Approaches for ultrafast imaging of transient materials processes in the transmission electron microscope

The growing field of ultrafast materials science, aimed at exploring short-lived transient processes in materials on the microsecond to femtosecond timescales, has spawned the development of time-resolved, in situ techniques in electron microscopy capable of capturing these events. This article gives a brief overview of two principal approaches that have emerged in the past decade: the stroboscopic ultrafast electron microscope and the nanosecond-time-resolved single-shot instrument. The high time resolution is garnered through the use of advanced pulsed laser systems and a pump-probe experimental platforms using laser-driven photoemission processes to generate time-correlated electron probe pulses synchronized with laser-driven events in the specimen. Each technique has its advantages and limitations and thus is complementary in terms of the materials systems and processes that they can investigate. The stroboscopic approach can achieve atomic resolution and sub-picosecond time resolution for capturing transient events, though it is limited to highly repeatable (>10(6) cycles) materials processes, e.g., optically driven electronic phase transitions that must reset to the material's ground state within the repetition rate of the femtosecond laser. The single-shot approach can explore irreversible events in materials, but the spatial resolution is limited by electron source brightness and electron-electron interactions at nanosecond temporal resolutions and higher. The first part of the article will explain basic operating principles of the stroboscopic approach and briefly review recent applications of this technique. As the authors have pursued the development of the single-shot approach, the latter part of the review discusses its instrumentation design in detail and presents examples of materials science studies and the near-term instrumentation developments of this technique.     

Shallow water rogue wavetrains in nonlinear optical fibers

In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the modulationally stable normal dispersion regime. A suitable phase or frequency modulation of a CW laser leads to chirp-free and flat-top pulses or flaticons which exhibit a stable self-similar evolution. Upon collision, flaticons at different carrier frequencies, which may also occur in wavelength division multiplexed transmission systems, merge into a single, high-intensity, temporally and spatially localized rogue pulse.     

Granularity and inhomogeneity are the joint generators of optical rogue waves

In the presence of many waves, giant events can occur with a probability higher than expected for random dynamics. By studying linear light propagation in a glass fiber, we show that optical rogue waves originate from two key ingredients: granularity, or a minimal size of the light speckles at the fiber exit, and inhomogeneity, that is, speckles clustering into separate domains with different average intensities. These two features characterize also rogue waves in nonlinear systems; thus, nonlinearity just plays the role of bringing forth the two ingredients of granularity and inhomogeneity.     

Rogue wave formation by accelerated solitons at an optical event horizon

Rogue waves, by definition, are rare events of extreme amplitude. At the same time, they are surprisingly ubiquitous, in the sense that they can exist in a wide range of physical contexts and possess probability distributions that exhibit heavier tails than the normal Gaussian distribution. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrödinger-type equation together with a concave dispersion profile around a zero-dispersion wavelength, we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism appears to be widely independent from interactions specific to the optical context, e.g., the Raman effect or other scattering processes that have no equivalent in other wave-supporting physical systems. In our system, a strong increase in the peak power may appear via reshaping while the pulse energy is nearly conserved. The conservative nature of the proposed reshaping-induced appearance of rogue waves makes this mechanism particularly robust.     

New dosimeters for solar-flare radiations

From the extensive investigations carried out since 1992 with the dosimetric ANPA-stack on 107 long-haul flights, it is possible to conclude that the cumulative dose per flight on a given route changes within less than 20% among different repeated routes, two different aircrafts (Boeings 747 and 767), and among different locations within the aircraft. In contrast to galactic cosmic rays, solar-flare radiation is totally unpredictable and extremely variable in terms of energy spectrum, intensity, direction, duration and starting time.

Most of the dosimetric systems used to date for the galactic cosmic rays may not be appropriate for solar-flare-radiation dosimetry. For this reason, different dosimetric systems have been investigated for both the retrospective and prospective dosimetry of solar flares. While waiting for the rare solar flare to occur, these dosimetric systems could be used for the validation of the computer-estimated route doses and/or for dosimetry in space, where frequent measurements of solar-flare events are needed.     

Extreme value theory for singular measures

In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and He?non maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.     

Rogue waves in a multistable system

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.     

Deterministic optical rogue waves

Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process.     

Photonic time‐stretch digitizer and its extension to real‐time spectroscopy and imaging

Real‐time wideband digitizers are the key building block in many systems including oscilloscopes, signal intelligence, electronic warfare, and medical diagnostics systems. Continually extending the bandwidth of digitizers has hence become a central challenge in electronics. Fortunately, it has been shown that photonic pre‐processing of wideband signals can boost the performance of electronic digitizers. In this article, the underlying principle of the time‐stretch analog‐to‐digital converter (TSADC) that addresses the demands on resolution, bandwidth, and spectral efficiency is reviewed. In the TSADC, amplified dispersive Fourier transform is used to slow down the analog signal in time and hence to compress its bandwidth. Simultaneous signal amplification during the time‐stretch process compensates for parasitic losses leading to high signal‐to‐noise ratio. This powerful concept transforms the analog signal's time scale such that it matches the slower time scale of the digitizer. A summary of time‐stretch technology's extension to high‐throughput single‐shot spectroscopy, a technique that led to the discovery of optical rouge waves, is also presented. Moreover, its application in high‐throughput imaging, which has recently led to identification of rogue cancer cells in blood with record sensitivity, is discussed.     

