode ring semiconductor laser with coherent forcing. Similarly to Bloch domain walls, such structures host a chiral charge. The numerical simulations based on a set of effective Maxwell-Bloch equations support the experimental evidence that only one sign of chiral charge is stable, which strongly affects the motion of the phase solitons. Furthermore, the reduction of the model to a modified Ginzburg Landau equation with forcing demonstrates the generality of these phenomena and exposes the impact of the lack of parity symmetry in propagative optical systems.Comment: 5 pages, 5 figure

Transverse Patterns in Nonlinear Optical Resonators

The book is devoted to the formation and dynamics of localized structures (vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. The theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given. This article contains the table of contents and the introductory chapter of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of the boo

Stable solitons in coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities

We introduce a model of a two-core system, based on an equation of the Ginzburg-Landau (GL) type, coupled to another GL equation, which may be linear or nonlinear. One core is active, featuring intrinsic linear gain, while the other one is lossy. The difference from previously studied models involving a pair of linearly coupled active and passive cores is that the stabilization of the system is provided not by a linear diffusion-like term, but rather by a cubic or quintic dissipative term in the active core. Physical realizations of the models include systems from nonlinear optics (semiconductor waveguides or optical cavities), and a double-cigar-shaped Bose-Einstein condensate with a negative scattering length, in which the active ``cigar'' is an atom laser. The replacement of the diffusion term by the nonlinear loss is principally important, as diffusion does not occur in these physical media, while nonlinear loss is possible. A stability region for solitary pulses is found in the system's parameter space by means of direct simulations. One border of the region is also found in an analytical form by means of a perturbation theory. Moving pulses are studied too. It is concluded that collisions between them are completely elastic, provided that the relative velocity is not too small. The pulses withstand multiple tunneling through potential barriers. Robust quantum-rachet regimes of motion of the pulse in a time-periodic asymmetric potential are found as well.Comment: 14 pages, 7 figure

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly stablished.Comment: 10 pages, 6 Post-Script figure

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation