Nonlinear Dynamics of a Single-Mode Semiconductor Laser with Long Delayed Optical Feedback: A Modern Experimental Characterization Approach

Semiconductor lasers can exhibit complex dynamical behavior in the presence of external perturbations. Delayed optical feedback, re-injecting part of the emitted light back into the laser cavity, in particular, can destabilize the laser’s emission. We focus on the emission properties of a semiconductor laser subject to such optical feedback, where the delay of the light re-injection is large compared to the relaxation oscillations period. We present an overview of the main dynamical features that emerge in semiconductor lasers subject to delayed optical feedback, emphasizing how to experimentally characterize these features using intensity and high-resolution optical spectra measurements. The characterization of the system requires the experimentalist to be able to simultaneously measure multiple time scales that can be up to six orders of magnitude apart, from the picosecond to the microsecond range. We highlight some experimental observations that are particularly interesting from the fundamental point of view and, moreover, provide opportunities for future photonic applications.

Multi-temporal runoff-sediment discharge relationships

To understand the runoff-sediment discharge relationship , this study examined the annual runoff and sediment discharge data obtained from the Tangnaihai hydrometric station. The data were decomposed into multiple time scales through Complete Ensemble Empirical Mode Decomposition with adaptive noise (CEEMDAN). Furthermore, double cumulative curves were plotted and the cointegration theory was employed to analyze the microscopic and macroscopic multi-temporal correlations between the runoff and the sediment discharge and their detailed evolution.

Spatial and Temporal Analyses of Vegetation Changes at Multiple Time Scales in the Qilian Mountains

The Qilian Mountains (QLMs), an important ecological protective barrier and major water resource connotation area in the Hexi Corridor region, have an important impact on ecological security in western China due to their ecological changes. However, most existing studies have investigated vegetation changes and their main driving forces in the QLMs on the basis of a single scale. Thus, the interactions among multiple environmental factors in the QLMs are still unclear. This study was based on normalised difference vegetation index (NDVI) data from 2000 to 2019. We systematically analysed the spatial and temporal characteristics of the QLMs at multiple time scales using trend analysis, ensemble empirical mode decomposition, Geodetector, and correlation analysis methods. At different time scales under single-factor and multi-factor interactions, we examined the mechanisms of the vegetation changes and their drivers. Our results showed that the vegetation in the QLMs showed a trend of overall improvement in 2000–2019, at a rate of 0.88 × 10−3, mainly in the central western regions. The NDVI in the QLMs showed a short change cycle of 3 and 5 years and a long-term trend. Sunshine time and wind speed were the main drivers of the vegetation variation in the QLMs, followed by temperature. Precipitation affected the vegetation spatial variation within a certain altitude range. However, temperature and precipitation had stronger explanatory powers for the vegetation variation in the western QLMs than in the eastern part. Their interaction was the dominant factor in the regional differences in vegetation. The responses of the NDVI to temperature and precipitation were stronger in the long time series. The main drivers of vegetation variation were land surface temperature and precipitation in the east and temperature and evapotranspiration in the west. Precipitation was the main driver of vegetation growth in the northern and southwestern QLMs on both the short- and long-term scales. Vegetation changes were more significantly influenced by short-term temperature changes in the east but by a combination of temperature and precipitation in most parts of the QLMs on a 5-year time scale.

Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales

We experimentally, numerically and theoretically investigate the nonlinear interaction between a cavitation bubble and the interface of two immiscible fluids (oil and water) on multiple time scales. The underwater electric discharge method is utilized to generate a cavitation bubble near or at the interface. Both the bubble dynamics on a short time scale and the interface evolution on a much longer time scale are recorded via high-speed photography. Two mechanisms are found to contribute to the fluid mixing in our system. First, when a bubble is initiated in the oil phase or at the interface, an inertia-dominated high-speed liquid jet generated from the collapsing bubble penetrates the water–oil interface, and consequently transports fine oil droplets into the water. The critical standoff parameter for jet penetration is found to be highly dependent on the density ratio of the two fluids. Furthermore, the pinch-off of an interface jet produced long after the bubble dynamics stage is reckoned as the second mechanism, carrying water droplets into the oil bulk. The dependence of the bubble jetting behaviours and interface jet dynamics on the governing parameters is systematically studied via experiments and boundary integral simulations. Particularly, we quantitatively demonstrate the respective roles of surface tension and viscosity in interface jet dynamics. As for a bubble initiated at the interface, an extended Rayleigh–Plesset model is proposed that well predicts the asymmetric dynamics of the bubble, which accounts for a faster contraction of the bubble top and a downward liquid jet.

