Delay Time Of Reflection Research Articles

An exact tunneling model and its application to transmission and reflection delay times

Electron emission into a nanogap is not instantaneous, which presents a difficulty in simulating ultra-fast behavior using particle models. A method of approximating the transmission and reflection delay (TARD) times of a wave packet interacting with barriers described by a delta function, a metal–insulator–metal (MIM, rectangular) barrier, and a Fowler Nordheim (FN, triangular) barrier is given and has application to simulation. It is based on the superposition of a finite number of exact basis states obtained from Schrödinger’s equation, analogous to how quantum carpets are simulated. As a result, it can exactly and uniquely follow exponentially small tunneling currents. A Bohm-like trajectory is obtained from the time evolution of the density: it shows delay in both the transmitted and reflected packets that can be simply evaluated. The relations to prior studies of the analytic [Formula: see text]-function barrier and the Wigner distribution function (WDF) methods are described. A comparison of the TARD times is contrasted to alternate times in the Büttiker–Landauer (BL) and McColl–Hartman (MH) times; the MH approach is further reformulated explicitly in terms of Gamow factors to consider how the McColl–Hartman effect is to be related, particularly in the case of the FN barrier of field emission.

Validity of delay time identification during standing based on steady-state response

Delay time of reflection is widely used to evaluate neurological disorders and child development. The delay time is generally measured from a button press to a visual stimulus or from surface electromyography (EMG) response to an external stimulus. Due to its variability, however, it is not easy to estimate accurately. In the previous study, we proposed a delay time estimation method from steady-state response based on a delayed feedback control model during standing. The method allows us to estimate the delay time with reproducibility. The purpose of this study is to verify the validity of the delay times estimated from the steady-state response analysis by comparing it with the response of surface EMG to impulse stimulation. In addition, we investigated time delay changes according to the degree of tension by varying the magnitude of the external stimulus. From the validation experiments involving 10 young healthy subjects, no correlation was found between the delay times estimated from the steady-state response and the EMG responses. Furthermore, there was no change in the delay time with the degree of tension caused by the magnitude of support surface sway. Since the delay time estimated from EMG measurement according to impulse stimulus has a high variable, it is necessary to improve the estimation method.

Wigner wave packets: Transmission, reflection, and tunneling

A numerical solution to the time evolution equation of the Wigner distribution function (WDF) with an accuracy necessary to simulate the passage of a wave packet past a barrier is developed, where quantum effects require high accuracy and fine discretization. A wave packet incident on a barrier, a portion of which tunnels through, demonstrates behavior that can define various characteristic transmission and reflection delay (TARD) times useful in the simulation of electron emission. A model for the TARD times is proposed that relies only on the asymptotic maxima of the position $\ensuremath{\rho}(x,t)$ and wave number $\ensuremath{\rho}(k,t)$ densities given by the WDF and applied to a ballistic trajectory model for the (faster) transmitted and (slower) reflected parts. The dependence of the TARD times on barrier width, symmetry, and abruptness is analyzed. For symmetrical barriers with characteristics similar to field emission barrier heights and widths, TARD times are on the order of a fraction of a femtosecond. The TARD times for when tunneling predominates are contrasted to tunneling times in the literature. Use of the TARD times in simulations of field emission in nanogap devices or to model ultrashort pulses generated under rapidly changing conditions for electron sources are proposed.

Comparison of density of states and scattering parameters in coaxial photonic crystals: Theory and experiment

We present an analytical and experimental study of the scattering parameters in a one dimensional (1D) symmetric photonic crystal and their relation to the density of states (DOS). The 1D photonic crystal is constituted by $N$ alternating wires and loops that are either inserted horizontally or attached vertically between the source and load on a transmission line. The complete knowledge of the scattering matrix coefficients (${S}_{ij}$) allows us to access the DOS and eigenvalues of the finite periodic structure as well as the DOS and dispersion curves of an infinite periodic system. We show the usefulness of the transmission and reflection delay times and highlight their similarities and differences with respect to the DOS, in particular as a function of the absorption strength in the system. For both horizontal and vertical geometries, we show analytically that in a lossless structure, the DOS is proportional to the Friedel phase, namely the derivative of the argument of the determinant of the scattering matrix S. For a low loss system, this proportionality remains still valid with a good approximation and can be used as a practical tool to derive the DOS and therefore the dispersion curves from experimental data. Also, the absorption can be accurately extracted from the measurement of the modulus of the determinant of $S$. However, for increasing strength of dissipation, we show how and why these relationships cease to be valid. Still, the transmission delay time can remain an efficient tool to derive DOS even at relatively high dissipation strength. Additionally, we show that in the vertical geometry the transmission and reflection delay times exhibit negative delta peaks which are related directly to the eigenmodes of the finite system with different boundary conditions on its extremities. Our theoretical results are obtained by means of the Green's function approach, whereas the experimental demonstrations are performed using standard coaxial cables in the radio-frequency domain.

