Pulse Evolution Research Articles

The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning

We apply the deep learning approach to learn some nonlinear wave solutions of the Lakshmanan-Porsezian-Daniel (LPD) model characterizing the evolution of ultrashort optical pulse in optical fibers. Based on the strong universal approximation theorem, we give the initial-boundary value data and residual collocation points, choose the parameters initialization Xavier method and parameters optimization Adam and L-BFGS algorithms to construct the optimal neural network model. Then, we derive the data-driven solutions of the rogue wave, anti-dark soliton, multi-peak soliton, non-rational W-shaped soliton, rational W-shaped soliton as well as periodic-wave solutions for the LPD model. Finally, we study the parameters discovery of such model via the anti-dark soliton solution with 1% perturbation (or without perturbation).

Evidence for neutron star triaxial free precession in Her X-1 from Fermi/GBM pulse period measurements

ABSTRACT Her X-1/HZ Her is one of the best studied accreting X-ray pulsars. In addition to the pulsating and orbital periods, the X-ray and optical light curves of the source exhibit an almost periodic 35-d variability caused by a precessing accretion disc. The nature of the observed long-term stability of the 35-d cycle has been debatable. The X-ray pulse frequency of Her X-1 measured by the Fermi/GBM demonstrates periodical variations with X-ray flux at the main-on state of the source. We explain the observed periodic sub-microsecond pulse frequency changes by the free precession of a triaxial neutron star (NS) with parameters previously inferred from an independent analysis of the X-ray pulse evolution over the 35-d cycle. In the Fermi/GBM data, we identified several time intervals with a duration of half a year or longer where the NS precession period describing the pulse frequency variations does not change. We found that the NS precession period varies within one per cent in different intervals. Such variations in the free precession period on a year time-scale can be explained by $\lesssim 1{{\ \rm per\ cent}}$ changes in the fractional difference between the triaxial NS’s moments of inertia due to the accreted mass readjustment or variable internal coupling of the NS crust with the core.

Damage threshold affected by the spatiotemporal evolution of femtosecond laser pulses in multilayer structures

We propose a figure of merit that characterizes the femtosecond laser damage behavior of optical coatings. This figure of merit, based on the complete spatiotemporal evolution of the field in a multilayer system, can be included in optics design. The monochromatic intensity enhancement widely used in “electric field-engineering” is sufficient only in certain structures such as high-reflectivity quarter-wave mirrors. In more complex systems, for example, in group delay dispersion mirrors and frequency tripling mirrors, one should consider the actual (typically smaller) intensity enhancement produced by short pulses and the change (typically increase) of pulse duration within the stack.

Modeling pulse propagation in fiber optical parametric amplifier by a long short-term memory network

The ultrashort pulse evolution in fiber optical parametric amplifier (FOPA) systems is a highly complex nonlinear dynamic. Here, the long short-term memory network (LSTM) is applied to predicting the pulse propagation of signal waves in the FOPA system, rather than calculating the nonlinear Schrödinger equation (NLSE) numerically. The LSTM network only requires the initial signal power waveform, and the signal pulse propagation is realized in the feedback loop. Besides, we focus on predicting the evolution of signal pulse by varying the initial signal power and the initial signal pulse width to test the performance of our proposed method. The predictions of the LSTM network show great consistency with the NLSE results in each propagation stage of two cases, which reveal that the signal pulse evolution in FOPA is achieved precisely. The realization reduces the computational burden and further gives an effective way to optimize and guide the experiment and application in the FOPA systems.

Noise-like pulse generation and amplification from soliton pulses.

