Frequency-dependent Time Delay Research Articles

Time-delay fourier transform spectrometer for high-speed spectral measurement

In the field of optics, there exist numerous chaotic processes like dissipative soliton dynamics, random laser generation, and laser scattering. It's very challenging to accurately capture the dynamics of these stochastic processes from the wavelength perspective with traditional spectrometers due to their slow signal integration speeds. Here, we propose a new approach, named time-delay Fourier transform spectrometer (TDFTS), to characterize the spectra of laser pulses with durations ranging from fs to ns with high speeds. Based on a fiber array with different lengths to impose frequency-dependent time delay, TDFTS efficiently maps the spectral distribution of light pulses to the temporal domain, and the spectrum can thus be detected with a photodiode and an oscilloscope. In experimental operation, the TDFTS provides spectral acquisition speeds up to 56 MHz frame rates and a bandwidth of tens of nanometers, while keeping comparable fidelity to traditional grating-scan spectrometers. While its spectral resolution of the current configuration is ∼0.1 nm, it can be further improved to 0.001 nm through optimizing the system. Based on its high speed, high spectral resolution, broad-bandwidth coverage, and compact configuration, TDFTS can be used to monitor nanosecond-scale spectral dynamics of non-repetitive optical processes.

Electron vortex generations in photoionization of hydrogen atoms by circularly-polarized chirped attosecond pulses

By numerically solving the time-dependent Schrödinger equation and employing the analytical perturbative model, we investigated the chirp-induced electron vortex in the photoionization of hydrogen atoms by a pair of counter-rotating circularly polarized chirped attosecond extremely ultraviolet pulses. We demonstrated that single-photon ionization of hydrogen atoms generates photoelectron momentum distributions (PMDs) with distinct helical vortex structures either with or without a time delay between two counter-rotating circularly polarized laser pulses. These structures are highly sensitive to both the time delay between the pulses and their chirp parameters. Our analytical model reveals that the splitting of vortex spirals is caused by the sign changing of the chirp-induced frequency-dependent time delay. We showed that to obtain the counterpart of the PMD under a pair of counter-rotating circularly polarized chirped pulses, both chirp parameters and ordering of pulses need to be reversed.

Accelerating Dedispersion Using Many-core Architectures

Astrophysical radio signals are excellent probes of extreme physical processes that emit them. However, to reach Earth, electromagnetic radiation passes through the ionized interstellar medium, introducing a frequency-dependent time delay (dispersion) to the emitted signal. Removing dispersion enables searches for transient signals like fast radio bursts or repeating signals from isolated pulsars or those in orbit around other compact objects. The sheer volume and high resolution of data that next-generation radio telescopes will produce require high-performance computing solutions and algorithms to be used in time-domain data-processing pipelines to extract scientifically valuable results in real time. This paper presents a state-of-the-art implementation of brute force incoherent dedispersion on NVIDIA graphics-processing units and on Intel and AMD central-processing units. We show that our implementation is 4× faster (8-bit 8192 channels input) than other available solutions, and we demonstrate, using 11 existing telescopes, that our implementation is at least 20× faster than real time. This work is part of the AstroAccelerate package.

Coherenceogram for leak detection in water pipes

A widely used technique for locating leaks in buried water distribution pipes is the cross-correlation between two measured acoustic signals at either side of a leak. The technique is not always effective in identifying leaks with high certainty due to the dispersion of the hydro-acoustic waves, unknown frequency characteristics of the leak signal and the potential presence of strong ambient noise. In this paper, a new method termed “coherenceogram” has been proposed for leak detection in water pipes. The frequency-dependent time delay of the leak signal at two measurement stations is estimated based on the principle that the coherence of the two signals will maximize when they are synchronized to contain the same segment of the leak signal. The effect of temporal windowing is investigated, along with the removal of uncertainty, to enhance the efficacy of the coherenceogram for leak detection. Field validations were then carried out on a water pipe (a part of a water distribution system in a busy city area) and a trunk main. The results of the field experiments in comparison with other methods (cross correlations and cross time-frequency spectrum) illustrate that: 1) the coherenceogram does not need any signal filtering and is easy to implement; 2) it can guide the selection of the signal filter for cross-correlation techniques; 3) it accommodates the frequency-dependent characteristics of the leak signals and can be also used in many other fields for time-delay estimation, such as processing acoustic waves and seismic waves which possess strong wave dispersion.

Excitation of unidirectional SH wave within a frequency range of 50 kHz by piezoelectric transducers without frequency-dependent time delay

Unidirectional generation of a pure guided wave mode is of practical importance in structural health monitoring (SHM). Currently, unidirectional propagation guided waves can only be generated by using transducer array in a phased array form, which is limited within a very narrow frequency range. If a variable-wavelength unidirectional wave source is required, both the transducer spacing and time delay usually need to be changed with frequency, which is against the permanent arrangement demand of transducers in SHM. In this work, inspired by the unique features of bidirectional SH0 wave (the fundamental shear horizontal mode) piezoelectric face-shear and thickness-shear transducers, a new method was proposed for generating unidirectional SH0 wave. Two types of transducer configurations (double-side and single-side) were designed to unidirectionally generate SH0 wave without frequency-dependent time delay. Both finite element simulations and experiments were conducted to validate the unidirectional features of the proposed double-side and single-side transducer configurations. Results shows that the double-side transducer configuration is capable of generating unidirectional propagation SH0 wave at the frequency range from 100 kHz to 150 kHz, while the corresponding working frequency range for the single-side one is from 100 kHz to 140 kHz. The proposed method provides a cheap way for generation of the unidirectional SH0 wave within a certain frequency range without adjusting the relative transducer spacing and the time delay with frequency, so it will have great potential applications in SHM.

A stochastic propagation model to the energy dependent rapid temporal behaviour of Cygnus X-1 as observed by AstroSat in the hard state

Abstract We report the results from analysis of six observations of Cygnus X-1 by Large Area X-ray Proportional Counter (LAXPC) and Soft X-ray Telescope (SXT) onboard AstroSat, when the source was in the hard spectral state as revealed by the broad-band spectra. The spectra obtained from all the observations can be described by a single-temperature Comptonizing region with disc and reflection components. The event mode data from LAXPC provides unprecedented energy dependent fractional root mean square (rms) and time-lag at different frequencies which we fit with empirical functions. We invoke a fluctuation propagation model for a simple geometry of a truncated disc with a hot inner region. Unlike other propagation models, the hard X-ray emission (>4 keV) is assumed to be from the hot inner disc by a single-temperature thermal Comptonization process. The fluctuations first cause a variation in the temperature of the truncated disc and then the temperature of the inner disc after a frequency dependent time delay. We find that the model can explain the energy dependent rms and time-lag at different frequencies.

Space–Time Metamaterials

Despite more than a decade of active research, the fundamental problem of material loss remains a major obstacle in fulfilling the promise of the recently emerged fields of metamaterials and plasmonics to bring in revolutionary practical applications. In the present work, we demonstrate that the problem of strong material absorption that is inherent to plasmonic systems and metamaterials based on plasmonic components, can be addressed by utilizing the time dimension. By matching the pulse profile to the actual response of a lossy metamaterial, this approach allows to offset the effect of the material absorption. The existence of the corresponding solution relies on the fundamental property of causality, that relates the absorption in the medium to the variations in the frequency-dependent time delay introduced by the material via the Kramers–Kronig relations. We demonstrate that the proposed space-time approach can be applied to a broad range of metamaterial-based and plasmonic systems, from hyperbolic me...

Cochlear spike synchronization and neuron coincidence detection model.

