Carsten Draeger

One-channel time-reversal in chaotic cavities: Theoretical limits

One-channel time-reversal experiments in closed chaotic cavities produce excellent, but not perfect, time-reversed focusing. This paper investigates such experiments by a simple eigenmode analysis of the system. It shows that the process is, even for long reversed signals, subject to an information loss during recording and re-emission which prevents perfect time-reversal. This fact can be expressed by a simple equation, called the cavity equation, which states that the signal of a one-channel time-reversal is equal to the signal of a perfect time-reversal after convolution with the backscattering impulse response of the reversal point (i.e., from this point to this point). The latter convolution describes the introduction of the loss of information. Furthermore, arguments are presented suggesting that one third of the total energy of the time-reversed wave field is actually contained in the refocusing wavefront. The predictions are verified by numerical finite-difference time-domain simulations.

ONE-CHANNEL TIME-REVERSAL IN CHAOTIC CAVITIES : EXPERIMENTAL RESULTS

Experiments are presented that show the feasibility of reconstructing a point source using acoustic time-reversal with a single transmitter/receiver. The propagation medium is a closed 2-D silicon cavity with chaotic ray dynamics and negligible absorption. Injection of a short pulse at one point yields a long signal at a second one; by reversing a part of this signal, we obtain a focus at the initial injection point. The characterization of the focus was observed by scanning with an optical interferometer and by measuring the signal at the focal spot. With circular converging wavefronts, the reconstructed focus was excellent (corresponding to an aperture of 360°), but not perfect. The increase in quality of the focus with growing length of the reversed signal is described by a statistical ray model. Despite the irreversibility in classical chaos (due to strong sensitivity to initial conditions), the underlying chaotic ray dynamics is useful in this case.

Theory of the time-reversal process in solids

In this paper, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves. A plane time-reversal mirror (TRM) is used, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM. The basic approach is similar to the case of a plane fluid–fluid interface [D. Cassereau and M. Fink, J. Acoust. Soc. Am. 96, 3145–3154 (1994)]; it is extended to take into account the different wave types. It is shown that the TRM is able to recreate properly in time and space the reversed fields of the longitudinal wave and the vertical polarization SV of the transverse waves, but not the horizontal polarization SH. The focusing quality of the backpropagating waves is limited by their respective wavelengths, so the slower SV wave can be better focused. Additional, unwanted wavefronts are created in the solid, too, but they are of weak amplitude and they are not focused. Numerical simulations ...

ACOUSTIC TIME REVERSAL WITH MODE CONVERSION AT A SOLID-FLUID INTERFACE

Acoustic time-reversal experiments are mostly carried out in fluid media. This letter presents experiments proving the capability of a time-reversal mirror to obtain simultaneous focusing of both propagation modes inside a solid. The mirror is located in a surrounding fluid and records the longitudinal and transverse wavefronts (created by a laser impact on the solid) after conversion into pressure waves at the solid-fluid interface. We show that the time-reversed pressure wavefronts are reconverted mostly to their original propagation mode and focus simultaneously at the location of the laser impact.

A two‐dimensional array system for studies of ultrasonic imaging with aberration correction

A two‐dimensional array system is described for pulse‐echo studies of aberration correction. The transducer array is an 80×80 array with a center frequency of 3.0 MHz and a −6‐dB bandwidth of 56%. At the center frequency, each element has a physical size of 1.04 wavelength and spacing of 1.2 wavelength. A multiplexer accesses any contiguous 128 elements for transmission and any contiguous 16 elements for simultaneous reception. Transmit electronics have independently programmable waveforms. Each receive channel includes a 20‐MHz, 12‐bit A/D converter, and a time varied gain programmable over 40 dB. Transmit and receive apertures up to the size of the array are formed synthetically. A method that iteratively predistorts transmit waveforms to produce a transmit focus compensated for aberration has been implemented. Point‐spread functions have been measured for propagation through a water path and through a tissue‐mimicking aberration path. Pulse‐echo images have been formed through a water path, through a t...