The evolution of soliton pulses into noise-like pulses in a nonlinear fiber externally to the laser oscillator is demonstrated at 1.9 µm, for the first time. Soliton collapse based mechanisms induce noise-like pulses with varying properties as a function of nonlinear fiber length without requiring any laser cavity feedback. The proposed method allows the generation of noise-like pulses with a sub-300 fs spike and sub-40 ps pedestal duration. Power scaling of the noise-like pulses is demonstrated in a double-clad thulium-doped fiber amplifier with amplification up to an average power of 5.19 W, corresponding to a pulse energy of 244 nJ. This method provides an alternative route for generating fully synchronized noise-like pulses and solitons in the same system, without relying on the conventionally used mechanism of changing the intracavity nonlinearity within the laser cavity.

Pulse shaping by spectral-domain polarization gratings.

We consider the spectral-domain counterparts of spatial-domain polarization gratings and study their effect on the temporal evolution of femtosecond-scale light pulses. These devices divide an incident light pulse to several orders via spectral polarization modulation, permitting pulse splitting and shaping with controlled time-domain polarization dynamics.

Spatiotemporal nonlinear evolution of the laser pulse and turbulence generation in laser produced plasmas

This study presents a model to understand the behavior of the turbulence generated in the magnetic field of mega gauss order during high-intensity laser interaction with magnetized plasma. The modified nonlinear Schrödinger (MNLS) equation is developed by contemplating the effect of the group velocity dispersion, diffraction, and nonlinearity induced by the relativistic variation of electron mass and the nonlinear ponderomotive force. Numerical simulation is carried out to solve the dimensionless MNLS equation. The simulation results show the generation of the solitary wave type coherent structures in the nonlinear spatiotemporal evolution of the laser pulse at the early stage, but subsequent turbulence generation has also been observed. The ensemble-averaged turbulent power spectrum has been studied and the power-law scaling is approximately ∼ k−1.85(a solid red line of scaling k−1.85 is given for reference). To get insight into the spatiotemporal nonlinear development of the laser pulse, while propagating in the plasma medium, a semi-analytical model has also been presented. The present study could be substantial in replicating astrophysical scenarios by laboratory simulations along with understanding the underlying quintessential physics of magnetic turbulence.

Investigation of unsteady cryogenic cavitating flow and induced noise around a three-dimensional hydrofoil

In this paper, the Large Eddy Simulation (LES) combined with the Schnerr–Sauer cavitation model and the permeable Ffowcs Williams–Hawkings (FW-Hpds) acoustic analogy approach are introduced to study the unsteady cavitation behaviors and the radiated noise characteristics of the transient liquid nitrogen (LN2) cavitating flow around a NACA66 (National Advisory Committee for Aeronautics) hydrofoil. Satisfactory agreement is obtained between the numerical predictions and experimental measurements. The cavitation noise is predicted based on the sound radiation theory for spherical bubbles and compared with the sound pressure levels of non-cavitating flow from the FW-Hpds equation. It is found that the cavity volume acceleration is directly responsible for driving the generation of cavitation noise, and the sound pressure caused by the development of LN2 cavitation is shown to vary with the periodic pulsing cavity volume evolution, indicating a strong link between cavity evolutions and radiated noises. The transient cavitation structures of the sheet and cloud cavitation are well captured, and the evolution features of the cavities and vortex structures are analyzed in detail. The collapse of the detached small cloud cavity downstream is the main mechanism for generating intense acoustic impulses for both sheet and cloud cavitation. While the strong interaction between the re-entrant jet and the main flow results in violent pressure fluctuations, and thus produces instantaneous extreme dipole noise, which accounts for another distinctive mechanism to induce intense acoustic impulses for cloud cavitation, the presented study provides a deep understanding of the nature of cavitation-dominated noise for cryogenic cavitating flow.

Femtosecond fiber oscillator based on a 3×3-coupler-NALM: numerical model and realizations at 1 and 2 µm.

In this article, we present robust passively mode-locked femtosecond lasers operating at 1030 and approximately 2000 nm, respectively. The all-fiber, all-polarization-maintaining (PM) lasers are mode-locked by a nonlinear amplifying loop mirror (NALM) which is attached to the cavity by a 3×3-coupler. The NALM is phase-biased by the coupler, enabling turn-key operation of the oscillator. Femtosecond pulse generation is demonstrated using Ytterbium and Thulium doped active fibers. Depending on the wavelength and the installed dispersive elements, pulse formation can be aided by a range of attractors including self-similar pulse evolution, soliton, or dispersion-managed soliton formation.