Coincidence detection of a spike pattern fed from the cochlea into a single neuron is investigated using a physical Finite-Difference model of the cochlea and a physiologically motivated neuron model. Previous studies have shown experimental evidence of increased spike synchronization in the nucleus cochlearis and the trapezoid body [Joris et al., J. Neurophysiol. 71(3), 1022-1036 and 1037-1051 (1994)] and models show tone partial phase synchronization at the transition from mechanical waves on the basilar membrane into spike patterns [Ch. F. Babbs, J. Biophys. 2011, 435135]. Still the traveling speed of waves on the basilar membrane cause a frequency-dependent time delay of simultaneously incoming sound wavefronts up to 10 ms. The present model shows nearly perfect synchronization of multiple spike inputs as neuron outputs with interspike intervals (ISI) at the periodicity of the incoming sound for frequencies from about 30 to 300 Hz for two different amounts of afferent nerve fiber neuron inputs. Coincidence detection serves here as a fusion of multiple inputs into one single event enhancing pitch periodicity detection for low frequencies, impulse detection, or increased sound or speech intelligibility due to dereverberation.

A magnetohydrodynamic model for multiwavelength flares from Sagittarius A⋆ (I): model and the near-infrared and X-ray flares

Flares from the supermassive black hole in our Galaxy, Sagittarius A⋆ (Sgr A⋆), are routinely observed over the last decade or so. Despite numerous observational and theoretical efforts, the nature of such flares still remains poorly understood, although a few phenomenological scenarios have been proposed. In this work, we develop the Yuan et al. scenario into a magnetohydrodynamic model for Sgr A⋆ flares. This model is analogous with the theory of solar flares and coronal mass ejection in solar physics. In the model, magnetic field loops emerge from the accretion flow on to Sgr A⋆ and are twisted to form flux ropes because of shear and turbulence. The magnetic energy is also accumulated in this process until a threshold is reached. This then results in a catastrophic evolution of a flux rope with the help of magnetic reconnection in the current sheet. In this catastrophic process, the magnetic energy is partially converted into the energy of non-thermal electrons. We have quantitatively calculated the dynamical evolution of the height, size and velocity of the flux rope, as well as the magnetic field in the flare regions, and the energy distribution of relativistic electrons in this process. We further calculate the synchrotron radiation from these electrons and compare the obtained light curves with the observed ones. We find that the model can reasonably explain the main observations of near-infrared and X-ray flares including their light curves and spectra. It can also potentially explain the frequency-dependent time delay seen in radio flare light curves.

Orbital-Angular-Momentum Polarization Mode Dispersion in Optical Fibers

The orbital-angular-momentum (OAM) modes in optical fibers have polarization mode dispersion (PMD) properties similar to those of single-mode fibers (SMFs). The + l and − l order OAM modes supported by the same fiber vector modes undergo random cross coupling and exhibit a frequency-dependent time delay. We name this effect “OAM-PMD” and extend the formalism developed for PMD in SMFs to describe OAM-PMD. The characteristics of the modal beat lengths, birefringence correlation lengths, and the mean value of OAM-PMD are investigated. A fixed-analyzer technique is proposed and demonstrated to characterize this phenomenon in OAM fibers. Two different types of OAM fiber are examined. The measured results are compared with the theoretical calculations.

Surface Acoustic Wave Devices in Electronic WarFare

In this paper the applications of acoustic surface wave device technology to electronic warfare systems have been reviewed. A variety of signal processing tasks such as simple time delay, frequency dependent time delay, programmable and discretely variable time delay, band pass filtering and generation and recognition of various coded waveforms can be performed by surface wave devices to improve the performance of EW system.

Some Aspects of the Discrete Wavelet Analysis of Bivariate Spectra for Business Cycle Synchronisation

Abstract The paper considers some of the issues emerging from the discrete wavelet analysis of popular bivariate spectral quantities such as the coherence and phase spectra and the frequency-dependent time delay. The approach utilised here is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, via a broad set of simulation experiments, we examine the small and large sample properties of two wavelet estimators of the scale-dependent time delay. The estimators are the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for the empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Further, we point out a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme, which was proposed earlier in the context of the dual-tree complex wavelet transform. In addition, we show how MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronisation between 11 euro zone countries. The study is supplemented by a wavelet analysis of the variance and covariance of the euro zone business cycles. The empirical examination underlines the good localisation properties and high computational efficiency of the wavelet transformations applied and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as the wavelet evidence on dating the Great Moderation in the euro zone.

