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

Stability of multi-hump optical solitons

We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the experimental results reported by M. Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657 (1998)].Comment: 4 pages, 5 figures, to appear in PR

Interaction of cavity solitons in degenerate optical parametric oscillators

Numerical studies together with asymptotic and spectral analysis establish regimes where soliton pairs in degenerate optical parametric oscillators fuse, repel, or form bound states. A novel bound state stabilized by coupled internal oscillations is predicted.Comment: 3 page

Rheology of protein-stabilised emulsion gels envisioned as composite networks. 1 - Comparison of pure droplet gels and protein gels

Protein-stabilised emulsion gels can be studied in the theoretical framework of colloidal gels, because both protein assemblies and droplets may be considered as soft colloids. These particles differ in their nature, size and softness, and these differences may have an influence on the rheological properties of the gels they form. Pure gels made of milk proteins (sodium caseinate), or of sub-micron protein-stabilised droplets, were prepared by slow acidification of suspensions at various concentrations. Their microstructure was characterised, their viscoelasticity, both in the linear and non-linear regime, and their frequency dependence were measured, and the behaviour of the two types of gels was compared. Protein gels and droplet gels were found to have broadly similar microstructure and rheological properties when compared at fixed volume fraction, a parameter derived from the study of the viscosity of the suspensions formed by proteins and by droplets. The viscoelasticity displayed a power law behaviour in concentration, as did the storage modulus in frequency. Additionally, strain hardening was found to occur at low concentration. These behaviours differed slightly between protein gels and droplet gels, showing that some specific properties of the primary colloidal particles play a role in the development of the rheological properties of the gels.Comment: 27 pages, 6 figure

Optomechanical self-structuring in cold atomic gases

The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the pump axis - are spontaneously broken. We observe the simultaneous spatial structuring of the density of a cold atomic cloud and an optical pump beam. The resulting patterns have hexagonal symmetry. The experiment demonstrates the manipulation of matter by opto-mechanical self-assembly with adjustable length scales and can be potentially extended to quantum degenerate gases.Comment: 20 pages, 6 figure

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.Comment: 5 pages, 7 figure

Frequency selection by soliton excitation in nondegenerate intracavity downconversion

We show that soliton excitation in intracavity downconversion naturally selects a strictly defined frequency difference between the signal and idler fields. In particular, this phenomenon implies that if the signal has smaller losses than the idler then its frequency is pulled away from the cavity resonance and the idler frequency is pulled towards the resonance and {\em vice versa}. The frequency selection is shown to be closely linked with the relative energy balance between the idler and signal fields.Comment: 5 pages, 3 figures. To appear in Phys Rev Let

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199

New possibilities for research on reef fish across the continental shelf of South Africa

[From introduction] Subtidal research presents numerous challenges that restrict the ability to answer fundamental ecological questions related to reef systems. These challenges are closely associated with traditional monitoring methods and include depth restrictions (e.g. safe diving depths for underwater visual census), habitat destruction (e.g. trawling), mortality of target species (e.g. controlled angling and fish traps), and high operating costs (e.g. remotely operated vehicles and large research vessels. Whereas many of these challenges do not apply or are avoidable in the shallow subtidal environment, the difficulties grow as one attempts to sample deeper benthic habitats. This situation has resulted in a paucity of knowledge on the structure and ecology of deep water reef habitats around the coast of South Africa and in most marine areas around the world. Furthermore, the inability to effectively survey deep water benthic environments has limited the capacity of researchers to investigate connectivity between shallow and deep water habitats in a standardised and comparable fashion

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure