Dependence Of Bandwidth Research Articles

Wavelength Dependence of Modal Bandwidth of Multimode Fibers for High Data Rate Transmission and Its Implications

Vertical-cavity surface-emitting laser (VCSEL)-based transmission over multimode fiber (MMF) has achieved data rates of 100G per lane and is progressing towards 200G per lane. Recently, high-data-rate MMFs derived from OM3 and OM4 have been proposed. These fibers exhibit higher effective modal bandwidths at 910 nm, leading to a different wavelength dependence compared to conventional OM3 and OM4 MMFs. Understanding the wavelength dependence of these fibers is crucial to address their utilization in a broader range of applications. Through Monte Carlo simulations, we have obtained the low-end boundary of the effective modal bandwidths (EMBs) for these fibers, revealing capability improvements over the existing OM3 and OM4. The high-data-rate OM4 performs the same as or better than OM5 from 840 nm to 920 nm, while also showing a high bandwidth for the 850–870 nm wavelength window, favoring VCSELs with center wavelengths shifted toward 860 nm. We also obtained the link bandwidth, which includes both modal bandwidth and chromatic dispersion contributions, and the transmission reaches for various types of transceivers. We find that for both high-data-rate OM3 and high-data-rate OM4, the link bandwidth stays above the value at 850 nm until around 910 nm, delivering a similar transmission performance from 850 to 910 nm without declining towards longer wavelengths, unlike the standard OM3 and OM4. This characteristic favors a wider range of wavelength choices for VCSELs and enables optimal deployments for various applications.

Window size dependence of gain and bandwidth in avalanche photodiodes with multiple multiplication layers under near Geiger-mode operation

We consider avalanche photodiodes (APDs) functioning under near Geiger-mode operation for extremely weak light (single or several photons) detection, such as in LiDAR receivers. To meet such demands, APDs which simultaneously have a large active window size, moderate bandwidth (∼GHz), and high internal gain (responsivity), are highly desired. However, it is difficult to design APDs capable of meeting the afore-mentioned performance requirements due to the intrinsic limitations of the gain-bandwidth product (GBP). In this work, we demonstrate that the GBP bottleneck in the APDs can be overcome by using multiple (3) In0.52Al0.48As based multiplication (M-) layers with a thick In0.53Ga0.47As absorber (2 µm). Moreover, the characteristic invariant 3-dB bandwidth in our APDs, from low to an extremely high operation gain, becomes more pronounced with an increase of its active window diameter (40 to 200 µm). This characteristic makes it very attractive for collecting weak light in free space as is required for LIDAR receiver applications. Comparison shows that the 200 µm APD exhibits a higher 0.9 Vbr responsivity (15 vs. 7 A/W), larger maximum gain (460 vs. 110), and higher GBP (468 vs. 131 GHz) than does the 40 µm reference sample and can sustain a constant 3-dB bandwidth (1.4 GHz) over a wide range of operation gains (10 to 460). The dependence of the APD performance on the window size can be attributed to the influence of the surface states on the edge of the etched mesa. Here, we further demonstrate a backside-illuminated structure with a flip-chip bonding package which minimizes this phenomenon in small APDs ensuring high-speed performance. Compared with the top-illuminated reference samples, the flip-chip bonding packaged device shows a further enhancement of the responsivity (10.7 vs. 7 A/W), 3-dB bandwidth (4.1 vs. 3.9 GHz), and saturation current (4.25 vs. 3.6 mA). The excellent static and dynamic performance of our flip-chip APD in turn leads to an unprecedented high velocity sensitivity (5 µm/sec) and superior quality 4-D FMCW LiDAR images compared to that obtainable with p-i-n-based or top-illuminated reference devices with the same small active window size (40 µm).

THz-TDS with gigahertz Yb-based dual-comb lasers: noise analysis and mitigation strategies

We investigate terahertz time-domain spectroscopy using a low-noise dual-frequency-comb laser based on a single spatially multiplexed laser cavity. The laser cavity includes a reflective biprism, which enables generation of a pair of modelocked output pulse trains with slightly different repetition rates and highly correlated noise characteristics. These two pulse trains are used to generate the THz waves and detect them by equivalent time sampling. The laser is based on Yb:CALGO, operates at a nominal repetition rate of 1.18 GHz, and produces 110 mW per comb with 77 fs pulses around 1057 nm. We perform THz measurements with Fe-doped photoconductive antennas, operating these devices with gigahertz 1 µm lasers for the first time, to our knowledge, and obtain THz signal currents approximately as strong as those from reference measurements at 1.55 µm and 80 MHz. We investigate the influence of the laser’s timing noise properties on THz measurements, showing that the laser’s timing jitter is quantitatively explained by power-dependent shifts in center wavelength. We demonstrate reduction in noise by simple stabilization of the pump power and show up to 20 dB suppression in noise by the combination of shared pumping and shared cavity architecture. The laser’s ultra-low-noise properties enable averaging of the THz waveform for repetition rate differences from 1 kHz to 22 kHz, resulting in a dynamic range of 55 dB when operating at 1 kHz and averaging for 2 s. We show that the obtained dynamic range is competitive and can be well explained by accounting for the measured optical delay range, integration time, as well as the measurement bandwidth dependence of the noise from transimpedance amplification. These results will help enable a new approach to high-resolution THz-TDS enabled by low-noise gigahertz dual-comb lasers.

Validating the sub-burst slope law: a comprehensive multisource spectro-temporal analysis of repeating fast radio bursts

ABSTRACT We conduct a comprehensive spectro-temporal analysis of repeating fast radio bursts (FRBs) utilizing nine distinct sources, the largest sample to date. Our data set includes 175 sub-bursts and 31 multicomponent bursts from 11 data sets, with centre frequencies ranging from 149 to 7144 MHz and durations spanning from 73 µs to 13 ms. Our findings are consistent with the predictions of the triggered relativistic dynamical model (TRDM) of FRB emission. We affirm the predicted quadratic relationship between sub-burst slope and central frequency, as well as a linear dependence of the sub-burst bandwidth on central frequency that is consistent with mildly relativistic Doppler broadening of narrow-band emission. Most importantly, we confirm the sub-burst slope law, a predicted inverse relationship between sub-burst slope and duration, to hold consistently across different sources. Remarkably, we also discover that the drift rates of multicomponent bursts follow the same law as the sub-burst slopes, an unexplained result that warrants further investigation. These findings not only support the TRDM as a viable framework for explaining several aspects of FRB emission, but also provide new insights into the complex spectro-temporal properties of FRBs.

Improvement of response bandwidth and sensitivity of Rydberg receiver using multi-channel excitations

We investigate the response bandwidth of a superheterodyne Rydberg receiver at a room-temperature vapor cell, and present an architecture of multi-channel lasers excitation to increase the response bandwidth and keep sensitivity, simultaneously. Two microwave fields, denoted as a local oscillator (LO) E_{text{LO}} and a signal field E_{text{SIG}}, couple two Rydberg states transition of |52D_{5/2}rangle to |53P_{3/2}rangle . In the presence of the LO field, the frequency difference between two fields can be read out as an intermediate frequency (IF) signal using Rydberg electromagnetically induced transparency (EIT) spectroscopy. The bandwidth of the Rydberg receiver is obtained by measuring the output power of IF signal versus the frequency difference between two fields. The bandwidth dependence on the Rabi frequency of excitation lasers is presented, which shows the bandwidth decrease with the probe Rabi frequency, while it is quadratic dependence on the coupling Rabi frequency. Meanwhile, we investigate the effect of probe laser waist on the bandwidth, showing that the bandwidth is inversely proportional to the laser waist. We achieve a maximum response bandwidth of the receiver about 6.8 MHz. Finally, we design an architecture of multi-channel lasers excitation for increasing the response and keeping the sensitivity, simultaneously. Our work has the potential to extend the applications of Rydberg atoms in communications.

The influence of bandwidth on the energetics of intermediate to deep water laboratory breaking waves

An experimental investigation of two-dimensional dispersively focused laboratory breaking waves is presented. We describe the bandwidth effect on breaking wave energetics, including spectral energy evolution, characteristic group velocity, energy dissipation and its rate, and breaking strength parameter, $b$ . To evaluate the role of bandwidth, three definitions of wave group steepness are adopted where $S_s$ and $S_n$ are bandwidth-dependent and $S_p$ remains constant when bandwidth is changed. Our data show two regimes of spectral energy evolution in breaking wave groups, with both regimes bandwidth-dependent: energy dissipation and gain occur at $f > 0.95f_p$ ( $f_p$ is the peak frequency) and $f < 0.95f_p$ , respectively. The characteristic group velocity, which is used in energy dissipation calculations, increases by up to 7 % after wave breaking, being larger for higher bandwidth breaking waves. An unambiguous bandwidth dependence is found between $S_p$ and both the fractional and absolute wave energy dissipation. Wave groups of larger bandwidth break at a lower value of $S_p$ and consequently lose relatively more energy. The energy dissipation rate depends on the breaking duration which itself is bandwidth dependent. Consequently, no clear bandwidth effect is observed in energy dissipation rate when compared with either $S_p$ or $S_s$ . However, there is a systematic bandwidth dependence in the variation of $b$ when parameterised in terms of $S_p$ , with their relationship becoming increasingly nonlinear as bandwidth increases. When parameterised with $S_s$ , $b$ shows a markedly reduced bandwidth dependence. Finally, the numerical breaking onset and relationship between $b$ and $S_s$ in the numerical study of Derakhti & Kirby (J. Fluid Mech., vol. 790, 2016, pp. 553–581) is validated experimentally.

Theoretical study of small signal modulation behavior of Fabry-Perot germanium-on-silicon lasers

This work investigated the modulation responses of Fabry–Perot Ge-on-Si lasers by modeling and simulations. The 3 dB bandwidth dependence on the structure parameters such as poly-Si cladding thickness, Ge cavity width and thickness, and minority carrier lifetime were studied. A 3 dB bandwidth of 33.94 GHz at a biasing current of 270.5 mA is predicted after Ge laser structure optimization with a defect limited carrier lifetime of 1 ns. The eye diagrams simulated show a stable eye-opening window at 20 Gb·s−1 NRZ. The improvement to 10 ns minority carrier lifetime would reduce the threshold current to 6.85 mA, and increase the 3 dB bandwidth to 36.89 GHz.

Widely Tunable Femtosecond Sources with Continuously Tailorable Bandwidth Enabled by Self‐Phase Modulation

AbstractGenerating ultrafast pulses with better spectrotemporal control is crucial for optimizing and characterizing nonlinear light–matter responses, yet it is limited by the gain bandwidth of laser media or the phase‐matching geometry of nonlinear processes. This work proposes a simple approach to independently manage a femtosecond source's spectral location and bandwidth. Self‐phase‐modulation‐enabled spectral broadening is first analyzed, which is potentially energy‐scalable using hollow‐core capillaries or multipass cells. It is demonstrated that the outmost lobes in the broadened spectrum show different dependencies on the initial pulse energy and duration. A simple yet effective toy model is introduced that successfully predicts broadband spectral tuning, and the impact of other nonlinear effects, dispersion, and input pulse asymmetry on the experimental scenario is also discussed. Thus a fiber‐based versatile source is demonstrated, which is compressible down to its transform‐limit duration, as short as 12.2 fs centered at 920 nm. In addition, bandwidth‐dependent third‐harmonic generation spectroscopy is performed from a dielectric metasurface with an optimized nonlinear response, and the dependency of laser bandwidth and pulse duration is investigated on the signal‐to‐background ratio of two‐photon images. It is believed that this demonstration will advance the investigation of bandwidth‐dependent nonlinear spectroscopy and microscopy.

Quality assurance and temporal stability of a 1.5 T MRI scanner for MR-guided Photon and Particle Therapy

PurposeTo describe performance measurements, adaptations and time stability over 20 months of a diagnostic MR scanner for integration into MR-guided photon and particle radiotherapy. Material and methodsFor realization of MR-guided photon and particle therapy (MRgRT/MRgPT), a 1.5 T MR scanner was installed at the Heidelberg Ion Beam Therapy Center. To integrate MRI into the treatment process, a flat tabletop and dedicated coil holders for flex coils were used, which prevent deformation of the patient external contour and allow for the use of immobilization tools for reproducible positioning. The signal-to-noise ratio (SNR) was compared for the diagnostic and therapy-specific setup using the flat couch top and flexible coils for the a) head & neck and b) abdominal region as well as for different bandwidths and clinical pulse sequences. Additionally, a quality assurance (QA) protocol with monthly measurements of the ACR phantom and measurement of geometric distortions for a large field-of-view (FOV) was implemented to assess the imaging quality parameters of the device over the course of 20 months. ResultsThe SNR measurements showed a decreased SNR for the RT-specific as compared to the diagnostic setup of (a) 26% to 34% and (b) 11% to 33%. No significant bandwidth dependency for this ratio was found. The longitudinal assessment of the image quality parameters with the ACR and distortion phantom confirmed the long-term stability of the MRI device. ConclusionA diagnostic MRI was commissioned for use in MR-guided particle therapy. Using a radiotherapy specific setup, a high geometric accuracy and signal homogeneity was obtained after some adaptions and the measured parameters were shown to be stable over a period of 20 months.

Different spin relaxation properties observed in linearly and circularly polarized laser induced terahertz emission from a Bi/Co bilayer

Recently, helicity-dependent photocurrent was reported in Bi single thin fi lms. It is proposed that the origin of this photocurrent is the combination of photo-spin conversion and spin-charge conversion effects in Bi and efficient spin conversion in Bi is expected. In this study, we measured two types of terahertz (THz) emissions from Bi/Co bilayer films induced by spin current generation using laser-induced demagnetization of the Co layer and photo-spin conversion effect in the Bi layer to investigate the spin current induced by the two mechanisms simultaneously. We clearly observed diff erent Bi thickness dependence of peak intensity and that of bandwidth for THz spin current in two experiments, i.e., spin current induced by demagnetization of Co and that by photo-spin conversion in Bi. The different Bi thickness dependence of spin current intensity and bandwidth in two experiments is caused by different spin relaxation properties of optically excited spin currents in Bi layers.

Incorporating Meta‐Atom Interactions in Rapid Optimization of Large‐Scale Disordered Metasurfaces Based on Deep Interactive Learning

Surface symmetry breaking and disorder have been recently explored to overcome operation bandwidth, unwanted diffraction, and polarization dependence issues in the conventional metasurface designs thanks to their increasing degrees of design freedom. However, efficient full‐wave simulation and optimization of electrically large electromagnetic structures have been a longstanding problem. Herein, an interactive learning approach is developed to build new meta‐atom datasets which include the effect of mutual coupling. A deep learning‐based model is developed to extract features of incident/reflection waves and their neighboring interaction responses from a limited number of known meta‐atoms. Finally, the deep neural network is incorporated with optimization algorithms to design, as an example, large‐scale metasurfaces for beam manipulation and wideband scattering reduction. The results demonstrate that the proposed architecture can be successfully applied to rapidly design aperture‐efficient metasurfaces or metalenses at large scales of over tens of thousands of meta‐atoms.

