Tunneling time through a rectangular barrier

Aquino, V. M.; Aguilera‐Navarro, V. C.; Goto, Mario; Iwamoto, Hiroaki

doi:10.1103/physreva.58.4359

Cited by 27 publications

(25 citation statements)

References 5 publications

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“…At the outset the first pair can already be distinguished from the latter three in that the volume under consideration is effectively taken to be infinite in the former (as evidenced by the time being the energy derivative of the scattering phase) whereas the corresponding volume for the latter refers to the finite spatial interaction region (i.e., the time is the derivative of the scattering potential in the region under consideration) at which the issue of time is being directed in the first place. Most tunneling-time calculations center on one-dimensional models within a scattering configuration [5,[10][11][12]. In this report we show that even with these models some of the gathered intuitive ideas might require modification.…”

Section: Introductionmentioning

confidence: 83%

Transit and Reflection Times for a Non-Symmetric Barrier and a Symmetric Double Barrier

Martı́nez¹,

Polatdemir²

2003

Phys. Scr.

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Many calculations of transit and reflection times focus on symmetric barriers in which the dwell time equals the Larmor precession time. We show for a nonsymmetric barrier that this is not generally true and that all the characteristic transmission and reflection times (except the phase time) are finite for all ranges of the incident momentum. We also verify these observations for a symmetric double barrier (except for the finiteness of the reflection time).Ã

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Section: Introductionmentioning

confidence: 83%

Transit and Reflection Times for a Non-Symmetric Barrier and a Symmetric Double Barrier

Martı́nez¹,

Polatdemir²

2003

Phys. Scr.

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“…Beyond its intrinsic quantum mechanics interest, the significance of tunneling time comes from the requirement of understanding the tunneling dynamics in high-speed devices due to the fact that the time is one of key parameters for ultimate performance evaluation of different kinds of electronic devices. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] Therefore, since Condon and Morse 24 posed the question of the alacrity of the tunneling process, even for a simple single-barrier potential, the tunneling time has been studied extensively by various theoretical approaches, such as phasedelay method, 25 dwell time approach, 26 Larmor Clock time and its generalizations, 27 and the wave packets evolvement method. 28 In 1932 MacColl 29 asserted that there is "no appreciable delay" in the transmission of the packet through the barrier.…”

Section: Introductionmentioning

confidence: 99%

Spin-dependent delay time and the Hartman effect in tunneling through diluted-magnetic-semiconductor/semiconductor heterostructures

2005

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We investigate spin-dependent group delay and dwell time in diluted-magnetic-semiconductor/ semiconductor ͑DMS/S͒ heterostructures, where the sp-d exchange interaction gives rise to a giant spin splitting when an external magnetic field applied along the growth direction of the heterostructures. It is found that both the group delay and the dwell time strongly depend not only on the incident energy and the structural configuration, but also on spin orientations. In the spectra of both the group delay and the dwell time, there are some sharp peaks with larger peak-to-valley ratios for spin-up electrons through the DMS/S heterostructures with a single or double DMS layers, while the curves become more smoothed for spin-down ones through the same heterostructure. The difference of the group delay or of the dwell time between spin-up and spin-down cases reaches its maximum when resonant tunneling occurs. The numerical results indicate that the spin-up and spin-down processes are separated on the time scales. Further, for spin-down electrons, the group delay can be negative at low energy under some magnetic fields.

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“…There are very different way to calculate the tunneling times [4,10,14,17,18]. Here we consider the transit time t for a wave packet propagating through a given region could be measured as the intelval between the arrival time of the signal envelope at the two ends of that region whose distance is U .…”

Section: Reflection Delay Time and Coeftlcient-mentioning

confidence: 99%

“…Note that we have ignored the time dependent factor eia evevwhere in the wave functions in Eq. (2,3,4). The coefficients R, T, A and B can be calculated by considering the boundary conditions.…”

Section: Reflection Delay Time and Coeftlcient-mentioning

confidence: 99%

“…Most of these works are based on the numerical and analytical analysis of Schrodinger equation with some initial condition on the wave packets [2-41, and have been approved experimentally [5][6][7][8]. So the tunneling time of a particle can be obtain in different ways [4,14]. The analogy between quantum tunneling of particle and evanescent electromagnetic wave found in a lowdielectric constant region separating two regions of high dielectric constant, can be considered and one can find a suitable approach for tunneling time of photon from this classically forbidden region [I].…”

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confidence: 99%

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Goos-Hanchen shift description in planar optical waveguides

Rostami

International Conference on Communication Technology Proceedings, 2003. ICCT 2003.

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In this paper, using the Helmholtz wave equation and the tunneling time of a photon [I] through a index of refraction barrier, the reflktion delay time and reflection coefficient calculated and analytical expression for these quantities are introduced. It p,edicts that, the reflection delay time and coefficients depends on the refraction indeq the thickness of barrier, the incident angle, and the incident wave frequency. Using these relations, we obtain the light penetration depth as well as horizontal shifts for reflection component of incident light to the interface of two media as shown in Fig.(l-a). Our results completely describe the nature of Goos-Hanchen shifts in planar optical slab waveguides as a common device in optical integrated circuits (OIC). Also. the experimental data and our prediction completely close together. 1. Jntroduction-In recent years, the tunneling time of a particle passing through a potential barrier opaque classically has recently been one of the most striking subject. Most of these works are based on the numerical and analytical analysis of Schrodinger equation with some initial condition on the wave packets [2-41, and have been approved experimentally [5-8]. So the tunneling time of a particle can be obtain in different ways [4,14]. The analogy between quantum tunneling of particle and evanescent electromagnetic wave found in a lowdielectric constant region separating two regions of high dielectric constant, can be considered and one can find a suitable approach for tunneling time of photon from this classically forbidden region [I]. With reference to Fig.(l-a), a light beam impinges from a dielectric medium with index n, onto a dielectric slab waveguide with index nz < n, . If the incident angle is greater than the critical value 0, = sin-' (A) , all of the light beam must be reflected, but in practice some part of it tunnels through the slab and emerges in the second dielectric medium with index n, and another part of this light beam reflected. The reflected component, from practical point of view, have the horizontal shifts named Goos-Hanchen shifts [19], n "1which was explained as penetration of light into the forbidden region. Using the tunneling phenomena, we propose the analytical relation for reflection delay time, the reflection coefficient and the penetration depth. Based on these results, we calculate the horizontal shifts and show that the predicted our results completely describe the Gws-Hanchen shift. Organization of this paper are as follows:In section 11, the basic idea for reflection delay time and the reflection coefficient discussed. The Gws-Hanchen shifts based on the reflection delay time discussed in section 111. Finally paper is ended with a conclusion, including the discussion about simulated results. II. Reflection Delay Time and Coeftlcient-We study onedimensional problem in which wave packet propagates along one direction say the z -axis. Let us consider a wave packet moving along z-axis incident on a region [ O , U ] with a refractive index n(z), as dep...

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Tunneling time through a rectangular barrier

Cited by 27 publications

References 5 publications

Transit and Reflection Times for a Non-Symmetric Barrier and a Symmetric Double Barrier

Transit and Reflection Times for a Non-Symmetric Barrier and a Symmetric Double Barrier

Spin-dependent delay time and the Hartman effect in tunneling through diluted-magnetic-semiconductor/semiconductor heterostructures

Goos-Hanchen shift description in planar optical waveguides

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