Characterization of time‐reversed elastic waves in ergodic billiards

One year ago, this laboratory showed experimentally and numerically that an elastic wave can be time reversed in a highly reflecting cavity with a single pointlike source [Draeger and Fink, J. Acoust. Soc. Am. 101, 3090(A) (1997)]. This is possible because the cavity is low dissipative and its shape is ergodic. Now the properties of this experiment are better understood. Clearly, two parameters are involved. The first one (T) is the beginning of the time reversal window; the second one is its duration ΔT. The lowest value of T which gives an isotropic focusing is the ‘‘angular mixing time;’’ it may be related to the ergodicity time. There is another characteristic time: beyond a certain limit, increasing ΔT does not improve the quality of focusing any longer. This ‘‘saturation time’’ is very dependent on the initial pulse length; it is analogous to the Heisenberg time. Also, the difference beteween the perfect theoretical time reversal and the experimental one is explained.

One‐channel time‐reversal in a chaotic two‐dimensional silicon cavity

Acoustic time‐reversal experiments usually need large arrays of transducers. An element reduction normally decreases the aperture and thus degrades reversal or focusing quality. However, one can use reflections to increase artificially the transducer aperture. It is shown that in a reflecting cavity with negligible absorption, a time‐reversal of a pointlike source can be performed using a single element. The wave field is measured by the transducer over a long period of time at a point inside the cavity, and then the time‐reversed signal is reinjected at the same location. The wave field thus created forms wave fronts of the same shape as the initially emitted ones, but propagating in the opposite direction. They finally collapse at the location of the initial source, leading to excellent focusing which is not aperture limited. The difference between a perfect and a one‐channel time‐reversal can be quantified. A chaotic shape of the system guarantees a successful time‐reversal; in some regular cavities, t...

Time reversal in solids: theory and experiment

We present the first theoretical approach to determine the ability of an acoustic time reversal mirror (TRM) to focus through a liquid fluid-solid interface on a point located in a homogeneous isotropic solid. We consider both P- and S-waves and their transmission into a fluid where TRMs work. A general way to obtain refocusing quality is shown and illustrated by the example of the reversal of a laser source working in the ablation regime. The theoretical results are compared with experiments carried out in our laboratory.

Computation of transient Green’s functions through plane interfaces

This work studies the acoustical field generated by a point source after reflection or transmission by a plane interface. There are two classical approaches to calculate such transient Green’s functions, using either a Laplace or a Fourier transform over time. However, the second approach involves numerical integrations that are difficult to carry out because of singularities of the integrand. It is shown that it is possible to avoid this difficulty using an excitation in the form of a temporal Lorentz function of variable width, introducing several judicious variable changes and finally deforming the integration path in the complex plane. By developing the expression of the transmission/reflection coefficient into Taylor’s series around suitable points, it is even possible to carry out a piecewise integration analytically, therefore resulting in an approximate expression of the acoustical field as a function of space and time. Since this expression turns out to be in a closed form, it can be evaluated fa...

Time reversal of ultrasonic waves in solids: Theory and experiments

In previous works, the capacity of time‐reversal mirrors (TRM) has been presented to optimize ultrasonic focusing on a pointlike source. However, the evaluation of the focusing quality has so far been limited to fluid media. In this paper, the first theoretical approach is presented to determine the capacity of the TRM to focus on a point situated in a homogeneous isotropic solid. P and S waves emitted by a pointlike source in the solid yield the generation of transmitted pressure waves in a fluid that limits the solid via a plane boundary. A TRM placed in the fluid behind the interface measures both incoming wavefronts and is hence able to reverse them one by one. The reversed pressure fields backpropagate to the interface, resulting in P and S waves in the solid. It is shown that, in spite of the losses at the interface, both kinds of waves focus at the location of the initial source. Numerical simulations are carried out, showing that the time reversal is more favorable using the S waves than the P waves, in terms of the width of the focal spot as well as in terms of displacement amplitude. The results are compared with experiments carried out with a laser source working in the ablation regime.