Resonant radiation emitted by solitary waves via cascading in quadratic media.

We present a systematic investigation of the resonant radiation emitted by localized soliton-like wave-packets supported by second-harmonic generation in the cascading regime. We emphasize a general mechanism which allows for the resonant radiation to grow without the need for higher-order dispersion, primarily driven by the second-harmonic component, while radiation is also shed around the fundamental-frequency component through parametric down-conversion processes. The ubiquity of such a mechanism is revealed with reference to different localized waves such as bright solitons (both fundamental and second-order), Akhmediev breathers, and dark solitons. A simple phase matching condition is put forward to account for the frequencies radiated around such solitons, which agrees well with numerical simulations performed against changes of material parameters (say, phase mismatch, dispersion ratio). The results provide explicit understanding of the mechanism of soliton radiation in quadratic nonlinear media.

From regular to pseudo-stochastic recurrence of modulation instability in cascaded second-harmonic generation.

We address the recurrent regime of depleted two-color modulational instability in second-harmonic generation in the cascading limit. We validate a description based on simple algebraic formulas, based on asymptotic matching, establishing quantitatively the limit of validity of this approach. In the low mismatch regime, where such description breaks down, the system is found to undergo pseudo-stochastic alterations between two types of deterministic recurrence.

Quadratic Peregrine solitons resonantly radiating without higher-order dispersion.

We show that two-color Peregrine solitary waves in quadratic nonlinear media can resonantly radiate dispersive waves even in the absence of higher-order dispersion, owing to a phase-matching mechanism that involves the weaker second-harmonic component. We give very simple criteria for calculating the radiated frequencies in terms of material parameters, finding excellent agreement with numerical simulations.

ECG waveform dataset for predicting defibrillation outcome in out-of-hospital cardiac arrested patients.

The provided database of 260 ECG signals was collected from patients with out-of-hospital cardiac arrest while treated by the emergency medical services. Each ECG signal contains a 9 second waveform showing ventricular fibrillation, followed by 1 min of post-shock waveform. Patients' ECGs are made available in multiple formats. All ECGs recorded during the prehospital treatment are provided in PFD files, after being anonymized, printed in paper, and scanned. For each ECG, the dataset also includes the whole digitized waveform (9 s pre- and 1 min post-shock each) and numerous features in temporal and frequency domain extracted from the 9 s episode immediately prior to the first defibrillation shock. Based on the shock outcome, each ECG file has been annotated by three expert cardiologists, - using majority decision -, as successful (56 cases), unsuccessful (195 cases), or indeterminable (9 cases). The code for preprocessing, for feature extraction, and for limiting the investigation to different temporal intervals before the shock is also provided. These data could be reused to design algorithms to predict shock outcome based on ventricular fibrillation analysis, with the goal to optimize the defibrillation strategy (immediate defibrillation versus cardiopulmonary resuscitation and/or drug administration) for enhancing resuscitation.

Predicting defibrillation success in out-of-hospital cardiac arrested patients: Moving beyond feature design.

OBJECTIVE: Optimizing timing of defibrillation by evaluating the likelihood of a successful outcome could significantly enhance resuscitation. Previous studies employed conventional machine learning approaches and hand-crafted features to address this issue, but none have achieved superior performance to be widely accepted. This study proposes a novel approach in which predictive features are automatically learned. METHODS: A raw 4s VF episode immediately prior to first defibrillation shock was feed to a 3-stage CNN feature extractor. Each stage was composed of 4 components: convolution, rectified linear unit activation, dropout and max-pooling. At the end of feature extractor, the feature map was flattened and connected to a fully connected multi-layer perceptron for classification. For model evaluation, a 10 fold cross-validation was employed. To balance classes, SMOTE oversampling method has been applied to minority class. RESULTS: The obtained results show that the proposed model is highly accurate in predicting defibrillation outcome (Acc = 93.6 %). Since recommendations on classifiers suggest at least 50 % specificity and 95 % sensitivity as safe and useful predictors for defibrillation decision, the reported sensitivity of 98.8 % and specificity of 88.2 %, with the analysis speed of 3 ms/input signal, indicate that the proposed model possesses a good prospective to be implemented in automated external defibrillators. CONCLUSIONS: The learned features demonstrate superiority over hand-crafted ones when performed on the same dataset. This approach benefits from being fully automatic by fusing feature extraction, selection and classification into a single learning model. It provides a superior strategy that can be used as a tool to guide treatment of OHCA patients in bringing optimal decision of precedence treatment. Furthermore, for encouraging replicability, the dataset has been made publicly available to the research community.

Fundamental Peregrine Solitons of Ultrastrong Amplitude Enhancement through Self-Steepening in Vector Nonlinear Systems.

We report the universal emergence of anomalous fundamental Peregrine solitons, which can exhibit an unprecedentedly ultrahigh peak amplitude comparable to any higher-order rogue wave events, in the vector derivative nonlinear Schrödinger system involving the self-steepening effect. We present the exact explicit rational solutions on either a continuous-wave or a periodical-wave background, for a broad range of parameters. We numerically confirm the buildup of anomalous Peregrine solitons from strong initial harmonic perturbations, despite the onset of competing modulation instability. Our results may stimulate the experimental study of such Peregrine soliton anomaly in birefringent crystals or other similar vector systems.

Super chirped rogue waves in optical fibers.

The super rogue wave dynamics in optical fibers are investigated within the framework of a generalized nonlinear Schrödinger equation containing group-velocity dispersion, Kerr and quintic nonlinearity, and self-steepening effect. In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n+1 times the background level, which results from the superposition of n(n+1)/2 Peregrine solitons. Particularly, we demonstrate that these super rogue waves involve a frequency chirp that is also localized in both time and space. The robustness of the super chirped rogue waves against white-noise perturbations as well as the possibility of generating them in a turbulent field is numerically confirmed, which anticipates their accessibility to experimental observation.

General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive Darboux transformation.

We formulate a non-recursive Darboux transformation technique to obtain the general nth-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions.

Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber.

The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

Two-color walking Peregrine solitary waves.

We study the extreme localization of light, evolving upon a non-zero background, in two-color parametric wave interaction in nonlinear quadratic media. We report the existence of quadratic Peregrine solitary waves, in the presence of significant group-velocity mismatch between the waves (or Poynting vector beam walk-off), in the regime of cascading second-harmonic generation. This finding opens a novel path for the experimental demonstration of extreme rogue waves in ultrafast quadratic nonlinear optics.

Akhmediev breathers and Peregrine solitary waves in a quadratic medium.

I investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave in a dispersive quadratic medium. I show the existence of quadratic Akhmediev breathers and Peregrine solitary waves in the regime of cascading second-harmonic generation. This finding opens a novel path for the excitation of extreme rogue waves and for the description of modulation instability in quadratic nonlinear optics.

Spatiotemporal optical dark X solitary waves.

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations.

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

Complementary optical rogue waves in parametric three-wave mixing.

We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Optical Dark Rogue Wave.

Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.

Vector rogue waves and baseband modulation instability in the defocusing regime.

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.

Broadband parametric processes in χ(2) nonlinear photonic crystals.

We develop a general model, based on a (2+1)D unidirectional pulse propagation equation, for describing broadband noncollinear parametric interactions in 2D quadratic lattices. We apply it to the analysis of twin-beam optical parametric generation in hexagonally poled LiTaO3, gaining further insights into experimental observations.