Application of Kirchhoff prestack time migration method of the 2D marine seismic data for mapping the subsurface structures in dip case Southern Aru, West Papua, Indonesia

The natural resources of oil and gas potential in the West Papua waters constitute a significant expansion of oil and gas investments in Indonesia’s maritime specifically the eastern region. South Aru is located at the eastern edge of the basin trough Aru and includes one of the most potential oil and gas basins. Complex geological structures such as the case of large dip make seismic cross section results do not represent the subsurface structure of the earth nearing the actual subsurface geological conditions. The working principle of Kirchhoff prestack time migration is looking for reflector positions using delay time of wave energy reflection to get a better seismic section on the tilted reflector with less diffraction effect and have little effect arch (smiling effect) which generates seismic section that can represent the subsurface structure of the earth. Reflectivity cross section of generally more clearly observed after the migration process is carried out so that the resolution of cross section seismic better, which can be useful as the data is ready to be interpreted as the purposes of determination prospects of natural resources, especially regarding the hydrocarbon potential of the South Aru, West Papua waters.

Distribution of cold and temperate ice in glaciers on the Nordenskiold Land, Spitsbergen, from ground-based radio-echo sounding

Data of ground-based radio-echo sounding of 16 glaciers located on the Nordenskiold Land, Spitsbergen, carried out in springs of 1999, 2007 and 2010–2013, allowed defining five glaciers as of the cold thermal type while other eleven ones were polythermal glaciers. In the last ones (polythermal) the average thickness of the upper layer of cold ice and the bottom layer of temperate ice was equal to 11-66 m and 15-96 m, respectively. The ratio of these thicknesses varies from 0.32 to 2.28, and the volume fraction of temperate ice in the total volume of the glaciers varies from 1 to 74% and changes from 0 to 50% in the ablation zone up to 80% in the accumulation zone. Thickness of cold ice was determined by measured delay time of radar reflections from cold-temperate surface (CTS) while thickness of temperate ice was derived as a difference between the total thickness of the glacier and the thickness of its cold ice. For interpretation of radar reflections from CTS we used the noticeable distinction in character of the radar reflections from the upper and lower thicknesses of glacier: absence of internal reflections (excluding reflections from buried crevasses and glacier wells) from upper cold ice layer and a great number of reflections of hyperbolic form from the lower layer related to strong scattering of radio waves by water inclusions in the temperate ice. According to the measurements, relative power of the radar reflections from CTS is by 5,5–14,2 dB smaller than those from the bedrock, that can be considered as an indicator of smaller water content at CTS; so, the repeated measurements of their relative power can be used for estimation of temporal changes in the water content at these boundaries. In layers of the temperate ice, the series of vertical hyperbolic reflections penetrating the cold ice down to CTS and further to the bedrock were detected. Such reflections are related to buried crevasses and/or the glacier wells and can serve as sources of the water permeating during the melt periods from the glacier surface down to CTS and bedrock and, thus, influencing on the ice viscosity and fluidity as well as on velocity of the bottom sliding in the polythermal glaciers. Repeated measurements of relative power of reflections from buried crevasses and wells can also be used to study processes of freezing them through and emptying during the period before start of the surface melting. Relation between volume of temperate ice and area of 16 studied glaciers was used to estimate the probability of existence of polythermal glaciers with a temperate ice core in all 202 glaciers in the Nordenskiold Land. 72 glaciers with areas exceeding 1.79 km2 may be referred to the polythermal type. The probable total volume of temperate ice in these glaciers amounts roughly to 10 km3, and with the 95% confidence it is within the interval from 8 to 33 km3. Almost 80% of the whole temperate ice may be concentrated in only five glaciers with area more than 17 km2, that makes up 2.5% of the total number of glaciers and about 30% of their total area. Data presented in this paper demonstrate more sophisticated pattern of the cold and temperate ice distribution within the glaciers than it was earlier known that should be taken into consideration when modeling and forecasting dynamics of the polythermal glaciers and investigating internal processes of the temperate ice formation in such glaciers.

