Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network

In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the short-term $x(t+6)$. The performance prediction was evaluated and compared with another studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute uncertainties of predictions for noisy Mackey--Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level ($\sigma_{N}$) from 0.01 to 0.1.Comment: 11 pages, 8 figure

Beam optics of gain-guided soft-x-ray lasers in cylindrical plasmas

Includes bibliographical references (page 2851).We analyze soft-x-ray beam propagation and amplification in gain-guided amplifiers of cylindrical geometry for arbitrary gain and density profiles. A general relation that must be fulfilled for refraction not to be an impediment to the exponential growth of the intensity is obtained. It is shown that for sufficiently long plasma columns the effective gain, reduced by refraction, is determined solely by the gain and the curvature of the density profile at the position of maximum density, even when the location of the gain and the density maxima do not coincide. We analyze the case of amplifiers with gain-length approaching saturation and show that refraction reduces the effective gain-length product at which gain saturation occurs. The theoretical results are used to analyze the output of a capillary discharge soft-x-ray laser

A reduced subduction graph and higher multiplicity in S_n transformation coefficients

Transformation coefficients between {\it standard} bases for irreducible representations of the symmetric group $S_n$ and {\it split} bases adapted to the $S_{n_1} \times S_{n_2} \subset S_n$ subgroup ($n_1 +n_2 = n$) are considered. We first provide a \emph{selection rule} and an \emph{identity rule} for the subduction coefficients which allow to decrease the number of unknowns and equations arising from the linear method by Pan and Chen. Then, using the {\it reduced subduction graph} approach, we may look at higher multiplicity instances. As a significant example, an orthonormalized solution for the first multiplicity-three case, which occurs in the decomposition of the irreducible representation $[4,3,2,1]$ of $S_{10}$ into $[3,2,1] \otimes [3,1]$ of $S_6 \times S_4$, is presented and discussed.Comment: 12 pages, 1 figure, iopart class, Revisited version (several typographical errors have been corrected). Accepted for publication in J. Phys. A: Math. Ge

Origin of photoluminescence signals obtained by picosecond-excitation correlation measurements

Includes bibliographical references (page 14355).We have developed a theory that explains the spectral distribution and the different time decay behaviors of the signals observed in picosecond excitation-correlation measurements of semiconductor materials. The results display good quantitative agreement with experiments on multiple quantum wells and show that band filling has an important role in determining the characteristics of the correlation signals. Two limit cases are found and mathematically characterized: the nondegenerate regime, where the signals are positive with exponential-like decays, and the degenerate regime, where band filling gives rise to negative signals. It is shown that the technique is a sensitive probe of the carrier dynamics not fully exploited in previous work

Polarization switching in vertical-cavity surface emitting lasers observed at constant active region temperature

Includes bibliographical references (page 3352).Polarization switching in gain-guided, vertical-cavity, surface-emitting lasers was studied as a function of the active region temperature. We show that polarization switching occurs even when the active region temperature is kept constant during fast pulse low duty cycle operation. This temperature independent polarization switching phenomenon is explained in terms of a recently developed model

Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings

Includes bibliographical references (page 358).We report the demonstration of an amplitude-division soft-x-ray interferometer that can be used to generate high-contrast interferograms at the wavelength of any of the saturated soft-x-ray lasers (5.6-46.9 nm) that are available at present. The interferometer, which utilizes grazing-incidence diffraction gratings as beam splitters in a modified Mach-Zehnder configuration, was used in combination with a tabletop 46.9-nm laser to probe a large-scale (~2.7-mm-long) laser-created plasma

Transient response of vertical-cavity surface-emitting lasers of different active-region diameters

Includes bibliographical references (pages 614-615).The multimode dynamics of vertical-cavity surface-emitting lasers with different active-region diameters was measured under subnanosecond electrical excitation (800-ps pulse duration, 100-ps risetime). The dynamics is characterized by the delayed onset of higher order modes which have a turn-on delay that is dependent on the active-region diameter and the excitation parameters. A simple model that can be used to estimate this turn-on delay for large-area devices is presented. Polarization resolved measurements show that, under this fast excitation condition, both orthogonal polarization states are isomorphic. The influence of the observed dynamics on the relative intensity noise of these devices is also discussed

Ultrahigh frequency oscillations and multimode dynamics in vertical cavity surface emitting lasers

Includes bibliographical references (page 187).We report the observation of ultrahigh frequency oscillations of up to 240 GHz in optically gain switched vertical cavity surface emitting lasers. These oscillations are shown to be produced by multimode emission through mode competition (10-30 GHz) or mode beating (above 100 GHz). Although these oscillations are not related to the intrinsic modulation bandwidth, some of them could be mistaken for relaxation oscillations, calling for careful interpretation of the results of this type of experiments. The highest frequencies observed for single mode relaxation oscillations were about 9 GHz in agreement with values of modulation bandwidth reported in the literature

Dense plasma interferometry with a tabletop soft X-ray laser and an amplitude division interferometer based on diffraction gratings

Includes bibliographical references (page 486).We have demonstrated a novel Mach-Zehnder soft x-ray interferometer that uses diffraction gratings as beam splitters. The interferometer was used together with a 46.9nm tabletop soft x-ray laser, to map the evolution of the electron density distribution of a large-scale laser created plasma

Soft-x-ray interferometer for single-shot laser linewidth measurements

Includes bibliographical references (page 957).A soft-x-ray Mach-Zehnder interferometer configuration that makes use of the time delay introduced by diffraction gratings to conduct single-shot measurements of the linewidth of soft-x-ray laser amplifiers is proposed and analyzed. The scheme was experimentally demonstrated in the near-IR region of the spectrum by measurement of the mode separation of a semiconductor laser. A symmetric configuration with compensated time delays that can be implemented for plasma diagnostics and for evaluating soft-x-ray optics is also discussed