Bandwidth Dependence of the Propagation Channel in Circular Metallic BAN Environments

In this paper, the bandwidth dependence of the propagation channel for Body Area Networks (BANs) in circular metallic environments is addressed and models are proposed to evaluate the appropriate short-term fading margins that should be considered as a function of the system bandwidth. The deployment of BANs in metallic indoor environments, such as ships, factories, warehouses and other similar environments, involves additional challenges compared to other indoor environments due to the specific propagation effects in this type of environments (i.e., with strong reflections). No studies of this kind and for this type of environment can be found in literature, giving the motivation for this work. Bandwidth dependent values of delay spread are also presented and discussed. It is observed that for a system bandwidth up to 100 MHz the fading depth is composed of three main stages, with the transitions between these stages being associated with the system ability to discriminate arriving rays at the receiver. Average values of fading depth are 16.4, 13.2 and 11.0 dB for stages 1, 2 and 3, respectively, the difference between consecutive stages ranging between 2.2 to 3.2 dB. For a system bandwidth larger than 100 MHz, the fading depth decreases with an increasing system bandwidth, with an average decay rate close to 3 dB per 100 MHz bandwidth, being about 2 dB for system bandwidths above 400 MHz.

Expansion Dynamic and Characterization of Stagnation Layer in Laterally Colliding Plasmas: Dependence of Observation Bandwidth and Plasma Plume Separation

The colliding laser-produced plasma (CLPP) has a wide range of applications in various contexts, that might start with astrophysical applications or pulsed laser deposition or Laser-Induced Breakdown Spectroscopy (LIBS), which is a powerful analytical technique for elemental analysis and material identification.In CLPP experiments, the stagnation layer might form at the interface region when two dense laser-induced plasmas collide, and the degree of stagnation can be diagnosed by the collisionality parameter that is used to determine what kind of interaction will take place, i.e., soft or hard stagnation.Our experimental work presents the results of the temporal, spatial and semi-spectrally imaging of colliding plasmas of aluminium and silicon targets. The analysis is focused on describing the velocity of the expanding plasma front for the interaction zone. The aim of the work presented here is to further advance and study colliding plasma techniques, as well as other methods to realize and control species density and expansion, with a view to a deep understanding of these complex mechanisms and optimising emission in the visible wavelength range.All investigation sequences were based on a similar experimental setup, where two different focusing lenses were used with an effective focal length (EFL) of approx. 100mm or 125mm to achieve seed separation around 1.66mm or 2.16mm, respectively. Time-resolved emission imaging was employed to track the stagnation layer‛s size and shape, which might act as a signature of hard versus soft stagnation.The study provides a considerable amount of detailed data related to the expansion velocity of the interaction zone which extends the understanding of the behaviour of particular species within colliding laser-produced plasmas.

Statistical Characteristics of the Local Proton Cyclotron Band Emissions Observed by the CSES

AbstractWe present observations on the local proton cyclotron band emissions (PCBEs), which is one type of hiss wave in the upper ionosphere, recorded by the China Seismo‐Electromagnetic Satellite (CSES). The PCBEs are characterized by narrow‐band electromagnetic emissions along the local proton cyclotron frequency (), exhibiting a sharp cutoff effect. The lower cutoff frequency () is closely along the local , decreasing with magnetic latitude, while the upper cutoff frequency () is diffuse and deviates from the local . We developed an algorithm to automatically extract PCBEs from CSES's massive electromagnetic data and statistically examined their occurrence and bandwidth's dependence on location and season. The global morphology of PCBEs in 2019 shows that they primarily occur in the mid‐high magnetic latitude (approximately 20°–55°) dayside ionosphere, with the maximum occurrence happening around the South Atlantic Anomaly region. Their bandwidth shows a decreasing tendency with magnetic latitude and strong seasonal dependence, with a wider bandwidth in local winter and a narrower one in local summer. The ratio of and also shows a seasonal dependence, with greater values in local summer and smaller values in local winter. This characteristic of is similar to that of the H+‐He+ cutoff frequency (). This study provides statistical characteristics of occurrence and the cutoff features of PCBEs based on the CSES operating in the upper ionosphere.

