Pulse Evolution Research Articles

Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Crystal Fiber with Three Zero-Dispersion Points

The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four photonic crystal fibers with different barrier widths was discussed, and the optimal fiber was determined after considering the factors of width and flatness. By analyzing the mechanism of supercontinuum generation in photonic crystal fibers with single, double and three zero-dispersion points, it is found that the photonic crystal fiber with three zero-dispersion points have a larger spectral width due to the component of tunneling solitons. Then, the effects of four characteristic parameters (truncation factor a, distribution factor χ0, initial chirp C and central wavelength λ) on forming the supercontinuum spectrum of Airy-Gaussian pulses are analyzed in detail. The results show that the spectral width and energy intensity of the dispersive wave and tunneling soliton generation can be well controlled by adjusting the barrier width and initial parameters of the pulse. These research results provide a theoretical basis for generating and manipulating high-power mid-infrared supercontinuum sources.

Predicting nonlinear multi-pulse propagation in optical fibers via a lightweight convolutional neural network.

The nonlinear evolution of ultrashort pulses in optical fiber has broad applications, but the computational burden of convolutional numerical solutions necessitates rapid modeling methods. Here, a lightweight convolutional neural network is designed to characterize nonlinear multi-pulse propagation in highly nonlinear fiber. With the proposed network, we achieve the forward mapping of multi-pulse propagation using the initial multi-pulse temporal profile as well as the inverse mapping of the initial multi-pulse based on the propagated multi-pulse with the coexistence of group velocity dispersion and self-phase modulation. A multi-pulse comprising various Gaussian pulses in 4-level pulse amplitude modulation is utilized to simulate the evolution of a complex random multi-pulse and investigate the prediction precision of two tasks. The results obtained from the unlearned testing sets demonstrate excellent generalization and prediction performance, with a maximum absolute error of 0.026 and 0.01 in the forward and inverse mapping, respectively. The approach provides considerable potential for modeling and predicting the evolution of an arbitrary complex multi-pulse.

Предельно короткие оптические импульсы в среде ориентированных углеродных нанотрубок с нелинейностью 3 и 5 порядков

In the work, a theoretical study was carried out as well as numerical simulation of the interaction of three-dimensional extremely short pulses with an inhomogeneous array of oriented semiconductor carbon nanotubes, with polarization nonlinearities of 3 and 5 orders. The results of the temporal evolution of such pulses and the dependence of the pulse strength on the parameters of the inhomogeneity of an array of oriented nanotubes are shown. Extremely short pulses (ESP), in this case, mean optical pulses of high intensity, containing one to five periods of the electromagnetic field, with a duration of up to 100 ps. The pulse frequency lies in the near-infrared range. A necessary condition for the stable propagation of extremely short pulses is the presence of nonlinear effects that would make it possible to compensate for their dispersion and diffraction spreading. Therefore, an array of oriented carbon nanotubes (CNTs), which have nonlinear properties, was chosen as the pulse propagation medium. The use of nonlinear optical media can be used to create coherent radiation sources, light sources with variable frequency, etc.

Watt-level 1.6 μm dissipative soliton ultrafast laser and external generation of ∼70 fs noise-like pulses for supercontinuum generation

Here, we propose a high power dissipative soliton (DS) laser with a central wavelength of ∼1612 nm. The whole laser system includes the mode-locking oscillator and the corresponding master oscillator power amplifier (MOPA). The mode-locking oscillator is a nonlinear amplifier loop mirror (NALM) cavity, which has a net normal dispersion enabling the generation of nJ-level DS pulses. To further enhance the output power of the 1.6 μm DS pulses, the specially-designed MOPA system consisting of multiple-stage single-pass amplifier is constructed, which can amplify the output power to watt level and meanwhile keeps a high suppression ratio to C-band amplified spontaneous emission (ASE). This high power 1.6 μm DS laser will have further applications in biomedical research and material processing. In the amplifier, we observe the automatic evolution of the DS pulses into the noise-like (NL) pulses under high pumping strength. At the maximum pump power, the MOPA system delivers the NL pulses with an output power of over 2 W. The narrowest spike duration is ∼70 fs (fs). This 1.6 μm fs-scale NL laser is a good pump source for generating the mid-infrared supercontinuum without short wavelength region loss. To demonstrate the superiority of this NL laser, a broad supercontinuum from ∼0.87 μm to ∼3.75 μm waveband is achieved with a piece of highly germanium-doped (Ge-doped) fiber.