Visualizing events in time-varying scientific data

In time-varying scientific datasets from simulations or experimental observations, scientists always need to understand when and where interesting events occur. An event is a complex spatial and temporal pattern that happens over a course of timesteps and includes the involved features and interactions. Event detection allows scientists to query a time-varying dataset from a much smaller set of possible choices. However, with many events detected from a dataset, each spanning different time intervals, querying and visualizing these events pose a challenge. In this work, we propose a framework for the visualization of events in time-varying scientific datasets. Our method extracts features from a data, tracks features over time, and saves the evolution process of features in an event database where a set of database operations are provided to model an event by defining the stages or individual steps that make up an event. Using the feature metadata and the event database, three types of event visualizations can be created to give a unique insight into the dynamics of data from temporal, spatial, and physical perspectives and to summarize multiple events or even the whole dataset. Three case studies are used to demonstrate the usability and effectiveness of the proposed approach.     

Quantum Field Theory of Black-Swan Events

Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.     

Emergence of rogue waves from optical turbulence

We provide some general physical insights into the emergence of rogue wave events from optical turbulence by analyzing the long term evolution of the field. Depending on the amount of incoherence in the system (i.e., Hamiltonian), we identify three turbulent regimes that lead to the emergence of specific rogue wave events: (i) persistent and coherent rogue quasi-solitons, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light or intense flashes.     

A simple study of the correlation effects in the superposition of waves of electric fields: The emergence of extreme events

In this paper, we study the effects of correlated random phases in the intensity of a superposition of N wavefields. Our results suggest that regardless of whether the phase distribution is continuous or discrete if they are random correlated variables, we will observe a denser tail distribution and the emergence of extreme events (amplitudes 30-40 times larger than their average) as the phases correlation increase. Recent results in the literature discuss the role of phase correlations on the emergence of rogue waves both in linear and nonlinear systems, but the mechanisms to generate them are not always straightforward. We show here a simple way to correlate the wavefield that makes it clear that rogue waves or denser tails appear mainly due to wave correlations instead of any particular system property.     

Low Reynolds number hydrodynamics of asymmetric,oscillating dumbbell pairs

Numerical simulations are used to discuss various aspects of “optical rogue wave” statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show that the unfiltered statistical distribution can still exhibit a long-tail, but the extreme-events in this case correspond to collisions between solitons of different frequencies. These results confirm the importance of collision dynamics in supercontinuum generation. We also show that the collision-induced events satisfy an extended hydrodynamic definition of “rogue wave” characteristics.     

Control of Spectral Extreme Events in Ultrafast Fiber Lasers by a Genetic Algorithm

Extreme wave events or rogue waves (RWs) are both statistically rare and of exceptionally large amplitude. They are observed in many complex systems ranging from oceanic and optical environments to financial models and Bose–Einstein condensates. As they appear from nowhere and disappear without a trace, their emergence is unpredictable and non-repetitive, which makes them particularly challenging to control. Here, the use of genetic algorithms (GAs), which are exclusively designed for searching and optimizing stationary or repetitive processes in nonlinear optical systems, is extended to the active control of extreme events in a fiber laser cavity. Feeding real-time spectral measurements into a GA controlling the electronics to optimize the cavity parameters, the wave events are able to be triggered in the cavity that have the typical statistics of RWs in the frequency domain. The intensity of the induced RWs can also be tailored. This accurate control enables the generation of optical RWs with a spectral peak intensity 32.8 times higher than the significant intensity threshold. A rationale is proposed and confirmed by numerical simulations of the laser model for the related frequency up- and downshifting of the optical spectrum that are experimentally observed.     

Differentiation in a globally coupled circle map with growth and death

A key characteristic of biological systems is the continuous life cycle where cells are born, grow and die. From a dynamical point of view the events of cell division and cell death are of paramount importance and constitute a radical departure from systems with a fixed size. In this paper, a globally coupled circle map where elements can dynamically be added and removed is investigated for the conditions under which differentiation of roles can occur. In the presence of an external source, it is found that populations of very long-living cells are sustained by short-living cells. In the case without an external source, it is found that at higher nonlinearities of the local map, large populations cannot be sustained with a previously employed division strategy but that a different and conceptually equally natural division strategy allows for differentiation of roles.     

Describing supercontinuum noise and rogue wave statistics using higher-order moments

We show that the noise properties of fiber supercontinuum generation and the appearance of long-tailed “rogue wave” statistics can be accurately quantified using statistical higher-order central moments. Statistical measures of skew and kurtosis, as well as the coefficient of variation provide improved insight into the nature of spectral fluctuations across the supercontinuum and allow regions of long-tailed statistics to be clearly identified. These moments – that depend only on analyzing intensity fluctuations – provide a complementary tool to phase-dependent coherence measures to interpret supercontinuum noise.