Mechanisms of dual-wavelength dissipative soliton mode-locking in net-normal dispersion fiber lasers

Dual-wavelength mode-locked fiber lasers have attracted great attention due to their enormous potential in facilitating dual-comb spectroscopy. However, mechanism for dual-wavelength dissipative soliton mode-locking and the intracavity dynamics are still elusive. In this paper, we construct a simple and universal model to numerically investigate the intracavity buildup dynamics of dual-wavelength mode-locking in an all-normal dispersion fiber laser. By resolving the pulses evolution and their interactions, we find that the chromatic dispersion induced pulse collision plays an important role in dual-wavelength pulses formation and propagation. At the chaotic stage, the collision-induced energy upheaval results in drastic nonlinear coupling effects, which contribute to the dual-wavelength mode-locking and formation of dual-wavelength soliton molecules. While at the stable dual-wavelength mode-locking stage, the two asynchronous pulses periodically collide, accompanying extremely intense wave generation and spectral explosion. Moreover, cavity energy and gain competition are modeled and optimized to realize the self-started pulse-splitting-free dual-wavelength mode-locking.

Interchanging Space and Time in Nonlinear Optics Modeling and Dispersion Management Models

Interchanging the role of space and time is widely used in nonlinear optics for modeling the evolution of light pulses in glass fibers. A phenomenological model for the mathematical description of light pulses in glass fibers with a periodic structure in this set-up is the so-called dispersion management equation. It is the purpose of this paper to answer the question whether the dispersion management equation or other modulation equations are more than phenomenological models in this situation. Using Floquet theory we prove that in case of comparable wave lengths of the light and of the fiber periodicity the NLS equation and NLS like modulation equations with constant coefficients can be derived and justified through error estimates under the assumption that rather strong stability and non-resonance conditions hold. This is the first NLS approximation result documented for time-periodic dispersive systems. We explain that the failure of these conditions allows us to prove that these modulation equations in general make wrong predictions. The reasons for this failure and the behavior of the system for a fiber periodicity much larger than the wave length of light shows that interchanging the role of space and time for glass fibers with a periodic structure leads to unwanted phenomena.

Pulse Shape Estimation in a DSR Fiber Laser Using the Genetic Algorithm

Exploiting the computing power of the genetic algorithm, a numerical study of dissipative soliton resonance (DSR) in a ring laser mode-locked by a real saturable absorber (SA) is conducted. A section of photonic crystal fiber (PCF) is inserted into the laser cavity design to facilitate accurate control of both dispersion and nonlinearity. The influence of the cavity parameters on the evolution of the DSR pulses is systematically analyzed. The genetic algorithm demonstrates that the generation of DSR square pulses depends directly on the PCF dispersion, the PCF nonlinearity, the PCF length, and the modulation depth of the SA. Finally, the sensitivity of the DSR pulse width, peak power and energy to perturbations in a few key design parameters are highlighted.

Real time revealing relaxation dynamics of ultrafast mode-locked lasers

Single-shot measurement of ultrashort time with a dispersive temporal interferometer (DTI) paves the way for exploring intracavity dynamics in ultrafast lasers. Here, we report observations of pulse evolution dynamics after mode-locking buildup in ultrafast lasers. We observe the roundtrip time and phase evolution of the mode-locked pulses after buildup, and we unveil that the pulse experiences three different stages before stabilization, i.e., the soliton breathing stage, the relaxation oscillation stage, and the long-term relaxation stage. We find that the gain depletion effect makes the pulse move forward but does not shift its phase, and it can be distinguished by a DTI from the refractive index change. With this, the dynamics of the three stages is analyzed. Moreover, it is unveiled that the gain relaxation dynamics can intensively affect a laser's stability. These results provide additional perspectives on the intracavity dynamics of mode-locked lasers and of complex nonlinear systems, and they can help to improve the laser stability, which may impact laser design, ultrafast diagnostics, and nonlinear optics.

