5,101 research outputs found
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
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