Ultra-compact lithium niobate microcavity electro-optic modulator beyond 110 GHz

A lithium-niobate-on-insulator (LNOI) electro-optic (EO) modulator based on a 2 × 2 FP-cavity was designed and realized with an ultra-compact footprint and an ultra-high bandwidth. A comprehensive analysis on the present LNOI FP-cavity modulator was conducted to reveal the dependence of modulation bandwidth and modulation efficiency on the cavity Q-factor and the operation wavelength detuning to the resonance. In particular, the 2 × 2 FP cavity was designed to achieve an optimal Q factor by reducing the reflectivity of reflectors and the cavity length, thus reducing the photon lifetime in the cavity . An ultra-short effective cavity length of only∼ 50 µm was achieved for the designed LNOI FP-cavity modulator, with itsfootprint being as compact as ∼ 4 × 500 µm2. It was demonstrated theoretically that the modulation bandwidth could be improved significantly to be over 200 GHz by utilizing the peaking enhancement effect. The fabricated device exhibited an excess loss of ∼ 1 dB and an extinction ratio of ∼ 20 dB in experiments, while the measured 3-dB bandwidth was higher than 110 GHz (beyond the maximal range of the facilities in experiments). Up till now, to our best knowledge, this has been the first LNOI microcavity modulator with a bandwidth higher than 110 GHz. Finally, high-quality eye-diagrams of 100 Gbps on-off keying (OOK) and 140 Gbps 4-pulse amplitude modulation (PAM4) signals were demonstrated experimentally, and the energy consumption for the OOK signals was as low as 4.5 fJ/bit.

Delivery of Gas onto the Circumplanetary Disk of Giant Planets: Planetary-mass Dependence of the Source Region of Accreting Gas and Mass Accretion Rate

Gas accretion onto the circumplanetary disks and the source region of accreting gas are important to reveal dust accretion that leads to satellite formation around giant planets. We performed local three-dimensional high-resolution hydrodynamic simulations of an isothermal and inviscid gas flow around a planet to investigate the planetary-mass dependence of the gas accretion bandwidth and gas accretion rate onto circumplanetary disks. We examined cases with various planetary masses corresponding to M p = 0.05–1M Jup at 5.2 au, where M Jup is the current Jovian mass. We found that the radial width of the gas accretion band is proportional to for the low-mass regime with M p ≲ 0.2M Jup while it is proportional to M p for the high-mass regime with M p ≳ 0.2M Jup. We found that the ratio of the mass accretion rate onto the circumplanetary disk to that into the Hill sphere is about 0.4 regardless of the planetary mass for the cases we examined. Combining our results with the gap model obtained from global hydrodynamic simulations, we derive a semi-analytical formula of mass accretion rate onto circumplanetary disks. We found that the mass dependence of our three-dimensional accretion rates is the same as the previously obtained two-dimensional case, although the qualitative behavior of accretion flow onto the circumplanetary disk is quite different between the two cases.

Closed form solutions for the strain localization problem in a softening circular bar in pure torsion with the continuum damage and the embedded discontinuity models

The boundary value problems and closed form solutions for the strain localization in a softening bar under pure torsion with the continuum damage and the embedded discontinuity formulations are developed. In this formulation, quasi-brittle materials such as concrete or mortar are considered. The boundary value problem is developed from a variational formulation and the corresponding Euler-Lagrange differential equation. These formulations include not only the continuum damage model, in which the twist angle jump and the angular strain concentration are smeared into the volume of the bar, but also the embedded discontinuity model, in which the twist angle jump and the angular strain localization are lumped into a zero thickness localization zone. The non-linear behaviour of the materials is described by a continuous constitutive model for the continuum damage model and by a discrete constitutive model for the embedded discontinuity model; both constitutive relationships include linear or exponential softening. Solutions to overcome the problem of crack bandwidth dependency when modelling strain localization with continuous models are developed, these solutions are based on a rational analysis of the kinematics of the strain model and on the fracture energy per unit area. To validate the developed closed form solutions for the strain localization problem in a softening bar under torsion, three examples of concrete cylindrical specimens under torsion are presented. The relationship between the total area under the twisting moment-twist angle curves and the fracture energy of the material guarantees the correctness of the developed closed form solutions.