Design and demonstration of ultrafast holographic microscopic system based on time stretching

Evolving from time stretching technique based on ultrashort optical pulse, wavelength-to-space-mapping imaging has become a common strategy for single-shot ultrafast imaging. In the technique, chirped broadband child pulses are generated and used to probe the transient scene typically, and the frames with temporal resolution up to picosecond scale can be achieved. Here we propose a single-shot ultrafast holographic microscopic system through a wide-spectrum pulse. A digital micromirror device (DMD)-based quasi-4f system and a dispersive medium are involved to generate chirped multi-wavelengths child pulses in sequence. A series of off-axis holograms are spatially dispersed and separated by a grating and captured simultaneously. The time-resolved three-dimensional (3D) profiles are retrieved using the reconstruction algorithm. In the paper, the temporal evolution of optical pulse and the mechanism of holographic imaging are detailed and numerically analyzed. A 10-frames holographic microscopic system with field of view (FOV) of 0.2 mm × 0.2 mm, frame rate of 6.8 × 1010 fps and exposure time of 5.4 ps is realized, where the interval and linewidth of the multi-wavelengths are 10 nm and 0.25 nm, respectively.

Effect of small pre-strain on the resistance of molybdenum [100] single crystal to high strain rate deformation and fracture

The evolution of shock compressive pulses and dynamic tensile (spall) strength of pristine and pre-strained (0.6% and 5.4% compression) samples of pure [100]-oriented molybdenum single crystals were studied in a series of planar impact tests accompanied by continuous monitoring of the free surface velocity of the samples by an optic velocimeter. The impact loading of Mo samples of different thicknesses was produced by copper impactors accelerated in the smooth bore gun up to a velocity of about 350 m/s. Analyzing the recorded waveforms showed that pre-straining results in a substantial decrease of the molybdenum Hugoniot elastic limit while the dynamic tensile (spall) strength increases with pre-straining. The spall fracture of all tested (and spalled) samples was found to be brittle and characterized by a weak dependence of spall strength on the tensile strain rate. The obtained results are discussed in the terms of generally accepted theories of elastic precursor decay in ductile and spall fracture in brittle solids.

Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber

This article proposes an advanced algorithm for the numerical solution of a coupled nonlinear Schrödinger equations system describing the evolution of a high-power femtosecond optical pulse in a single-mode polarization-maintaining optical fiber. We use the algorithm based on a variant of the split-step method with the Madelung transform to calculate the complex amplitude when executing a nonlinear operator. In contrast to the known solution, the proposed algorithm eliminates the need to numerically solve differential equations directly, concerning the phase of complex amplitude when executing the nonlinear operator. This made it possible, other things being equal, to reduce the computation time by more than four times.

Ultra-Short Pulse Generation From Optical Parametric Oscillators With a Cavity-Length Detuning

We report that the pulse compression mechanism in cavity-length-detuned optical parametric oscillators (OPOs) could be used to generate high-quality, soliton-like optical pulses with sub-100 fs duration. By numerical simulations, we illustrated the pulse and spectral evolution in an OPO with respect to cavity-length detuning, including central wavelength shift, spectral broadening and pulse compression. Experimentally, from an OPO pumped by 180 fs pulses, we obtained 42 fs signal pulses with a time-bandwidth product of 0.32. At elevated pump powers, the formation of multiple pulses was observed. Nonetheless, we demonstrated that the high-quality optical pulses could be obtained by simply slightly increasing the cavity-length detuning.

Modeling Pulsed Evolution and Time-Independent Variation Improves the Confidence Level of Ancestral and Hidden State Predictions.