Perceptual threshold of apparent source width in relation to the azimuth of a single reflection.

An investigation into the perceptual threshold of apparent source width (ASW) in relation to a single reflection azimuth was performed in binaural reproduction. In the presence of a direct sound, subjects compared the ASW produced by a single 90° reference reflection against ASW produced by a test reflection with a varying angle for four reflection delay times between 5 and 30 ms. Threshold angles were found to be approximately 40° and 130°, and did not appear to be dependent on delay time. It was also found that these threshold angles were associated to saturation in [1-IACCE3] versus reflection azimuth.

Comparison between high- and zero-contrast gratings as VCSEL mirrors

This study presents a comparison between high-contrast gratings (HCGs) and zero-contrast gratings (ZCGs) for high-speed vertical-cavity surface-emitting lasers (VCSELs). Both types of gratings exhibit high reflectivities beyond 99.5% due to the destructive interference at the output plane, but the HCG has a broader high reflectivity band. The HCG has a lower reflection delay time and smaller energy penetration length than the ZCG. The HCG has poorer mode selectivity for the VCSEL than the ZCG. The fabrication of the ZCG is less complex but with tight fabrication tolerances.

Model of binaural speech intelligibility in rooms

Many models of speech intelligibility in rooms are based on monaural measures. However, the effect of binaural unmasking improves speech intelligibility substantially. The binaural speech intelligibility model (BSIM) uses multi-frequency-band equalization-cancellation (EC), which models human binaural noise reduction, and the Speech-Intelligibility-Index (SII), which calculates the resulting speech intelligibility. The model analyzes the signal-to-noise ratios at the left and the right ear (modeling better-ear-listening) and the interaural cross correlation of target speech and binaural interferer(s). The effect of the hearing threshold is modeled by assuming two uncorrelated threshold simulation noises for both ears. BSIM describes the (binaural) aspects of useful and detrimental room reflections, reverb, and background noise. Especially the interaction of delay time and direction of speech reflections with binaural unmasking in different acoustical situations was modeled successfully. BSIM can use eithe...

Longitudinal acoustic waves in layered media: Comparative study of Raman scattering and reflection delay time

Using a Green's function method, we present a theoretical analysis of the propagation of acoustic waves in multilayer structures. The structure studied consists of a finite superlattice (SL) made of a periodic repetition of N unit cells deposited on a substrate. Such a structure exhibits extended modes constituting the allowed bands separated by forbidden bands where localized modes associated to free surfaces, defect layers, ... may exist. These modes can be observed either by Raman scattering when an incident light is launched from vacuum towards the multilayer, or by the reflection delay time when an incident acoustic wave is launched from the substrate. Specific applications of our results are given for some available experiments in the literature (e.g., Si/GexSi1-x, GaSb-AlSb) and a good agreement has been obtained between our theoretical results and the experimental data.

Blind dereverberation based on auto‐correlation functions of framewise time sequences of frequency components

Proposed is a new blind dereverberation method based on auto‐correlation function of framewise time series of each frequency component. Inverse filtering of source‐microphone transfer functions is widely employed for suppressing the effects of reflected waves, but this method cannot be employed for cases where source‐microphone transfer functions are not available or for time‐variant cases. Several methods of spectral subtraction have been proposed to cope with these cases. However, most of them require transfer functions among sources and microphones. The proposed method, however, does not require transfer function inverse filters. Moreover, the method can handle frequency characteristics of sound paths. To realize dereverberation, it is necessary to estimate the delay time and frequency characteristics of reflection, though most conventional methods assume flat frequency characteristics. The proposed method estimates these parameters based on auto‐correlation function of each time series of spectral components in frequency spectra obtained every frame‐shift interval. The proposed method improves dereverberation performance, comparing with methods that assume flat frequency characteristics. The proposed method raises average segmental SNR by 3.4 dB and reduces reverberation time from 390 to 109 ms for a room employed for experiments. [Work supported by Knowledge Cluster Project, MEXT, and by Academic Frontier Project Doshisha University.]

