Producing acoustic ‘Frozen Waves’: Simulated experiments with diffraction/attenuation resistant beams in lossy media

Abstract

The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction -self-healing- property (after obstacles with size smaller than the antenna's); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0⩽z⩽L, of the wave propagation axis. More specifically, the FWs are localized fields "at rest", that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization. In this paper we investigate, by simulated experiments, various cases of generation of ultrasonic FW fields, with the frequency of f0=1 MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80 mm, in attenuating media with absorption coefficient α in the range 70⩽α⩽170 dB/m. Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams. We pay due attention to the selection of the FW parameters, constrained by the rather tight restrictions imposed by experimental Acoustics, as well as to some practical implications of the transducer design. The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, as well as for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; also for kidney stone shuttering, etc.).

Modeling of space-time focusing of localized nondiffracting pulses

“…It is a much more powerful method because, we repeat, it allows us to choose multiple locations (spatial ranges) of space/time focalization, where the pulse intensities also can be chosen a priori. This technique can be seen as a pulsed version of the Frozen Wave method [26][27][28][29][30][31] (originally developed for beams) and it can be implemented for subluminal, luminal and superluminal pulsed solutions. It is important to note that within all focal lines, the resulting pulses will be nondiffracting.…”

“…Wave method [26][27][28][29][30][31] (originally developed for beams) and it can be implemented for subluminal, luminal and superluminal pulsed solutions. It is important to note that within all focal lines, the resulting pulses will be nondiffracting.…”

Acoustic (Ultrasonic) Non-Diffracting Beams: Some theory, and Proposals of Acoustic Antennas for several purposes

“…Happily enough we can always obtain ultrasonic beams, resisting for long distances to both diffraction and attenuation, by generalizing the method of ours for FWs [20,4,2] (our standard method for FWs is briefly summarized in an Appendix, for possible convenience of the reader).…”

“…25 -Our theoretical method [20,4,2] allows constructing an acoustic Frozen Waves with the characteristics specified in the Example above. This is shown in the present Figure . It is rather encouraging the theoretical possibility of obtaining ultrasonic beams, resisting the effects of diffraction and attenuation for distances very much longer than the ones attained by ordinary beams [4]. But, let us repeat, the high-power needed for the desired applications, is often a serious obtacle.…”

“…In the first part of this paper, we shall not deal, however, with the "(Acoustic) Frozen Waves", confinig ourselves here to quote other articles, like Refs. [3,4], in which they have been investigated.…”