Propagation dynamics of femtosecond pulse through subwavelength metallic hole arrays

We have studied the frequency-dependent transmission time delay of femtosecond (fs) laser pulses through subwavelength hole arrays in aluminum films using the up-conversion technique. The pulse delays measured at different wavelengths mainly follow the far-field transmission profile of the surface-plasmon polariton (SPP) resonances. Temporal delays of 60 and 100 fs were found at the major SPP resonance in the single-layer and double-layer samples. A coupled-SPP transmission model is used to explain the temporal dynamics of the transmission process. Our experiment shows that the weak coupling between the SPP waves on different metal-dielectric interfaces leads to the large temporal delay of the transmitted pulses.

Compensation of transmission channel effects in chaos synchronization

The synchronization of chaos is a well-known topic which attracted the attention of the scientific community in the last two decades. However, the robustness of the synchronous state has been not widely studied, especially considering real cases in which the effects introduced by the physical channel through which chaotic circuits interact, may deeply influence the quality of synchronization and even the onset of it. In this paper, the synchronization of two chaotic circuit coupled through a non–ideal channel is investigated. In particular, the effects of channels introducing a frequency–independent or frequency–dependent time–delay are investigated. Furthermore, two different design strategies to obtain a linear compensation block able to compensate the considered channel effects are presented and the recovery of the synchronous state is discussed.

On Some Problems in Discrete Wavelet Analysis of Bivariate Spectra with an Application to Business Cycle Synchronization in the Euro Zone

The paper considers some of the problems emerging from discrete wavelet analysis of popular bivariate spectral quantities like the coherence and phase spectra and the frequency-dependent time delay. The approach taken here, introduced by Whitcher and Craigmile (2004), is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, we point at a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme resembling the one applied in the context of the dual-tree complex wavelet transform of Kingsbury (see Selesnick et al., 2005). Secondly, via a broad set of simulation experiments we examine small and large sample properties of two wavelet estimators of the scale- dependent time delay. The estimators are: the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Besides, we show how the MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss certain issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronization between 11 euro zone member countries. The study is supplemented with wavelet analysis of variance and covariance of the euro zone business cycles. The empirical examination underlines good localization properties and high computational efficiency of the wavelet transformations applied, and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as a wavelet evidence on dating the Great Moderation in the euro zone.

Time-delay correlations and resonances in one-dimensional disordered systems

The frequency dependent time delay correlation function $K(\Omega)$ is studied analytically for a particle reflected from a finite one-dimensional disordered system. In the long sample limit $K(\Omega)$ can be used to extract the resonance width distribution $\rho(\Gamma)$. Both quantities are found to decay algebraically as $\Gamma^{-\nu}$, and $\Omega^{-\nu}$, $\nu\simeq 1.25$ in a large range of arguments. Numerical calculations for the resonance width distribution in 1D non-Hermitian tight-binding model agree reasonably with the analytical formulas.

Hamiltonian optics of nonuniform photonic crystals

The passage of light through slowly varying nonuniform photonic crystal structures is treated using Hamiltonian optics. The approach allows the inverse design of complex and highly compact optical elements as well as providing insight and an appealing physical picture. It can also be used to treat the trapping and deflection of light at distributed defects in one- and two-dimensional (2-D) crystals, and to study the frequency-dependent time delay in chirped one-dimensional (1-D) fiber.