Timing of Carbonatite Ultramafic Complexes of the Eastern Sayan Alkaline Province, Siberia: U–Pb (ID–TIMS) Geochronology of Ca–Fe Garnets

In this study, we present the results of U–Pb (ID-TIMS) geochronological studies of calcic garnet from the alkaline ultramafic complexes of Eastern Sayan province (eastern Siberia). New U–Pb ID–TIMS garnet ages obtained from different rocks of Bolshaya Tagna (632 ± 2 Ma) and Srednaya Zima intrusions (624 ± 5 Ma), as well as previously published garnet ages of the Belaya Zima complex (646 ± 6 Ma), allow us to constrain the timing and duration of episodes of alkaline ultramafic magmatism in Eastern Sayan province (619–651 Ma). Variations in the chemical compositions of rocks from three massifs indicate that the parental melts were separated from different magmatic chambers generated during the same episode of mantle melting. This study further highlights garnet U–Pb dating as a potentially robust, high-resolution geochronometer to constrain the evolution of the main pulse of alkaline ultramafic magmatism in the large magmatic provinces.

Build-up dynamics of different pulse types in a dispersion-managed Yb-doped fibre laser

We present a dispersion-managed mode-locked ytterbium fibre laser based on the nonlinear polarization evolution technique. Four single-pulse states could be generated by changing group delay dispersion values from anomalous (−0.0038 ps2) to normal (0.051 ps2) with a grating pair. In the normal dispersion regime, the pulse width was gradually decreased with the decrease of the net dispersion. In the anomalous dispersion region, the typical soliton was obtained, which time-bandwidth product could be calculated as 0.526. In addition, the dynamics of four states were also investigated by using the dispersive Fourier transformation technique. Different pulse evolution dynamics were observed from chaotic state to mode-locking.

All-Polarization-Maintaining Linear Cavity Fiber Lasers Mode-Locked by Nonlinear Polarization Evolution in Stretched Pulse Regime

Nonlinear polarization evolution (NPE) is among the most advanced techniques for obtaining ultrashort pulses with excellent optical performance. However, it is challenging to design environmentally stable NPE fiber oscillators using only polarization-maintaining (PM) fibers. Here, we use the same PM fiber and non-reciprocal phase shifter to design two different devices, which are capable of acting as effective NPE saturable absorbers (SAs) in two all-PM linear cavity fiber lasers. These two laser setups differ in the position of the non-reciprocal phase shifter, the presence of which is crucial for the proposed fiber lasers to reduce their mode-locking thresholds and achieve high repetition rates above 100 MHz. The mode-locking principle and pulse evolution in the laser cavity are investigated theoretically. The first all-PM fiber oscillator emits sub-200 fs stretched pulses with low peak powers. The second oscillator, with a simpler architecture, directly delivers stretched pulses with high peak powers, the spectral bandwidth greater than 30 nm, and the pulse duration less than 90 fs. To the best of our knowledge, 79 fs achieved in this design is the shortest pulse duration provided by PM fiber lasers using NPE mode-lockers.

Time Evolution of Plasmonic Features in Pentagonal Ag Clusters.

In the present work, we apply recently developed real-time descriptors to study the time evolution of plasmonic features of pentagonal Ag clusters. The method is based on the propagation of the time-dependent Schrödinger equation within a singly excited TDDFT ansatz. We use transition contribution maps (TCMs) and induced density to characterize the optical longitudinal and transverse response of such clusters, when interacting with pulses resonant with the low-energy (around 2-3 eV, A1) size-dependent or the high-energy (around 4 eV, E1) size-independent peak. TCMs plots on the analyzed clusters, Ag25+ and Ag43+ show off-diagonal peaks consistent with a plasmonic response when a longitudinal pulse resonant at A1 frequency is applied, and dominant diagonal spots, typical of a molecular transition, when a transverse E1 pulse is employed. Induced densities confirm this behavior, with a dipole-like charge distribution in the first case. The optical features show a time delay with respect to the evolution of the external pulse, consistent with those found in the literature for real-time TDDFT calculations on metal clusters.