Mid-IR quantum dot cascade VCSEL: feasibility study and feature extraction.

Quantum cascade lasers with quantum dot (QD) active regions have been developed to overcome the drawbacks of quantum-well-based cascade lasers. Low threshold current and enhanced bandwidth characteristics of QD lasers can be combined with promising energy-efficient features of vertical cavity surface emitting lasers (VCSELs) through introducing the novel, to the best of our knowledge, concept of a QD cascade VCSEL (QDC-VCSEL). Design steps and predicted features of a QDC-VCSEL operating at 4.5 µm wavelength are discussed in this paper, where the cavity and active region are optimized for TE mode using a high contrast grating design. Laser characteristics are investigated by developing rate equations for the cascade scheme. Threshold and L-I characteristics are obtained at different temperatures. Also, the dependency of threshold current, slope efficiency, and modulation bandwidth on design parameters, mainly the carrier tunneling time, is studied. Results exhibit output peak powers of ∼2 and ∼0.5mW at 150 and 273 K, respectively. In addition, threshold current increment and modulation bandwidth reduction are observed with the increase in tunneling time.

Frequency Band Characteristics of a Triboelectric Nanogenerator and Ultra-Wide-Band Vibrational Energy Harvesting.

Micromechanical vibration, as one of the most prevalent forms of energy in an ambient environment, has surpassing application potentials as the power source for self-powered electronics. A triboelectric nanogenerator (TENG) can effectively convert vibrational energy to electricity, which has the unique benefit of a wide-band over a traditional vibration energy harvester due to the contact electrification mechanism. Herein, the frequency band characteristics of vibrational TENG (V-TENG) were systematically elaborated. The mechanical model of V-TENG was established to explore its working mechanism for wide-band vibrational energy harvesting. By simulation analysis and experimental validation, the bandwidth dependence of V-TENG on acceleration magnitude, proof mass, stiffness, and gap distance was investigated in detail. With optimized structural parameters, an ultra-wide-band vibration energy harvester (UVEH) was developed by a tandem spring-mass structure. Within the ultra-wide-band range from 3 to 45 Hz, the UVEH can invariably illuminate 36 serial light-emitting diodes (LEDs) and charge a 33 μF capacitor to 1.5 V within 35 s. This work has quantitatively studied frequency band characteristics of V-TENG and provided a promising strategy for wide-band vibrational energy harvesting from a machine, bridge, water wave, and human motion.

Closed form solutions for the strain localization problem in a softening bar under tension with the continuum damage and the embedded discontinuity kinematics

The boundary value problems and closed form solutions for the strain localization in a softening bar with the continuum damage and the embedded discontinuity formulations are developed. The boundary value problem is developed from a variational formulation and the corresponding Euler-Lagrange differential equation. These formulations include not only the classical continuum damage model, in which the displacement jump and the strain concentration are smeared into the bar length, but also the embedded discontinuity model, in which the displacement jump and the strain concentration are lumped into a zero thickness localization zone. For the classical continuum damage model, the non-linear behaviour of the materials is described by a continuum constitutive model and for the embedded discontinuity model by a discrete constitutive model; both constitutive relationships may consider linear or exponential softening. Solutions to overcome the problem of crack bandwidth dependency when modelling strain localization with continuum models are developed. These solutions are based on a rational analysis of the kinematics of the continuum damage model and on the fracture energy per unit area. To validate the developed closed form solutions for the strain localization problem in a softening bar, two examples of cylindrical specimens of concrete under tension are presented. The relationship between the total area under the load-displacement curves and the fracture energy of the material guarantees the correctness of the developed closed form solutions.