Natural joints in rock: Mechanical, hydraulic and seismic behaviour and properties under normal stress

Abstract The mechanical and hydraulic properties of many rock masses are affected significantly by the additional mechanical compliance and fluid conductivity that result from joints, fractures or faults. The effects of these features, generally referred to as joints, can be so pronounced in many problems in geology or geophysics, mining or petroleum engineering, hydrogeology and waste management that it is important to be able to locate and characterize them remotely within a rock mass using geophysical methods. The effect of joints on seismic wave propagation, therefore, becomes important also. Experimental measurements of the deformation of natural joints are analyzed in terms of theories concerning the roughness of the two joint surfaces and their deformation under stress. For many rocks, the deformation of the surfaces is reversible after the first few cycles of loading and unloading and is, therefore, elastic. The highly non-linear stress-deformation curves for joints must be a result of changes in the geometry of the areas of contact between asperities brought about by the elastic deformation of adjacent voids in response to changes in the applied stress. The flow of fluids between the surfaces of a joint must also depend upon the geometry of the void space between these surfaces. Measurements using liquid metal porosimetry, show that when the two surfaces of a natural joint are in contact with one another, this geometry becomes so complex that fluid through the joint cannot be approximated as laminar flow between parallel surfaces leading to a cubic relation between flux and aperture. At low stresses, fluid flow through a joint decreases much faster than the cube of the joint closure. This is shown to be a result of changes in contact area, tortuosity and hydraulic aperture brought about by deformation of the void space between the two surfaces of the joint. At high stresses, fluid flow through a joint asymptotes to an irreducible level, largely independent of joint closure and further changes in stress. The slope of a tangent to the curve relating the average closure between the two surfaces of a joint to the stress across the joint defines a specific stiffness for the joint at that stress. The effect of joints on seismic waves can be analyzed by using this specific stiffness as a boundary condition in the seismic wave equation. Displacements across this boundary are discontinuous while stresses are continuous. Although the specific stiffness of the joint and the properties of the rock on each side of it are assumed to be completely elastic, the displacement discontinuity leads to frequently-dependent reflection and transmission coefficients for compressional and shear waves as well as frequency-dependent group time delay for the transmitted waves. This concept can be extended to include a velocity discontinuity across the joint, where the contained fluid or the properties of the rock provide viscous as well as elastic coupling across a joint. Theoretical predictions based on the displacement discontinuity and velocity discontinuity theories agree very well with the results of laboratory measurements of seismic pulses transmitted across natural joints with different specific stiffnesses.

Statistical filter theory and the O’Doherty–Anstey effect: Dependence on offset

This paper considers the effects of multiples, generated at plane bed interfaces, on the characteristics of a mean seismic wave propagating at an angle to the bedding plane. It is found that(a) the multiples produce frequency- and angle-dependent phase shifts to the coherent wave as well as providing an effective attenuation, which is also frequency and angle dependent; (b) a slim angular pencil of monochromatic waves rapidly loses information about its original angular width due to the multiples as the pencil propagates; (c) a seismic pulse, initially traveling at a fixed angle, has both its envelope amplitude and its phase distorted by multiples, and after a short distance of transmission into the medium, the wave shape is nearly completely determined by the generated multiples and is only slightly beholden to the initial pulse shape; (d) the phase and group directions of the mean seismic wave are different than the incident wave’s direction and are canted closer to the horizontal with the group direction being the most highly canted; and (e) lateral spreading information of the mean seismic wave is contained in the cross-correlated response of separated geophones and, in principle, can be extracted from cross-correlated measurements. How the generic response depends on the power spectrum of the reflectivity sequence is illustrated by comparing and contrasting results for a transitional sedimentation pattern with those from a cyclic sedimentation pattern; the former produces both a frequency-dependent time delay and attenuation while the latter produces a pure time delay except in the local vicinity of isolated, but periodic frequencies. Numerical estimates, using parameters believed representative of typical seismic conditions, indicate that all of the effects uncovered are large—in the sense that they fall squarely in the regime where they can be expected to have a significant impact both on the subsurface evolution of seismic waves and on interpretations of subsurface conditions made using surface-received signals.