The Lagrangian structure, the Euler equation, and second Newton’s law of ultrafast nonlinear optics

With a notable exception of space–time variable swap, pulse evolution equations of ultrafast optics are mathematically similar to the equations of quantum mechanics and beam dynamics. The Lagrangian structure of these equations is, however, much less intuitive. Here, we show that such a structure can be identified via a path-integral analysis of the pulse evolution equation, offering useful insights into the Lagrangian underpinning of ultrafast nonlinear optics. The Euler–Lagrange equation applied to the optical analog of the Lagrange function leads to a second-order differential equation that parallels in its structure second Newton’s law. Stationary-phase space–time paths found by solving such an equation reveal the hidden inner workings behind a vast class of field-waveform transformations in ultrafast optics, including the buildup of nonlinear phase, modulation instabilities, and soliton breather dynamics.

Ultra-Short Pulse-Train Generation of 30-GHz Repetition Rate Using Rational Harmonic Mode Locking and Nonlinear Polarization Rotation

A 30-GHz pulse-train is generated using the rational harmonic mode-locking technique, experimentally, using a Mach–Zehnder Lithium Niobate modulator. The width of the pulses is then reduced from 5.8-ps to 1.9-ps by incorporating nonlinear polarization rotation. This phenomenon arises due to the very high nonlinear behavior of the photonic crystal fiber (PCF) added to the ring laser cavity. Numerically solving the Generalized Nonlinear Schrödinger Equation provided insights into the pulse evolution behavior. The relative polarization angle and length of the PCF were varied to study their effects on the pulse-width.

Generation of Mid‐Infrared Noise‐Like Pulses from a Polarization‐Maintaining Fluoride Fiber Oscillator

Noise‐like pulses (NLPs) are becoming increasingly attractive for a variety of applications such as supercontinuum generation, materials processing, and low‐coherence spectral interferometry. Related research in the near‐infrared region is extensive, yet few studies have been reported in the mid‐infrared (MIR) region. Herein, a systematic investigation of MIR NLPs is made for the first time. An approach is presented by exploiting a polarization‐maintaining fluoride fiber in the mode‐locked oscillator to cause a polarization‐dependent delay between the orthogonal‐polarized components of intracavity circulating pulses, thus generating a series of ultrashort pulses which will eventually form a stable wave packet, namely, NLP. Numerical simulations based on the extended coupled nonlinear Schrödinger equations predict the generation of NLPs, and reveal key aspects of the pulse evolution. Experiments yield linearly polarized NLPs at 2.8 μm with a maximum average power of 498 mW and a spike width of 4.3 ps, corresponding to a pulse energy of 12 nJ. The experimental results are in good agreement with the simulation results. This work constitutes a major step toward the development of MIR ultrafast fiber lasers with NLPs output.

Accounting for 16S rRNA copy number prediction uncertainty and its implications in bacterial diversity analyses

16S rRNA gene copy number (16S GCN) varies among bacterial species and this variation introduces potential biases to microbial diversity analyses using 16S rRNA read counts. To correct the biases, methods have been developed to predict 16S GCN. A recent study suggests that the prediction uncertainty can be so great that copy number correction is not justified in practice. Here we develop RasperGade16S, a novel method and software to better model and capture the inherent uncertainty in 16S GCN prediction. RasperGade16S implements a maximum likelihood framework of pulsed evolution model and explicitly accounts for intraspecific GCN variation and heterogeneous GCN evolution rates among species. Using cross-validation, we show that our method provides robust confidence estimates for the GCN predictions and outperforms other methods in both precision and recall. We have predicted GCN for 592605 OTUs in the SILVA database and tested 113842 bacterial communities that represent an exhaustive and diverse list of engineered and natural environments. We found that the prediction uncertainty is small enough for 99% of the communities that 16S GCN correction should improve their compositional and functional profiles estimated using 16S rRNA reads. On the other hand, we found that GCN variation has limited impacts on beta-diversity analyses such as PCoA, NMDS, PERMANOVA and random-forest test.

