Non-Hermitian arrangement for stable semiconductor laser arrays.

We propose and explore a physical mechanism for the stabilization of the complex spatiotemporal dynamics in arrays (bars) of broad area laser diodes taking advantage of the symmetry breaking in non-Hermitian potentials. We show that such stabilization can be achieved by specific pump and index profiles leading to a PT-symmetric coupling between nearest neighboring lasers within the semiconductor bar. A numerical analysis is performed using a complete (2 + 1)-dimensional space-temporal model, including transverse and longitudinal spatial degrees of freedom and temporal evolution of the electric field and carriers. We show regimes of temporal stabilization and light emission spatial redistribution and enhancement. We also consider a simplified (1 + 1)-dimensional model for an array of lasers holding the proposed non-Hermitian coupling with a global axisymmetric geometry. We numerically demonstrate a two-fold benefit: the control over the temporal dynamics over the EELs bar and the field concentration on the central lasers leading to a brighter output beam, facilitating a direct coupling to an optical fiber.

Super-collimation by axisymmetric diffractive metamirror.

We propose and demonstrate experimentally super-collimation of light beams by an axisymmetric diffractive metamirror-an axisymmetric concentric dielectric ring structure positioned in front of a mirror at a distance of several micrometers. By super-collimation, we mean the formation of a well-collimated beam characterized by a substantial enhancement of its axial component in the far-field domain. In the reported experiments, the axial intensity of the field was enhanced by around six times. Such axisymmetric super-collimators could be especially useful for improving the emission spatial quality of micro-lasers, when integrated as one (or both) resonator mirrors.

Self-Induced Faraday Instability Laser.

We predict the onset of self-induced parametric or Faraday instabilities in a laser, spontaneously caused by the presence of pump depletion, which leads to a periodic gain landscape for light propagating in the cavity. As a result of the instability, continuous wave oscillation becomes unstable even in the normal dispersion regime of the cavity, and a periodic train of pulses with ultrahigh repetition rate is generated. Application to the case of Raman fiber lasers is described, in good quantitative agreement between our conceptual analysis and numerical modeling.

Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations.

We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.

Formation of high-order acoustic Bessel beams by spiral diffraction gratings.

The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.

Suppression of pattern-forming instabilities by genetic optimization.

We propose a versatile "stabilization on demand" method for the suppression of modulation instability in oscillatory spatially extended nonlinear systems, based on a genetically optimized multifrequency spatiotemporal modulation of the potential. The method, which ensures full stabilization even for very strong nonlinearities, forms a powerful tool allowing for an arbitrary design of the instability spectrum. The stabilization method is universal for complex oscillatory systems, based on a general complex Ginzburg-Landau model with varying degrees of nonlinearity, and could lead to the stabilization of arbitrarily complex systems-from high power lasers and Bose-Einstein condensates of attracting atoms, to spatially extended chemical and biological pattern-forming systems.

Pattern Generation by Dissipative Parametric Instability.

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.

Taming of Modulation Instability by Spatio-Temporal Modulation of the Potential.

Spontaneous pattern formation in a variety of spatially extended nonlinear systems always occurs through a modulation instability, sometimes called Turing instability: the homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of spatial patterns initiated by that instability. We show that a spatio-temporal periodic modulation of the potential of spatially extended systems results in a modification of its pattern forming instability. Depending on the modulation character the instability can be partially suppressed, can change its spectrum (for instance the long wave instability can transform into short wave instability), can split into two, or can be completely eliminated. The latter result is of special practical interest, as it can be used to stabilize the intrinsically unstable system. The result bears general character, as it is shown here on a universal model of the Complex Ginzburg-Landau equation in one and two spatial dimensions (and time). The physical mechanism of the instability suppression can be applied to a variety of intrinsically unstable dissipative systems, like self-focusing lasers, reaction-diffusion systems, as well as in unstable conservative systems, like attractive Bose Einstein condensates.

Suppression of modulation instability in broad area semiconductor amplifiers.

We show that a two-dimensional periodic modulation of the pump profile (modulation both along and perpendicular to the optical axis) can suppress the modulation instability in broad emission area semiconductor amplifiers. In the case of a realistic finite-width amplifier the modulation instability can be completely eliminated.

Beam focalization in reflection from flat dielectric subwavelength gratings.

We experimentally demonstrate the recently predicted effect of near-field focusing for light beams from flat dielectric subwavelength gratings (SWGs). This SWGs were designed for visible light 532 nm and fabricated by direct laser writing in a negative photoresist, with the refractive index n=1.5 and the period d=314 nm. The laterally invariant gratings can focus light beams without any optical axis to achieve the transversal invariance. We show that focal distances can be obtained up to 13 µm at normal reflection for TE polarization.