The reflection and transmission group delay times in an asymmetric single quantum barrier

The reflection and transmission group delay times are systematically investigated in an asymmetric single quantum barrier. It is reported that the reflection times in both evanescent and propagating cases can be either negative or positive, depending on the relative height of the potential energies on the two sides of the barrier. In the evanescent case where the energy of incident particles is less than the height of the barrier, the reflection and transmission times in the opaque limit are both independent of the barrier’s thickness, showing superluminality. On the other hand, in the propagating case where the energy of incident particles is larger than the height of the barrier, the reflection and transmission times as the periodical function of the barrier’s thickness can be greatly enhanced by the transmission resonance. It is also shown that the transmission time and the reflection times for the two propagation directions in the same asymmetric configuration satisfy the reciprocal relation, as consequence of time reversal invariance in quantum mechanics. These phenomena may lead to novel applications in electronic devices.

Identifying contributions of individual layers constituting multilayer dielectric mirrors

First-order approximations have been used to study the recursion expressions of the reflection and transmission coefficients of a weakly absorptive multilayer mirror. It has been proved that in the proximity of the central frequency ω 0 of a quarter-wave mirror, contributions of an individual layer to the reflection delay time and absorption-induced reflectivity reduction can be quantitatively specified with a single weighting factor pertinent to that layer. Derivations have indicated that the absorption-induced reductions of mirror reflectivity and reflection delay can be reduced by selecting an odd layer number and a large index ratio between alternating high and low refractive index coating materials. Calculations have also suggested that the absorbed incident light is not distributed, among the reflected and transmitting parts, according to the ratio between the reflectivity and potential transmission.

Subjective preference evaluation of sound fields by performing singers

A model of the auditory process is proposed for performing singers, which incorporates the added signal from bone conduction, as well as the psychological distance for subjective preference of the performer from the acoustic sound field of the stage. The explanatory power of previous scientific studies of vocal stage acoustics has been limited by a lack of an underlying theory of performer preference. Ando’s theory, using the autocorrelation function (ACF) for parametrizing temporal factors, was applied to interpretation of singer sound field preference determined by the pair comparison method. Melisma style singing (no lyrics) was shown to increase the preferred delay time of reflections from a mean of 14 ms with lyrics to 23 ms without (p<0.05). The extent of the shift in preferred time delay was shown to be directly related to minima of the effective duration of the running ACF, (τe)min, calculated from each singer’s voice. Voice matching experiments for singers demonstrated a strong overestimate of the voice outside the head compared with the singer’s own voice (22.4 dB overestimate, p<0.01). Individual singer melisma singing delay preferences were compared for “ah” versus “hum” syllables, and the increased delay preference (41 ms) was shown to be correlated with (τe)min (r2<0.68, p<0.01). When the proposed bone conduction model was applied, using the measured overestimate of sound level of the singer’s own voice for each singer (9.9 dB mean overestimate difference between “ah” and “hum,” p<0.01), the relationship of singer preference to (τe)min was improved (r2=0.97, p<0.01). Thesis advisor: Yoichi Ando Copies of this thesis are available from the author by inquiry at BRC Acoustics, 1741 First Avenue South, Seattle, WA 98134 USA. E-mail address: dnoson@brcacoustics.com

MAGNETOENCEPHALOGRAPHIC RESPONSES CORRESPONDING TO INDIVIDUAL SUBJECTIVE PREFERENCE OF SOUND FIELDS

To investigate human cortical responses that correspond to subjective preference of sound fields, an attempt is made here to analyze the autocorrelation function (ACF) of magnetoencephalography (MEG) under the condition of varying delay time of single reflections. According to previous studies, it is assumed that a similar repetitive feature of the MEG alpha-waves range (8–13 Hz) is related to subjective preference in terms of the effective duration of the ACF. The source signal was the word “piano” which had a 0·35 s duration. The delay time, Δt 1, was varied at five levels (0, 5, 20, 60, and 100 ms). The scale values of the subjective preference of each subject were obtained by the paired-comparison tests. To compare the results of the MEG measurements with the scale values of the subjective preference, combinations of a reference stimulus ( Δt 1=0 ms) and test stimuli ( Δt 1=0, 5, 20, 60, and 100 ms) were presented alternately 50 times, and the MEGs were analyzed. It is found that subjective preference for each individual and the effective duration of the ACF of the MEG alpha waves are linearly related.