Evolution of a Gaussian pulse in negative index Kerr medium about threshold intensity: A numerical simulation

Temporal evolution of a pico-sec Gaussian pulse is numerically simulated in a representative intensity dependent negative index Kerr medium about a threshold intensity to study the effect of Kerr non-linearity on a propagating pulse, using the non-linear Schroedinger equation solved by split step Fourier method. Results are obtained for both dispersive and non-dispersive cases, that show the pulse to bear characteristics of a fundamental soliton. Moreover, the speed of the soliton i.e., the group velocity may be controlled by tuning the intensity of the pulse around the threshold. Overall, the analysis indicates prospect of an intensity dependent non-linear transmission material with the provision to control transmission speed through intensity tuning.

Temporal and Spectral Evolution of Gamma-Ray Burst Broad Pulses: Identification of High-latitude Emission in the Prompt Emission

We perform a detailed analysis of broad pulses in bright gamma-ray bursts (GRBs) to understand the evolution of GRB broad pulses. Using the temporal and spectral properties, we test the high-latitude emission (HLE) scenario in the decaying phase of broad pulses. The HLE originates from the curvature effect of a relativistic spherical jet, where higher-latitude photons are delayed and softer than the observer’s line-of-sight emission. The signature of HLE has not yet been identified undisputedly during the prompt emission of GRBs. The HLE theory predicts a specific relation, ∝ , between the peak energy E p in ν F ν spectra and the spectral flux F ν measured at E p , . We search for evidence of this relation in 2157 GRBs detected by the Gamma-ray Burst Monitor on board the Fermi Gamma-ray Space Telescope from 2008 to 2017. After imposing unbiased selection criteria in order to minimize contamination in a signal by background and overlaps of pulses, we build a sample of 32 broad pulses in 32 GRBs. We perform a time-resolved spectral analysis on each of these 32 broad pulses and find that the evolution of 18 pulses (56%) is clearly consistent with the HLE relation. For the 18 broad pulses, the exponent δ in the relation of ∝ E p δ is distributed as a Gaussian function with a median and width of 1.99 and 0.34, respectively. This result provides a constraint on the emission radius of GRBs with the HLE signature.

Rotation of the polarization ellipse for broad-band and narrow-band optical pulses. Analytical solutions

In present days the evolution of broad-band laser pulses, propagating in various types of waveguides, has been of a great interest among the scientists. Currently, it is easy for phase-modulated femtosecond pulses the condition Δω≈ω0 to be obtained. It is known that nowadays it is possible also to reach the attosecond region where the spectral bandwidth of the pulse happens to be of order of the carrier frequency also. Light pulses who fulfil this initial condition are called broad-band. On the other hand, the non-fulfilling pulses are the narrow-band ones.In the present paper it is investigated the parametric interaction of two components of one optical pulse by using the Generalized System of Nonlinear Amplitude Equations (GSNAE). GSNAE was analytically solved. A difference in the period of oscillations of the energy exchange between the two components is found.

Spectral pulsations of evolving soliton molecules in an anomalous dispersion fiber laser

We investigate in detail the spectral pulsation of evolving soliton molecules in an anomalous dispersion fiber laser by utilizing the dispersive Fourier transform technique. The spectral pulsations of an evolving soliton molecule with different properties were achieved in our experiments, such as single-period and double-period pulsation. This type pulsation is characterized by the fact that the soliton molecules periodically experience oscillation in spectral profile and peak power due to the periodic vibration evolution of the internal pulses. However, the continuous weak energy exchange between the two solitons inside the soliton molecules results in an almost invariable pulse energy. In addition, analytical fitting models are given to further reveal the spectral pulsation phenomenon of the evolving soliton molecules. These experimental findings can shed some light on the dynamics of soliton molecules in fiber lasers.

Thermal and Chemical Evolution of an Archean Collision Zone: Insights from P–T–t History of Mafic Granulites from the Coorg Block, S. India

