Nonresonant third-order nonlinear properties of NaPO3-WO3-Bi2O3 glasses in the near infrared

nonlinear (NL) refractive index, n(2), of NaPO3-WO3-Bi2O3 glass with different relative amounts of the constituents was measured at 1064 and 800 nm using the Z-scan and the thermally managed eclipse Z-scan techniques, respectively. The values of n(2) >= 10(-15) cm(2)/W and negligible NL absorption coefficient were determined. The large values of the NL refractive index and the very small NL absorption indicate that these materials have large potential for all-optical switching applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3212972]

On the periodic orbits of the third-order differential equation x ′′′ − µx ′′ + x ′ − µx = εF (x, x ′ , x ′′)

In this paper we study the periodic orbits of the third-order differential equation x ′′′−µx ′′+ x ′ − µx = εF (x, x ′ , x ′′), where ε is a small parameter and the function F is of class C 2 .

Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonresonant third-order nonlinearity of antimony glasses at telecom wavelengths

We report measurements of the nonresonant nonlinear refractive index n(2) in antimony glasses at telecom wavelengths. The measurements were performed using the Z-scan technique with a 130 fs pulsed laser operating at five wavelengths in the range of 1400-1600 nm. Values of n(2)approximate to 10(-15) cm(2)/W were measured and a negligible two-photon absorption coefficient (< 0.003 cm/GW) was estimated for all glasses compositions. The samples present a good figure of merit for ultrafast all-optical switching. (c) 2006 American Institute of Physics.

Near-infrared third-order nonlinearity of PbO-GeO(2) films containing Cu and Cu(2)O nanoparticles

We report measurements of the nonlinear (NL) refractive index n(2) of lead-germanium films (LGFs) containing Cu and Cu(2)O nanoparticles (NPs). The thermally managed eclipse Z-scan technique with 150 fs pulses from a laser operating at 800 nm was used. The NL refractive index measured, n(2)=6.3x10(-12) cm(2)/W has electronic origin and the NL absorption coefficient alpha(2) is smaller than 660 cm/GW. The figure of merit n(2)/lambda alpha(2) is enhanced by more than two orders of magnitude in comparison with the result for the LGFs without the copper based NPs. (C) 2008 American Institute of Physics.

Third-order nonlinearities and other properties of molybdenum lead-pyrophosphate glass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files

When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second- and third-order ionospheric effects still remain. The first-, second- and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second- and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RINEX_HO that was developed to correct GPS observables for second- and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second- and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth's magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.

Second and Third Order Ionospheric Effects on GNSS Positioning: A Case Study in Brazil

The Global Positioning System (GPS) transmits signals in two frequencies. It allows the correction of the first order ionospheric effect by using the ionosphere free combination. However, the second and third order ionospheric effects, which combined may cause errors of the order of centimeters in the GPS measurements, still remain. In this paper the second and third order ionospheric effects, which were taken into account in the GPS data processing in the Brazilian region, were investigated. The corrected and not corrected GPS data from these effects were processed in the relative and precise point positioning (PPP) approaches, respectively, using Bernese V5.0 software and the PPP software (GPSPPP) from NRCAN (Natural Resources Canada). The second and third order corrections were applied in the GPS data using an in-house software that is capable of reading a RINEX file and applying the corrections to the GPS observables, creating a corrected RINEX file. For the relative processing case, a Brazilian network with long baselines was processed in a daily solution considering a period of approximately one year. For the PPP case, the processing was accomplished using data collected by the IGS FORT station considering the period from 2001 to 2006 and a seasonal analysis was carried out, showing a semi-annual and an annual variation in the vertical component. In addition, a geographical variation analysis in the PPP for the Brazilian region has confirmed that the equatorial regions are more affected by the second and third order ionospheric effects than other regions.

Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

INTEGRATION OF THE NONLINEAR POISSON BOLTZMANN-EQUATION FOR CHARGED VESICLES IN ELECTROLYTIC SOLUTIONS

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are assumed to be water- and ion-permeable hollow spheres and specific ion adsorption at the surfaces was calculated using a Volmer isotherm. We solved the PBE numerically for a range of amphiphile and salt concentrations (up to 0.1 M) and calculated co-ion and counterion distributions in the inside and outside of vesicles as well as the fields and electrical potentials. The calculations yield results that are consistent with measured values for vesicles of synthetic amphiphiles.

Femtosecond nonlinear optical properties of tellurite glasses

The third-order nonlinear optical properties of tellurite glasses with different compositions were investigated in the femtosecond regime at 810 nm. Using the I-scan technique, positive nonlinear refractive indices of similar to 10(-15) cm(2)/W were measured. The authors also determined that nonlinear absorption was negligible for all studied samples. This result, added to their good chemical stability, indicates that tellurite glasses are promising materials for ultrafast photonic applications. (c) 2006 American Institute of Physics.