MELISMA SINGING AND PREFERRED STAGE ACOUSTICS FOR SINGERS

Vocal performance characteristics, such as tempo, colour, and expressiveness of singers are part of the unique artistic impression of individual performers and individual performances. Subjective pair-comparison studies of singers in a previous study demonstrated that singers prefer added reflections with delays in the range of 10–20 ms. However, the range of values between singers, for the effective duration of the autocorrelation of the singer's voice, was limited, and insufficient to demonstrate a relationship between individual vocal characteristics and the preferred delay time of reflections. In this study, to investigate the singer's preferred acoustics with a change in singing style, subjects were asked to perform non-plosive, non-fricative text for the lyrics, using exclusively “la” syllables ( melisma singing). A resulting shift in preferred time delay was observed. The extent of the shift in preferred reflection time delays is shown to be directly related to the minima of the effective duration of the running autocorrelation function calculated from each singer's voice. Singers were also subjected to training, to assist in identifying sound fields. After training, the average preferred delay time of the reflection did not change, but the statistical variability of the singer's subjective rating of the sound fields was strongly reduced.

EFFECT OF MODULATED DELAY TIME OF REFLECTION ON AUTOCORRELATION FUNCTION AND PERCEPTION OF ECHO

An indoor sound field can be regarded more or less as a time-variant system. In this paper, the time-variant model of the impulse response, which consists of a direct sound and a reflection with a modulated delay time, is applied to simulate such a time-variant sound field. The effects of the modulated delay time of reflection are investigated in terms of physical properties and subjective evaluation of the temporal fluctuation of a sound field. The physical properties of the temporal fluctuation are analyzed by using the autocorrelation function (ACF) of the sound field and identified by the factors and behavior of the ACF. To examine subjective evaluation of the temporal fluctuation of a sound field, listening tests on the perception of echo were conducted. Such subjective evaluation may be associated with the ACF of a sound field. The relationship between the physical properties and the subjective evaluation of the temporal fluctuation of a sound field is also discussed.

Relation between Anderson and invariant imbedding models for transport in finite chains and study of phase and delay time distributions for strong disorder

The invariant-imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered one-dimensional chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection (transmission) coefficients of Anderson chains of N and $N\ensuremath{-}1$ atoms imbedded in infinite nondisordered chains. As an illustration of the equivalence of the invariant-imbedding equations and the Anderson model for a weak disorder, we show that various available analytical and numerical results for reflection-phase distributions for these models are in good qualitative agreement. We also discuss the distribution of reflection phases and of reflection delay times for an Anderson model with a simple distribution of on-site potentials characterizing extreme strong disorder.

Transmission delay times of localized waves.

We investigate the effects of wave localization on the delay time tau (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered waveguide. Localization results in a separation tau=chi+chi(') of the delay time into two independent but equivalent contributions, associated to the left and right end of the waveguide. For N=1 propagating modes, chi and chi(') are identical to half the reflection delay time of each end of the waveguide. In this case the distribution function P(tau) in an ensemble of random disorder can be obtained analytically. For N>1 propagating modes the distribution function can be approximated by a simple heuristic modification of the single-channel problem. We find a strong correlation between channels with long reflection delay times and the dominant transmission channel.

On the reduction of direct tunneling leakage through ultrathin gate oxides by a one-dimensional Schrödinger–Poisson solver

A full self-consistent one-dimensional Schrödinger–Poisson model is reported in this article, which is specifically dedicated to the study of direct tunneling current through ultrathin gate oxide of metal-oxide-semiconductor (MOS) structures. The gate current is obtained by estimating the quasibound state lifetimes within the formalism of the formal reflection delay time of wave packets using the transfer-matrix method. As an alternative design to conventional MOS structures, two strategies are investigated in this work to scale oxide thickness in the sub 1.5 nm range while keeping an acceptable gate current leakage of some A/cm2. These include nitride/oxide stacked gate dielectrics used to increase the insulator thickness, and heterostructure MOS capacitors to confine electrons in a buried quantum well. Tensile strained Si1−yCy/Si and Si/Si1−xGex heterostructures that provide a convenient conduction band offset are proposed in this order. A conduction band offset of 0.19 eV is shown to yield nearly the same but limited improvement than the stacked gate dielectrics structure. Compared with the conventional MOS device of equivalent oxide thickness, a gate current reduction by more than two orders of magnitude is reached by using a heterostructure with a conduction band offset of 0.31 eV. For MOS transistor application this significant gain may be in addition to the driving current increase that can be expected from the strain-induced improvement of electron transport properties.