Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Korteveg-de Vries solitons in a cold quark-gluon plasma

The relativistic heavy ion program developed at RHIC and now at LHC motivated a deeper study of the properties of the quark-gluon plasma (QGP) and, in particular, the study of perturbations in this kind of plasma. We are interested on the time evolution of perturbations in the baryon and energy densities. If a localized pulse in baryon density could propagate throughout the QGP for long distances preserving its shape and without loosing localization, this could have interesting consequences for relativistic heavy ion physics and for astrophysics. A mathematical way to prove that this can happen is to derive (under certain conditions) from the hydrodynamical equations of the QGP a Korteveg-de Vries (KdV) equation. The solution of this equation describes the propagation of a KdV soliton. The derivation of the KdV equation depends crucially on the equation of state (EOS) of the QGP. The use of the simple MIT bag model EOS does not lead to KdV solitons. Recently we have developed an EOS for the QGP which includes both perturbative and nonperturbative corrections to the MIT one and is still simple enough to allow for analytical manipulations. With this EOS we were able to derive a KdV equation for the cold QGP.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Customized Topography-guided Photorefractive Keratectomy With the MEL-70 Platform and Mitomycin C to Correct Hyperopia After Radial Keratotomy

PURPOSE: To evaluate topography-guided photorefractive keratectomy (PRK) for correcting hyperopia and astigmatism after radial keratotomy (RK). METHODS., Prospective study of 12 consecutive patients (19 eyes) who were treated with topography-guided PRK with 0.02% mitomycin C using an Asclepion-Meditec MEL-70 excimer laser with a 9.5-mm ablation zone. All eyes were operated by the same surgeon and followed for 1 year. RESULTS: Thirteen eyes had complete epithelialization by day 7 and all eyes by day 10. At 1 year, uncorrected visual acuity was 20/25 or better in 42.1% of eyes and 20/40 or better in 68.4%. Preoperative mean spherical equivalent refraction was +3.80 +/- 2.47 diopters (D) and +0.24 +/- 2.36 D (P <.001) 1 year postoperative, with 47.4% of eyes being within +/- 1.00 D and 73.7% within +/- 2.00 D. Preoperative mean cylinder was -2.30 +/- 1.41 D and -0.62 +/- 0.73 D (P <.1001) 1 year postoperative. At 1 year, 68.4% of eyes gained at least 1 line of best-spectacle corrected visual acuity, 36.8% gained more than 1 line, and only 2 eyes lost 1 line (one due to corneal haze). Three eyes developed central haze. Mean regression from 6 to 12 months in these 3 eyes was +1.83 D and in the remaining 16 eyes was -0.50 D. CONCLUSIONS: Topography-guided PRK with mitomycin C was safe and reasonably effective for the treatment of hyperopia after RK [J Refract Surg. 2008;24:911-922.]

Photorefractive keratectomy and butterfly laser epithelial keratomileusis: A prospective, contralateral study

PURPOSE: To evaluate results of two surface excimer laser refractive surgery techniques-photorefractive keratectomy (PRK) and butterfly laser epithelial keratomileusis (butterfly LASEK). METHODS: A prospective, randomized, double-masked study of 51 patients (102 eyes) who underwent laser refractive surgery. One eye of each patient was randomized to be operated with PRK and the fellow eye with butterfly LASEK Patients were followed for 1 year. RESULTS: No significant difference between groups for distance uncorrected visual acuity (UCVA) (P=.559) was noted. At 1 year, 98% (50 eyes) in the PRK group and 96.1% (49 eyes) in the butterfly LASEK group reached UCVA of 20/20. Predictability, efficacy, safety, and stability were not statistically significant between groups. Safety index was 1.0 for PRK and 0.996 for butterfly LASEK, One eye in the butterfly LASEK group lost one line of best-spectacle corrected visual acuity. At 12 months, 94.1% (48 eyes) and 86.3% (44 eyes) in the PRK and butterfly LASEK groups (P=.188), respectively, had a spherical equivalent refraction of +/- 0.50 diopters. Slight haze was observed in both groups. A statistical difference in haze between the groups was observed only in the first postoperative month, with higher intensity in the butterfly LASEK group (0.18 +/- 0.39) compared to the PRK group (0.08 +/- 0.21) (P=.04). CONCLUSIONS: Butterfly LASEK had similar predictability, efficacy, safety, stability, and haze incidence to PRK for the treatment of low to moderate myopia. However, on the second postoperative day, PRK showed better UCVA than butterfly LASEK.

