Turn-on-time statistics of modulated lasers subjected to resonant weak optical feedback

We present analytical calculations of the turn-on-time probability distribution of intensity-modulated lasers under resonant weak optical feedback. Under resonant conditions, the external cavity round-trip time is taken to be equal to the modulation period. The probability distribution of the solitary laser results are modified to give reduced values of the mean turn-on-time and its variance. Numerical simulations have been carried out showing good agreement with the analytical results.

Generator of ultrashort optical pulses for time division multiplexing

The performance of a device based on modified injection-locking techniques is studied by means of numerical simulations. The device incorporates master and slave configurations, each one with a DFB laser and an electroabsortion modulator (EAM). This arrangement allows the generation of high peak power, narrow optical pulses according to a periodic or pseudorandom bit stream provided by a current signal generator. The device is able to considerably increase the modulation bandwidth of free-running gain-switched semiconductor lasers using multiplexing in the time domain. Opportunities for integration in small packages or single chips are discussed.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general: it applies to arbitrary geometry and driving. Here we apply it to the channel geometry driven by gravity and pressure. The finite radius of convergence of the mode-coupling expansion is found. Calculation up to third-order couplings is done, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. The explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics of the system. We finally check the quantitative validity of different orders of approximation and a resummation scheme against a physically relevant, exact time-dependent solution. The agreement between the low-order approximations and the exact solution is excellent within the radius of convergence, and is even reasonably good beyond this radius.

Systematic weakly nonlinear analysis of radial viscous fingering

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

The nonlinear relaxation time and quasideterministic-theory approaches to characterize the decay of unestable states

We present the relationship between nonlinear-relaxation-time (NLRT) and quasideterministic approaches to characterize the decay of an unstable state. The universal character of the NLRT is established. The theoretical results are applied to study the dynamical relaxation of the Landau model in one and n variables and also a laser model.

Effect of External Noise Correlation in Optical Coherence Resonance

Coherence resonance occurring in semiconductor lasers with optical feedback is studied via the Lang-Kobayashi model with external nonwhite noise in the pumping current. The temporal correlation and the amplitude of the noise have a highly relevant influence in the system, leading to an optimal coherent response for suitable values of both the noise amplitude and correlation time. This phenomenon is quantitatively characterized by means of several statistical measures.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

Optical-model potential for electron and positron elastic scattering by atoms

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkur approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from ~100 eV up to ~5 keV. At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.

Critical frequency for vortex nucleation in Bose-Fermi mixtures in optical lattices

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb-40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

η'-nucleus optical potential and possible η' bound states

Starting from a recent model of the η′N interaction, we evaluate the η ′-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′, together with the second-order terms accounting for η′ absorption by two nucleons. We also calculate the formation cross section of the η′bound states from (π, p) reactions on nuclei. The η′-nucleus potential suffers from uncertainties tied to the poorly known η′N interaction, which can be partially constrained by the experimental modulus of the η′N scattering length and/or the recently measured transparency ratios in η′nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N|= 0.1 fm, we obtain an η′optical potential in nuclear matter at saturation density of Vη′=−(8.7 + 1.8i) MeV, not attractive enough to produce η′bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N|= 0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η′-nuclear bound states and to threshold enhancements in the unbound region.

Optical crop sensor for variable-rate nitrogen fertilization in corn: i - plant nutrition and dry matter production

Variable-rate nitrogen fertilization (VRF) based on optical spectrometry sensors of crops is a technological innovation capable of improving the nutrient use efficiency (NUE) and mitigate environmental impacts. However, studies addressing fertilization based on crop sensors are still scarce in Brazilian agriculture. This study aims to evaluate the efficiency of an optical crop sensor to assess the nutritional status of corn and compare VRF with the standard strategy of traditional single-rate N fertilization (TSF) used by farmers. With this purpose, three experiments were conducted at different locations in Southern Brazil, in the growing seasons 2008/09 and 2010/11. The following crop properties were evaluated: above-ground dry matter production, nitrogen (N) content, N uptake, relative chlorophyll content (SPAD) reading, and a vegetation index measured by the optical sensor N-Sensor® ALS. The plants were evaluated in the stages V4, V6, V8, V10, V12 and at corn flowering. The experiments had a completely randomized design at three different sites that were analyzed separately. The vegetation index was directly related to above-ground dry matter production (R² = 0.91; p<0.0001), total N uptake (R² = 0.87; p<0.0001) and SPAD reading (R² = 0.63; p<0.0001) and inversely related to plant N content (R² = 0.53; p<0.0001). The efficiency of VRF for plant nutrition was influenced by the specific climatic conditions of each site. Therefore, the efficiency of the VRF strategy was similar to that of the standard farmer fertilizer strategy at sites 1 and 2. However, at site 3 where the climatic conditions were favorable for corn growth, the use of optical sensors to determine VRF resulted in a 12 % increase in N plant uptake in relation to the standard fertilization, indicating the potential of this technology to improve NUE.

Optical crop sensor for variable-rate nitrogen fertilization in corn: II - indices of fertilizer efficiency and corn yield

Generally, in tropical and subtropical agroecosystems, the efficiency of nitrogen (N) fertilization is low, inducing a temporal variability of crop yield, economic losses, and environmental impacts. Variable-rate N fertilization (VRF), based on optical spectrometry crop sensors, could increase the N use efficiency (NUE). The objective of this study was to evaluate the corn grain yield and N fertilization efficiency under VRF determined by an optical sensor in comparison to the traditional single-application N fertilization (TSF). With this purpose, three experiments with no-tillage corn were carried out in the 2008/09 and 2010/11 growing seasons on a Hapludox in South Brazil, in a completely randomized design, at three different sites that were analyzed separately. The following crop properties were evaluated: aboveground dry matter production and quantity of N uptake at corn flowering, grain yield, and vegetation index determined by an N-Sensor® ALS optical sensor. Across the sites, the corn N fertilizer had a positive effect on corn N uptake, resulting in increased corn dry matter and grain yield. However, N fertilization induced lower increases of corn grain yield at site 2, where there was a severe drought during the growing period. The VRF defined by the optical crop sensor increased the apparent N recovery (NRE) and agronomic efficiency of N (NAE) compared to the traditional fertilizer strategy. In the average of sites 1 and 3, which were not affected by drought, VRF promoted an increase of 28.0 and 41.3 % in NAE and NRE, respectively. Despite these results, no increases in corn grain yield were observed by the use of VRF compared to TSF.

Optical absorption and graphitic clusters of hydrogenated amorphophous carbon thin films

The optical absorption of hydrogenated amorphous carbon films (a‐C:H) was measured by spectroscopic ellipsometry. The a‐C:H films were deposited at different substrate temperatures by rf‐plasma of methane. A volume distribution of graphitic cluster size was assumed to reproduce the experimental spectra of the absorption coefficient. The changes in the absorption coefficient and the optical gap, induced by deposition temperature, have been interpreted in terms of changes in the graphitic cluster size of the network. The increase in the deposition temperature produces an increase in the size of the graphitic clusters.