Ancestral state reconstruction is not only a fundamental tool for studying trait evolution, but also very useful for predicting the unknown trait values (hidden states) of extant species. A well-known problem in ancestral and hidden state predictions is that the uncertainty associated with predictions can be so large that predictions themselves are of little use. Therefore, for meaningful interpretation of predicted traits and hypothesis testing, it is prudent to accurately assess the uncertainty of the predictions. Commonly used constant-rate Brownian motion (BM) model fails to capture the complexity of tempo and mode of trait evolution in nature, making predictions under the BM model vulnerable to lack-of-fit errors from model misspecification. Using empirical data (mammalian body size and bacterial genome size), we show that the distribution of residual Z-scores under the BM model is neither homoscedastic nor normal as expected. Consequently, the 95% confidence intervals of predicted traits are so unreliable that the actual coverage probability ranges from 33% (strongly permissive) to 100% (strongly conservative). Alternative methods such as BayesTraits and StableTraits that allow variable rates in evolution improve the predictions but are computationally expensive. Here, we develop Reconstructing Ancestral State under Pulsed Evolution in R by Gaussian Decomposition (RasperGade), a method of ancestral and hidden state prediction that uses the Levy process to explicitly model gradual evolution, pulsed evolution, and time-independent variation. Using the same empirical data, we show that RasperGade outperforms both BayesTraits and StableTraits in providing reliable confidence estimates and is orders-of-magnitude faster. Our results suggest that, when predicting the ancestral and hidden states of continuous traits, the rate variation should always be assessed and the quality of confidence estimates should always be examined. [Bacterial genomic traits; model misspecification; trait evolution.].

Characterization of Annular Cement Permeability of a Logged Well Section Using Pressure–Pulse Decay Measurements

Abstract The cement behind casings is an important barrier element in wells that should provide zonal isolation along the well. The hardened cement does not always isolate permeable formations, either due to placement issues or loads that over time compromise the integrity of the barrier. The modern method used to characterize the annular material is ultrasonic logging which provides essential information concerning the type of material behind casing, but no measurement of the annular permeability. This study provides permeability characterization of a casing-cement sandwich joint retrieved from a 33 years old production well that has been logged at surface using a state-of-the-art ultrasonic tool. The joint contains an interval of low-permeable cement that previously has prevented permeability measurement by gas injection. A pressure–pulse decay test method has now been performed that is based on monitoring the evolution of a pressure pulse through the joint. Long-term pressure measurements show communication through the entire joint and are in qualitative agreement with the log. A pressure diffusion model is used to estimate local permeability along the joint, enabling comparison of log response and permeability. The low-permeable region is relatively short, situated directly on top of a casing collar, and has permeability that is orders of magnitude lower than the cement above and below. In the longer term, results from this and related studies can be used as input for future sustained casing pressure evaluations or for quantifying seepage risk behind casings for abandonment designs.

Principle-Driven Fiber Transmission Model Based on PINN Neural Network

In this paper, a novel principle-driven fiber transmission model based on physical induced neural network (PINN) is proposed. Unlike data-driven models which regard fiber transmission problem as data regression tasks, this model views it as an equation solving problem. Instead of adopting input signals and output signals which are calculated by SSFM algorithm in advance before training, this principle-driven PINN based fiber model adopts frames of time and distance as its inputs and the corresponding real and imaginary parts of NLSE solutions as its outputs. By taking into account of pulses and signals before transmission as initial conditions and fiber physical principles as NLSE in the design of loss functions, this model will progressively learn the transmission rules. Therefore, it can be effectively trained without the data labels, referred as the pre-calculated signals after transmission in data-driven models. Due to this advantage, SSFM algorithm is no longer needed before the training of principle-driven fiber model which can save considerable time consumption. Through numerical demonstration, the results show that this principle-driven PINN based fiber model can handle the prediction tasks of pulse evolution, signal transmission and fiber birefringence for different transmission parameters of fiber telecommunications.