Haze Development After Photorefractive Keratectomy: Mechanical vs Ethanol Epithelial Removal in Rabbits

PURPOSE: To compare mechanical and ethanol epithelial removal with respect to myofibroblast development and haze formation after photorefractive keratectomy (PRK). METHODS: Seventeen rabbits underwent mechanical or ethanol debridement, and the opposite eye of each rabbit served as an unwounded control. In both groups, the epithelium was removed with a spatula and discarded. A -9.00-diopter PRK was performed in each eye. The level of haze in each cornea at 4 weeks was graded at the slit-lamp microscope according to the Fantes scale. Myofibroblast generation was detected with immunocytochemistry for alpha-smooth muscle actin (alpha-SMA) and cells were quantitatively analyzed. RESULTS: No difference was noted between the two groups in alpha-SMA + myofibroblasts 4 weeks after surgery (43.6 +/- 2.0/400X field and 45.7 +/- 4.8/400X field in ethanol and mechanical groups, respectively) (P=.10). A slight difference was noted but did not reach statistical significance with regard to stromal haze between ethanol and mechanical groups (2.0 +/- 0.5 and 2.3 +/- 0.4, respectively, P=.063). The ethanol and mechanical groups were statistically different when compared to controls regarding stromal haze and alpha-SMA+ cells (P <.0001 for all comparisons). CONCLUSIONS:No difference was noted in clinical haze or myofibroblast generation between corneas that had PRK with mechanical,or ethanol epithelial debridement. [J Refract Surg., 2008;24:923-927.]

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

Light-induced lens analysis in photorefractive crystals employing phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities of phase-shifting real-time holographic interferometry for the analysis of light-induced lens in photoreffactive and nonlinear optical materials. We show that this technique can be used for quantitative evaluation of the phase distribution of a wavefront changed by a light-induced lens and, consequently, the refractive index changes in these materials. The basic principle of this technique combines real-time holographic interferometry with phase-shifting technique for interferogram analysis. This method is demonstrated with in situ visualization, monitoring and analysis in real-time and uses a Bi(12)SiO(20) crystal as the holographic medium and a Bi(12)TiO(20) as the test sample. (C) 2008 Elsevier B.V. All rights reserved.

Solitons of two-component Bose-Einstein condensates modulated in space and time

In this Letter we present soliton solutions of two coupled nonlinear Schrodinger equations modulated in space and time. The approach allows us to obtain solitons for a large variety of solutions depending on the nonlinearity and potential profiles. As examples we show three cases with soliton solutions: a solution for the case of a potential changing from repulsive to attractive behavior, and the other two solutions corresponding to localized and delocalized nonlinearity terms, respectively. (C) 2010 Elsevier B.V. All rights reserved.

Mastication effort study using photorefractive holographic interferometry technique

The purpose of this work was the force-displacement response analysis of the masticatory process in a dried human skull by Double-Exposure Photorefractive Holographic Interferometry Technique (2E-PRHI). The load concentration and dissipation of the forces from dried human skull were analysed at applied loading stands as a Simulation of Isolated Contraction (SIC) of some mastication muscles. The 2EHI and Fringe Analysis Method were used to obtain the quantitative results of this force-displacement response. These results document quantitatively the real biomechanical response from dried human skull under applied loading and it can be used for complementary study by finite element model and others analysis type. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.

Thermo-optics parameters measurements in photorefractive sillenite Bi(12)SiO(20) crystals by thermal lens technique

The present work reports on the thermo-optical properties of photorefractive sillenite Bi(12)SiO(20) (BSO) crystals obtained by applying the Thermal Lens Spectrometry technique (TLS). This crystals presents one high photorefractive sensitivity in the region blue-green spectra, since the measurements were carried out at two pump beam wavelengths (514.5 nm and 750 nm) to study of the light-induced effects in this material (thermal and/or photorefractive). We determine thermo-optical parameters like thermal diffusivity (D), thermal conductivity (K) and temperature coefficient of the optical path length change (ds/dT) in sillenite crystals. These aspects, for what we know, not was studied in details up to now using the lens spectrometry technique and are very important against of the promising potentiality of applications these crystals in non linear optics, real time holography and optical processing data.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Resultados preliminares de um algoritmo para ablação de lente de contato personalizada

OBJETIVO: Desenvolver simulação computadorizada de ablação para produzir lentes de contato personalizadas a fim de corrigir aberrações de alta ordem. MÉTODOS: Usando dados reais de um paciente com ceratocone, mensurados em um aberrômetro ("wavefront") com sensor Hartmann-Shack, foram determinados as espessuras de lentes de contato que compensam essas aberrações assim como os números de pulsos necessários para fazer ablação as lentes especificamente para este paciente. RESULTADOS: Os mapas de correção são apresentados e os números dos pulsos foram calculados, usando feixes com a largura de 0,5 mm e profundidade de ablação de 0,3 µm. CONCLUSÕES: Os resultados simulados foram promissores, mas ainda precisam ser aprimorados para que o sistema de ablação "real" possa alcançar a precisão desejada.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.