Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox

A simple acoustic device consisting of two dangling side resonators grafted at two sites on a slender tube is designed possibly to obtain transmission stop bands (where the propagation of longitudinal acoustic waves is forbidden). In contrast to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind within the framework of the Green's function method. The amplitude and the phase of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of side resonators. These results should have important consequences for the suppression of low-frequency noise and for designing filters.

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Transmission gaps and Fano resonances in an acoustic waveguide: analytical model

This paper deals with the similitude between the behaviours of linear filter gain and negative group delay NGD function. The transposition method of low-pass/high-pass, low-pass/band-pass and low-pass/band-stop NGD circuits is established. To the best of the author knowledge, it acts as the first paper devoted on the NGD function generalized theory. The introduced transform relationships simplify the synthesis of any NGD circuits from simple elementary low-pass NGD topologies. Families of innovative NGD topologies are identified. To verify the relevance of the concept proposed, frequency- and time-domain analysis results from realistic proofs of concept demonstrating the feasibility of developed NGD transforms were performed. Thanks to the NGD phenomenon, the possibility of the ultra-wideband pulse signals propagating in time-advance is verified. Finally, potential applications of NGD circuits are discussed. Copyright © 2013 John Wiley & Sons, Ltd.

Similitude between the NGD function and filter gain behaviours

Photon, electron, magnon, phonon and plasmon mono-mode circuits

This work examines a simple one-dimensional acoustic band gap system made from a diameter-modulated waveguide. Experimental and theoretical results are presented on perfectly periodic waveguide arrays showing the presence of band gaps—frequency intervals in which the transmission of sound is forbidden. The introduction of defects in the perfect periodicity leads to narrow frequency transmission bands—defect states—within the forbidden band gaps. The circular cross-section waveguide system is straightforward to simulate theoretically and experimental results demonstrate good agreement with theory. The experimental transmission of the periodic waveguide arrays is measured using an impulse response technique.

Band gaps and defect modes in periodically structured waveguides

We demonstrate the tunneling of audio pulses through the forbidden transmission zone of an acoustic band gap array. The acoustic band gap is created in a waveguide with a periodically spaced series of dangling sidebranches. Using an impulse response method, the transmission properties of the array are characterized and the regions of forbidden transmission identified. Tunneling pulses, whose frequency content lies completely with the forbidden transmission region, are used to explore the concepts of tunneling time and group velocity. In an analog of experiments that are well known for electromagnetic waves, we show that the group velocity of the tunneling pulse is considerably larger than the speed of sound. The dynamics of pulse reshaping that lead to this phenomenon are discussed.

J. Ash

Papers

Breaking the sound barrier: Tunneling of acoustic waves through the forbidden transmission region of a one-dimensional acoustic band gap array

Large collectivity in 29Ne at the boundary of the island of inversion