Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Light scattering in disordered honeycomb photonic lattices near the Dirac points

We address Anderson localization in disordered honeycomb photonic lattices and show that the localization process is strongly affected by the spectral position of the input wavepacket within the first Brillouin zone of the lattice. In spite of the fact that in regular lattice the expansion of the beam is much stronger for the excitation near the Dirac points, where light exhibits conical diffraction, than for the excitation at the center of the Brillouin zone, where the beam exhibits normal diffraction, we found that disorder leads to pronounced Anderson localization even around the Dirac points. We found that for the same disorder level the width of the averaged output intensity distribution for excitations around the Dirac points may be substantially larger than that for excitations at the center of the Brillouin zone.Comment: 4 pages, 5 figures, to appear in Optics Letter

Solitary-wave vortices in quadratic nonlinear media

We find families of vortex solitary waves in bulk quadratic nonlinear media under conditions for second-harmonic generation. We show that the vortex solitary waves are azimuthally unstable and that they decay into sets of stable spatial solitons. We calculate the growth rates of the azimuthal perturbations and show how those affect the pattern of output light. © 1998 Optical Society of AmericaPeer ReviewedPostprint (published version

Enhanced soliton interactions by inhomogeneous nonlocality and nonlinearity

We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a strongly nonlocal nonlinear response. We reveal that the variation of the nonlocality and nonlinearity along the propagation direction can substantially enhance or weaken the interaction between out-of-phase solitons. This phenomenon manifests itself as a slowdown or acceleration of the soliton collision dynamics in one-dimensional geometries or of the soliton spiraling rate in bulk media. Therefore, one finds that by engineering the nonlocality and nonlinearity variation rate one can control the output soliton location.Comment: 22 pages, 5 figures, to appear in Physical Review

Topological dragging of solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations, and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.Comment: 15 pages, 5 figures, to appear in Physical Review Letter

Sex Differential in 15-Hydroxyprostaglandin Dehydrogenase Levels in the Lumen of Human Intracranial Aneurysms.

BACKGROUND: Aspirin is a promising medical therapy for the prevention of intracranial aneurysm (IA) rupture. Recently, we found that men have a better response to aspirin than women. The purpose of this study was to determine whether a sex differential exists in the level of 15-hydroxyprostaglandin dehydrogenase (15-PGDH) in the lumen of human IAs. METHODS AND RESULTS: Consecutive patients undergoing coiling or stent-assisted coiling for a saccular IA at our institution were enrolled. Two samples (A and B) were collected from IA lumens, and the plasma level of 15-PGDH was measured using an ELISA-based method. The study included 38 patients, with 20 women and 18 men. Women and men were comparable on baseline characteristics. The mean plasma concentration of 15-PGDH did not differ statistically between sample A (62.8±16.2 ng/mL) and sample B (61.8±17.9 ng/mL; 95% confidence interval -6.6 to 9.4). The mean plasma concentration of 15-PGDH in IA lumens of samples A and B was significantly higher in men (73.8±13.5 ng/mL) than women (49.6±7.8 ng/mL; P\u3c0.0001). CONCLUSIONS: Higher enzyme levels of 15-PGDH exist in the lumen of IAs of men compared with women. This observation could explain why aspirin confers better protection against IA rupture in men than in women. The susceptibility of an individual to aspirin may differ according to the level of 15-PGDH

Nonlinear switching of low-index defect modes in photonic lattices

We address nonlinear signal switching between two low-index defect channels induced in periodic optical lattices. In contrast to conventional directional couplers, where the guiding mechanism is total internal reflection or refraction, in such Bragg-type coupler, the guidance is of a photonic-bandgap origin. The coupling length in the low-index coupler is controlled by the lattice parameters and by the channel spacing. In the nonlinear regime the Bragg-type coupler behaves as an all-optical switch, exhibiting a remarkable difference of switching power for focusing versus defocusing nonlinearity.Comment: 13 pages, 4 figures, to appear in Physical Review

Soliton excitation in waveguide arrays with an effective intermediate dimensionality

We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.Comment: 14 pages, 5 figures, to appear in Physical Review Letter