A separated representation involving multiple time scales within the Proper Generalized Decomposition framework

Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

Causal contributions of neural noise to left frontal networks subtending the modulation of conscious visual perception in the human brain

For several decades, the field of human neurophysiology has focused on the role played by cortical oscillations in enabling brain function underpinning behaviors. In parallel, a less visible but robust body of work on the stochastic resonance phenomenon has also theorized contributions of neural noise - hence more heterogeneous, complex and less predictable activity - in brain coding. The latter notion has received indirect causal support via improvements of visual function during non-regular or random brain stimulation patterns. Nonetheless, direct evidence demonstrating an impact of brain stimulation on direct measures of neural noise is still lacking. Here we evaluated the impact of three non frequency-specific TMS bursts, compared to a control pure high-beta TMS rhythm, delivered to the left FEF during a visual detection task, on the heterogeneity, predictability and complexity of ongoing brain activity recorded with scalp EEG. Our data showed surprisingly that the three non frequency-specific TMS patterns did not prevent a build-up of local high-beta activity. Nonetheless, they increased power across broader or in multiple frequency bands compared to control purely rhythmic high-beta bursts tested along. Importantly, non frequency-specific patterns enhanced signal entropy over multiple time-scales, suggesting higher complexity and an overall induction of higher levels of cortical noise than rhythmic TMS bursts. Our outcomes provide indirect evidence on a potential modulatory role played by sources of stochastic noise on brain oscillations and synchronization. Additionally, they pave the way towards the development of novel neurostimulation approaches to manipulate cortical sources of noise and further investigate their causal role in neural coding.

Systematical Evaluation of Three Gridded Daily Precipitation Products Against Rain Gauge Observations Over Central Asia

Understanding the precipitation variability and extreme precipitation over arid Central Asia (CA) has largely been hampered by the lack of daily precipitation observations. The gridded precipitation datasets over CA are large discrepancies. Here, three gauge-based gridded daily precipitation products from Asian Precipitation Highly-Resolved Observational Data Integration Towards Evaluation (APHRODITE), Global Precipitation Climatology Center (GPCC), and Climate Prediction Center Based Analysis of Global Daily Precipitation (CPC_global) were assessed and compared with 49 rain gauge daily observations precipitation (OBS) from January 1985 to December 2015 using different time-scales over CA and different climate regimes, specifically Northern CA with temperate continental climate (NCA), Southwestern CA with dry arid desert climate (SWCA), and Southeastern CA with Mediterranean continental climate (SECA). Four accuracy indices [correlation coefficient (R), Bias, root mean square error (RMSE), and relative bias (RBias)] were employed to evaluate the performance of the three products in depicting the spatiotemporal features of precipitation variation over CA at multiple time scales (including daily, monthly, seasonal, and yearly). The mean annual and daily precipitation of OBS and three gridded products exhibit the trend of a gradual precipitation decreased from SECA to NCA and SWCA. The best overall performance was obtained for APHRODITE and GPCC for daily and annual time-scale, whereas CPC shows noticeable underestimation precipitation in SECA. The monthly precipitation depicted distinct features with a bimodal pattern with a peak in March and another in December, include the SECA and SWCA regions. In contrast, precipitation was concentrated in summer with the peak in July over the NCA region. At monthly scale terms, APHRODITE was more accurate in the wet seasons (winter and spring months) in SWCA and SECA. Additionally, GPCC has fairly better capability in summer months in NCA. Considering the spatial distribution, the bias variability was largerly in mountainous areas than in the plains. Temporally, the bias largerly in the dry seasons than in the wet seasons. At the interannual variability scale, GPCC was capable of qualitatively increasing the CA (NCA and SECA) precipitation during the last 21 years, while APHRODITE underestimated the trends. The CPC overestimated the precipitation trends over all regions. This study can serve as a reference for selecting daily precipitation products with low densities of stations, complex topographies, and similar climatic regions.