Localized structures in dissipative media: from optics to plant ecology.

Localized structures (LSs) in dissipative media appear in various fields of natural science such as biology, chemistry, plant ecology, optics and laser physics. The proposal for this Theme Issue was to gather specialists from various fields of nonlinear science towards a cross-fertilization among active areas of research. This is a cross-disciplinary area of research dominated by nonlinear optics due to potential applications for all-optical control of light, optical storage and information processing. This Theme Issue contains contributions from 18 active groups involved in the LS field and have all made significant contributions in recent years.

Flat focusing mirror.

The control of spatial propagation properties of narrow light beams such as divergence, focusing or imaging are main objectives in optics and photonics. In this letter, we propose and demonstrate experimentally a flat focusing mirror, based on an especially designed dielectric structure without any optical axis. More generally, it also enables imaging any light pattern in reflection. The flat focusing mirror with a transversal invariance can largely increase the applicability of structured photonic materials for light beam propagation control in small-dimension photonic circuits.

Spatial filtering by axisymmetric photonic microstructures.

We propose and show experimentally axisymmetric spatial (angular) filtering of two-dimensional light beams by axisymmetric photonic microstructures. Such three-dimensional microstructures (similar to photonic crystals), in gapless configuration, were recorded in bulk of glass, where the refractive index has been point-by-point modulated using tightly focused femtosecond laser pulses. Axisymmetric angular filtering of approximately 25 mrad is demonstrated experimentally.

Flat lensing in the visible frequency range by woodpile photonic crystals.

We experimentally demonstrate full two-dimensional focalization of light beams at visible frequencies by a three-dimensional woodpile photonic crystal. The focalization (the flat lensing) with focal distances of the order of 50-70 µm is experimentally demonstrated. Experimental results are compared with numerical calculations and interpreted by harmonic expansion studies.

Beam shaping in spatially modulated broad-area semiconductor amplifiers.

We propose and analyze a beam-shaping mechanism that in broad-area semiconductor amplifiers occurs due to spatial pump modulation on a micrometer scale. The study, performed under realistic parameters and conditions, predicts a spatial (angular) filtering of the radiation, which leads to a substantial improvement of the spatial quality of the beam during amplification. Quantitative analysis of spatial filtering performance is presented based on numerical integration of the paraxial propagation model and on analytical estimations.

Nonlinear all-photonic-crystal Fabry-Perot resonator with angle-independent bistability.

We propose a nonlinear all-photonic-crystal (PhC) Fabry-Perot cavity tuned to the subdiffractive regime of the interior PhC, and we study angular-resolved nonlinear propagation of monochromatic plane wave excitations. With rigorous numerical simulations, we show that, for sufficiently large negative pump detunings and a focusing nonlinearity, the transmitted field has a bistable dependence on the pump field. Moreover, we reveal that, in contrast to a homogeneous resonator for different inclinations, the hysteresis curve is virtually unchanged for a fairly wide angular range. This may pave the way for obtaining novel kinds of nonlinear localized solutions in driven nonlinear resonators.

Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media.

We study parametric frequency conversion in quadratic nonlinear media with disordered ferroelectric domains. We demonstrate that disorder allows realizing broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We analyze both spatial and polarization properties of the emitted radiation and find the results in agreement with our theoretical predictions.

Subdiffractive all-photonic crystal Fabry-Perot resonators.

We propose subdiffractive all-photonic crystal Fabry-Perot resonators and study light propagation in this novel system. The photonic crystal in the cavity is tuned to the subdiffractive regime and the mirrors to the center of the photonic bandgap. We show that such all-photonic crystal resonators exhibit a broadband angular transmission at a fixed frequency and a high Q factor, resulting in a drastic reduction of the power threshold for all-optical switching.

Subdiffractive discrete cavity solitons.

We describe what we believe to be novel types of discrete cavity solitons in nonlinear waveguide arrays that are driven by an external holding beam. We demonstrate that a holding beam with a definite inclination drives the system in a subdiffractive regime and allows the formation of stable discrete cavity solitons. We predict the existence of both bright and dark moving midband discrete cavity solitons for an identical set of system parameters for both focusing and defocusing Kerr nonlinearities.

Subdiffractive light pulses in photonic crystals.

We investigate propagation of light pulses in photonic crystals in the vicinity of the zero diffraction point. We show that Gaussian pulses due to nonzero width of their temporal spectrum spread weakly in space and time during the propagation. We also find the family of nonspreading pulses, propagating invariantly in the vicinity of the zero diffraction point of photonic crystals.