Solitary Waves in Discrete Media with Four Wave Mixing

In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear inter-component coupling and four wave mixing. The relevant four branches of solutions consist of two single mode branches (transverse electric and transverse magnetic) and two mixed mode branches, involving both components (linearly polarized and elliptically polarized). These solutions are obtained explicitly and their stability is analyzed completely in the anti-continuum limit (where the nodes of the lattice are uncoupled), illustrating the supercritical pitchfork nature of the bifurcations that give rise to the latter two, respectively, from the former two. Then the branches are continued for finite coupling constructing a full two-parameter numerical bifurcation diagram of their existence. Relevant stability ranges and instability regimes are highlighted and, whenever unstable, the solutions are dynamically evolved through direct computations to monitor the development of the corresponding instabilities. Direct connections to the earlier experimental work of Meier et al. [Phys. Rev. Lett. {\bf 91}, 143907 (2003)] that motivated the present work are given.Comment: 13 pages, 10 figure

Spatial solitons under competing linear and nonlinear diffractions

We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, which is found in an exact analytical form, along with the largest total power (norm) that the waves may possess. Past a critical point, collapse effects are observed, caused by suitable perturbations. Interactions between two identical parallel solitary beams are explored by dint of direct numerical simulations. It is found that in-phase solitons merge into robust or collapsing pulsons, depending on the strength of the nonlinear diffraction

The effect of pictorial depth information on projected size judgments.

When full depth cues are available, size judgments are dominated by physical size. However, with reduced depth cues, size judgments are influenced less by physical size and more by projected size. By manipulating monocularly presented pictorial depth cues only, in this study we reduced depth cues further than had previous size judgment studies. Participants were presented monocularly with two shapes against a background of zero (control), one, two, or three pictorial depth cues. Each cue was added progressively in the following order: height in the visual field, linear perspective, and texture gradient. Participants made a same/different judgment regarding the projected size of the two shapes (i.e., ignoring any depth cues). As was expected, accuracy increased and response times decreased as the ratio between the projected size of the two shapes increased (range of projected size ratios, 1:1-1:5). In addition, with the exception of the larger size ratios (1:4 and 1:5), detection of projected size difference grew poorer as depth cues were added. One- and two-cue conditions had the most weighting in this performance decrement, with little weighting from the three-cue condition. We conclude that even minimal depth information is difficult to inhibit, which indicates that depth perception requires little focused attention

Vortex Structures Formed by the Interference of Sliced Condensates

We study the formation of vortices, vortex necklaces and vortex ring structures as a result of the interference of higher-dimensional Bose-Einstein condensates (BECs). This study is motivated by earlier theoretical results pertaining to the formation of dark solitons by interfering quasi one-dimensional BECs, as well as recent experiments demonstrating the formation of vortices by interfering higher-dimensional BECs. Here, we demonstrate the genericity of the relevant scenario, but also highlight a number of additional possibilities emerging in higher-dimensional settings. A relevant example is, e.g., the formation of a "cage" of vortex rings surrounding the three-dimensional bulk of the condensed atoms. The effects of the relative phases of the different BEC fragments and the role of damping due to coupling with the thermal cloud are also discussed. Our predictions should be immediately tractable in currently existing experimental BEC setups.Comment: 8 pages, 6 figures (low res). To appear in Phys. Rev. A. Full resolution preprint available at: http://www-rohan.sdsu.edu/~rcarrete/publications