Nonreciprocal feedback induces migrating oblique and horizontal banded vegetation patterns in hyperarid landscapes.

In hyperarid environments, vegetation is highly fragmented, with plant populations exhibiting non-random biphasic structures where regions of high biomass density are separated by bare soil. In the Atacama Desert of northern Chile, rainfall is virtually nonexistent, but fog pushed in from the interior sustains patches of vegetation in a barren environment. Tillandsia landbeckii, a plant with no functional roots, survives entirely on fog corridors as a water source.

Discrete light bullets in coupled optical resonators.

We consider arrays of coupled nonlinear optical cavities subject to coherent optical injection. These devices are described by the discrete generalized Lugiato-Lefever equation. We predict that stable three-dimensional localized structures, often called discrete light bullets, and clusters of them may form in the output of the coupled optical resonators.

Introduction to Focus Issue: Instabilities and nonequilibrium structures.

This Focus Issue on instabilities and nonequilibrium structures includes invited contributions from leading researchers across many different fields. The issue was inspired in part by the "VII Instabilities and Nonequilibrium Structures 2019" conference that took place at the Pontifica Universidad Católica de Valparaiso, Chile in December 2019. The conference, which is devoted to nonlinear science, is one of the oldest conferences in South America (since December 1985).

Control of dissipative rogue waves in nonlinear cavity optics: Optical injection and time-delayed feedback.

We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose: the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation.

Localized chaos of elliptically polarized cavity solitons in broad-area VCSEL with a saturable absorber.

We introduce a spin-flip model for a broad-area vertical-cavity surface-emitting laser (VCSEL) with a saturable absorber. We demonstrate simultaneous existence of orthogonally linearly polarized and elliptically polarized cavity solitons. We show that polarization degree of freedom leads to a period-doubling route to spatially localized chaos of the elliptically polarized cavity solitons.

Drifting cavity solitons and dissipative rogue waves induced by time-delayed feedback in Kerr optical frequency comb and in all fiber cavities.

Time-delayed feedback plays an important role in the dynamics of spatially extended systems. In this contribution, we consider the generic Lugiato-Lefever model with delay feedback that describes Kerr optical frequency comb in all fiber cavities. We show that the delay feedback strongly impacts the spatiotemporal dynamical behavior resulting from modulational instability by (i) reducing the threshold associated with modulational instability and by (ii) decreasing the critical frequency at the onset of this instability.

Coexistence of cavity solitons with different polarization states and different power peaks in all-fiber resonators.

We theoretically investigate a weakly birefringent all-fiber cavity subject to linearly polarized optical injection. We describe the propagation of light inside the cavity using, for each linear polarization component of the electric field, the Lugiato-Lefever model. These two components are coupled by cross-phase modulation.

Delay-induced depinning of localized structures in a spatially inhomogeneous Swift-Hohenberg model.

We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second-order critical point associated with bistability. The optical cavity is illuminated by an inhomogeneous spatial Gaussian pumping beam and subjected to time-delayed feedback.

Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics.

We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary.

Self-Replication of Localized Vegetation Patches in Scarce Environments.

Desertification due to climate change and increasing drought periods is a worldwide problem for both ecology and economy. Our ability to understand how vegetation manages to survive and propagate through arid and semiarid ecosystems may be useful in the development of future strategies to prevent desertification, preserve flora-and fauna within-or even make use of scarce resources soils. In this paper, we study a robust phenomena observed in semi-arid ecosystems, by which localized vegetation patches split in a process called self-replication.

Vector cavity solitons in broad area Vertical-Cavity Surface-Emitting Lasers.

We report the experimental observation of two-dimensional vector cavity solitons in a Vertical-Cavity Surface-Emitting Laser (VCSEL) under linearly polarized optical injection when varying optical injection linear polarization direction. The polarization of the cavity soliton is not the one of the optical injection as it acquires a distinct ellipticity. These experimental results are qualitatively reproduced by the spin-flip VCSEL model.

Chaotic behavior of cavity solitons induced by time delay feedback.

We investigate spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subject to time-delayed optical feedback. We show that the inclusion of feedback leads to a period doubling route to chaos of spatially localized light structures.

Experimental observation of localized structures in medium size VCSELs.

We report experimental evidence of spontaneous formation of localized structures in a 80 μm diameter Vertical-Cavity Surface-Emitting Laser (VCSEL) biased above the lasing threshold and under optical injection. Such localized structures are bistable with the injected beam power and the VCSEL current. We experimentally investigate the formation of localized structures for different detunings between the injected beam and the VCSEL, and different injection beam waists.

Delayed feedback induces motion of localized spots in reaction-diffusion systems.

We study the formation of localized structures, often called localized spots, in reaction-diffusion systems subject to time delayed feedback control. We focus on the regime close to a second-order critical point marking the onset of a hysteresis loop. We show that the space-time dynamics of the FitzHugh-Nagumo model in the vicinity of that critical point could be described by the delayed Swift-Hohenberg equation.

Family of probability distributions derived from maximal entropy principle with scale invariant restrictions.

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models.

Comment on "Maximum or minimum entropy production? How to select a necessary criterion of stability for a dissipative fluid or plasma".

In a recent paper, Phys. Rev. E 81, 041137 (2010), the author attempts to derive ten necessary conditions for the stability of dissipative fluids and plasmas.

High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities.

Near a zero-dispersion wavelength, high-order dispersion effects play a central role in a photonic crystal fiber cavity. The study of such effects reveals the existence of stable dissipative dark solitons in the anomalous dispersion regime. Such dark localized structures are not present without high-order dispersion.

Pattern formation without diffraction matching in optical parametric oscillators with a metamaterial.

We consider a degenerate optical parametric oscillator containing a left-handed material. We show that the inclusion of a left-handed material layer allows for controlling the strength and sign of the diffraction coefficient at either the pump or the signal frequency. Subsequently, we demonstrate the existence of stable dissipative structures without diffraction matching, i.

Dissipative structures in left-handed material cavity optics.

We study the spatiotemporal dynamics of spatially extended nonlinear cavities containing a left-handed material. Such materials, which have a negative index of refraction, have been experimentally demonstrated recently, and allow for novel electromagnetic behavior. We show that the insertion of a left-handed material in an optical resonator allows for controlling the value and the sign of the diffraction coefficient in dispersive Kerr resonators and degenerate optical parametric oscillators.

Introduction: dissipative localized structures in extended systems.

Localized structures belong to the class of dissipative structures found far from equilibrium. Contributions from the most representative groups working on a various fields of natural science such as biology, chemistry, plant ecology, mathematics, optics, and laser physics are presented. The aim of this issue is to gather specialists from these fields towards a cross-fertilization among these active areas of research and thereby to present an overview of the state of art in the formation and the characterization of dissipative localized structures.

Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion.

In the limit of a large duffusivity ratio, spotlike solutions in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are studied. It is shown analytically that such spots undergo an instability as the diffusivity ratio is decreased. An instability threshold is derived.

Three-dimensional structures in nonlinear cavities containing left-handed materials.

We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry.

Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump.

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light.

Modulated optical structures over a modulationally stable medium.

Evidence of modulated dissipative structures with an intrinsic wavelength in a nonlinear optical system devoid of Turing instability is given. They are found in the transverse field distribution of an optical cavity containing a liquid crystal light valve. Their existence is related to a transition from flat to modulated fronts connecting the unstable middle branch of a bistability cycle and either of the two stable uniform states.

Hyperbolic transverse patterns in nonlinear optical resonators.

We consider a nonlinear optical system in general, and a broad aperture laser, in particular, in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic Maxwell-Bloch equations, where the spatial coupling is provided by the D'Alambert operator rather than by the Laplace operator. We show that this system supports hyperbolic transverse patterns residing on hyperbolas in far-field domain, and consisting of stretched vortices in near-field domain.