Abstract Knowledge of pressure–temperature–time (P–T–t) evolution of Archean high-grade (deep crustal) metamorphic rocks is important for deciphering the nature of Archean tectonic processes. However, exposures of such rocks are limited in the present rock record. Here, we study a suite of high-grade, mafic rocks that are present along a crustal-scale shear zone (called the Mercara Shear Zone) between two Archean terrains of India, the Coorg block and the Dharwar Craton. Given that the Mercara Shear Zone is dated to be Mesoarchean, these shear zone rocks are well suited to elucidate Archean orogenic processes. Petrological investigation shows that these mafic rocks are characterized by a granulitic assemblage of orthopyroxene, clinopyroxene, plagioclase, quartz and amphibole ± garnet, and with accessory phases such as apatite, ilmenite, magnetite and rutile in some cases. We distinguish the investigated rocks into low-Mg and high-Mg varieties based on their whole-rock composition as well as their mode of occurrence in the field and mineral chemistry. This difference in the bulk composition led to different reaction histories—for example, the low-Mg mafic granulites underwent partial melting while high-Mg granulites were less fertile. Combining these observations with the results of geothermobarometry, phase equilibria modeling, geochronology (U–Pb in zircon and Lu–Hf in garnet ) and diffusion modeling, we have reconstructed a multi-stage P–T–t history for these rocks. The first phase (Stage 1) is represented by granulite-grade metamorphism at ~750–900°C and 8–13 kbar during ~3100 Ma (with uncertainties permitting a timing as recent as ~2700 Ma), after which they resided at T <500°C, likely at lower crustal levels (Stage 2). Subsequently, these rocks were reheated to a T of 700–750°C at 7–10 kbar at ~2400 Ma (Stage 3) and then again cooled down to ~500–600°C at 6–8 kbar (Stage 4). Application of diffusion chronometry shows that (1) the cooling rates of these granulites at high temperatures (>600°C) varied in the range of 25–50°C/Ma, and (2) the rocks resided for a long duration (~500 million years) at the Stage 2 metamorphic conditions, i.e. at T <500°C. We infer that such a protracted, high-T metamorphic history involving at least two heating pulses, and the relatively slow cooling rates on the order of 10’s °C/Ma are consistent with the operation of peel-back styled orogenesis (an embryonic form of plate tectonics) on an early hotter Earth (Mesoarchean to Paleoproterozoic). Moreover, the controls of bulk rock compositions on reaction histories provide a mechanism for intracrustal differentiation and generating Mg-rich, refractory material that may have eventually formed the lower continental crust over a protracted and pulsed thermal evolution spanning several hundred million years.

Ultrashort X-ray Free Electron Laser Pulse Manipulation by Optical Matrix

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems.

Dispersion Managed Mode-Locking in All-Fiber Polarization-Maintaining Nd-Doped Laser at 920 nm

We present a comprehensive study of dispersion managed ultrashort-pulse generation in Nd-doped polarization maintaining all-fiber laser at a 920 nm wavelength. We implement a linear laser scheme with a chirped fiber Bragg grating (CFBG) serving as a semitransparent mirror and semiconductor saturable absorber mirror (SESAM) as a mode-locker and as a second non-transparent mirror. Complete 1064 nm emission filtering is ensured by 920/1064 wavelength division multiplexer. The dispersion compensation by CFBG was sufficient to reach anomalous net dispersion in the shortest laser scheme allowing us to investigate mode-locking regimes in the −0.05 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ÷ 0.24 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> net dispersion range by varying the length of the passive fiber. With this approach we demonstrate high order harmonic mode-locking at dispersion closer to zero and large energy span near-parabolic shape single pulse operation in anomalous dispersion regime. The investigation is supported by numerical simulations used to optimize the laser resonator design and to investigate intracavity pulse evolution.

Nanosized indium selenide saturable absorber for multiple solitons operation in Er3+-doped fiber laser.

With the advances in the field of ultrafast photonics occurring so fast, the demand for optical modulation devices with high performance and soliton lasers which can realize the evolution of multiple soliton pulses is gradually increasing. Nevertheless, saturable absorbers (SAs) with appropriate parameters and pulsed fiber lasers which can output abundant mode-locking states still need to be further explored. Due to the special band gap energy values of few-layer indium selenide (InSe) nanosheets, we have prepared a SA based on InSe on a microfiber by optical deposition. In addition, we demonstrate that our prepared SA possesses a modulation depth and saturable absorption intensity about 6.87% and 15.83 MW/cm2, respectively. Then, multiple soliton states are obtained by dispersion management techniques, including regular solitons, and second-order harmonic mode-locking solitons. Meanwhile, we have obtained multi-pulse bound state solitons. We also provide theoretical basis for the existence of these solitons. The results of the experiment show that the InSe has the potential to be an excellent optical modulator because of its excellent saturable absorption properties. This work also is important for improving the understanding and knowledge of InSe and the output performance of fiber lasers.