LETTERS PUBLISHED ONLINE: 24 OCTOBER 2010 | DOI: 10.1038/NMAT2881
An acoustic rectifier B. Liang1,2† , X. S. Guo1† , J. Tu1† , D. Zhang1 * and J. C. Cheng1,2 * The detection of acoustic signals is of relevance for a range of practical applications, for example in medical diagnostics. However, whereas rectification of electric current and other energy forms such as thermal flux has been demonstrated1–6 , acoustic rectification has not yet been achieved. Here, on the basis of the earlier theoretical proposal of an ‘acoustic diode’7 , we present the first experimental demonstration of a rectified energy flux of acoustic waves. A one-dimensional acoustic rectifier is fabricated by coupling a superlattice with a layer of ultrasound contrast agent microbubble suspension. A significant rectifying effect is observed within two frequency bands at locations that agree well with theoretical predictions. Following optimization of the concentration of the microbubble suspension, rectifying ratios can be as high as ∼104 . This realization of an acoustic rectifier should have substantial practical significance, for example in the focusing of ultrasound in medical applications. The invention of electric diodes, which were the first devices to enable the rectification of current flux, marked the emergence of modern electronics and eventually led to worldwide revolutions in many aspects. Motivated by the significant rectifying capabilities of electric diodes, many contributions have been and continue to be devoted to investigations of the rectification of other energy forms1–6 . Rectifying effects have previously been identified both theoretically and experimentally for thermal flux1–5 and for solitary waves6 . As compared with electricity, the acoustic wave is an important form of classical wave that is more ubiquitous in nature and has a much longer research history. It is therefore apparent that counterpart devices for rectifying acoustic propagations, if they could be successfully fabricated, would have deep implications for acoustic devices, acoustic applications and the field of acoustics in general. Despite increasing interest in acoustic rectification, challenges still remain in achieving effective control of acoustic energy flux in practice. Recently the first theoretical model of an ‘acoustic diode’ (AD), which behaves like its electrical counterpart, was presented by our group7 . The proposed AD model partially fills the role by converting sound to a new frequency and blocking any backwards flow of the original frequency8 . This innovative model, which consists of a sonic crystal and another medium with strong acoustic nonlinearity, opens new design possibilities and promises potential applications in a variety of important situations that require special manipulations of acoustic waves. Examples of these include the construction of an acoustic one-way mirror to prevent an ultrasound source from being disturbed by backtracking waves or a unidirectional sonic barrier to block the environmental noise in a single direction; or, of particular interest, to control the acoustic energy transmission in medical applications of focused ultrasound, which has increasing significance nowadays8 . However, practical realization of an acoustic rectifier, which could give designers new
flexibility in making acoustic sources such as those used in medical imaging or therapy, has never been achieved. In this work, we attempted to explore experimentally the significant rectifying phenomenon in acoustic waves. A onedimensional (1D) system consisting of a superlattice coupled with a layer of ultrasound contrast agent (UCA) microbubble suspension was fabricated, which might be referred to as an ‘AD prototype’. This device allowed part of the acoustic energy flux incident from one particular side to pass, but behaved like an ‘insulator’ as the wave propagated in the opposite direction. Such a rectifying phenomenon occurred when the frequency of the incident wave fell within particular frequency bands. Furthermore, the measured pressure dependence of the transmitted acoustic energy flux exhibited a strong similarity to the voltage–ampere relationship of an electric diode. It is noteworthy that the rectifying efficiency was affected by the UCA concentration. With an appropriate UCA concentration, the rectifying ratio of the acoustic energy flux can reach nearly 104 . In theory, an effective AD model should include two components: a composite with its own band structure, such as a sonic crystal9 ; and another medium that has particularly strong acoustic nonlinearity7,8 . The sonic crystal serves as an effective acoustic filter to yield different transmission properties between the fundamental wave and the second harmonic wave (SHW). The nonlinear medium (NLM) is introduced to destroy the system symmetry and to break the restriction of the reciprocal theorem in linear acoustic systems. If the acoustic wave comes from the proximal side of the NLM, it will hit the nonlinear material first, creating a SHW that passes through the filter. However, any sound coming from the opposite direction at the fundamental-wave frequency is blocked before it reaches the NLM (refs 7,8). Therefore, an asymmetric propagation of acoustic waves can be expected and reasonably referred to as acoustic rectification. An effective AD device was constructed here by coupling a superlattice structure with a NLM layer. As the superlattice belongs to the class of sonic crystals but has a simple 1D structure, it is much easier to produce than 2D and 3D sonic crystals, and its structural parameters can be controlled more precisely. Meanwhile, the superlattice is complicated enough to yield band structures for normally incident acoustic waves, which is necessary for the rectification of acoustic energy flux. On the other hand, UCA suspensions were used in this study to produce the NLM samples. As the UCA microbubbles should have a relatively broad size distribution, it is possible to yield acoustic nonlinearity in a wide frequency range10 . Furthermore, the NLM made of UCA suspension exhibits extraordinary ‘physical’ nonlinearity that results from the inhomogeneous structure, rather than the ‘kinetic’ one related to the difference between the Lagrangian and the Eulerian descriptions of particle motion11–14 . As a result, particularly strong acoustic
1 Key
Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China, 2 State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190, China. † These authors contributed equally to this work. *e-mail:
[email protected];
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NATURE MATERIALS DOI: 10.1038/NMAT2881
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Figure 1 | Schematic of the experimental system and the cross-section configuration of the AD structure. The AD device was formed by coupling a superlattice with a NLM. The left and right parts of the sample refer to the superlattice and the NLM, respectively. The superlattice is fabricated by alternately laminating six water layers (denoted as I) and six glass layers (denoted as II) in a periodic manner. The grey regions represent the aluminium tubes containing the superlattice and the NLM. Two broadband transducers are used for measuring the acoustic transmission, one as a transmitter and the other as a receiver. The measurements are conducted within a water tank.
nonlinearity may exist even when the incident wave is relatively weak. Such a unique property helps to markedly enhance the sensitivity of practical AD devices. Figure 1 schematically describes the configuration of the proposed AD prototype. The superlattice was formed by alternately laminating two media (denoted as I and II) in a periodic manner. Media I and II were chosen as water and glass, respectively, and their thicknesses are defined as dI and dII . In practice, the superlattice sample was fabricated by inserting six identical round glass slabs (1.4-mm thickness) with a spatial interval of 1.2 mm in a cylindrical aluminium tube filled with water, which corresponded to the following parameter setting: dI = 1.2 mm, dII = 1.4 mm, and the total period number of the superlattice is 6. The radii of the glass slabs and the tube’s inner radius were both 50 mm, in which the propagating acoustic waves could be regarded as plane waves. The UCA microbubbles (SonoVue) were diluted using phosphate buffered saline, then sealed with polyethylene films (thin enough to be regarded as transparent to acoustic waves) in another 30-mm-long aluminium tube, with an inner radius that was also 50 mm. By coupling the resulting superlattice and NLM samples, a practical AD device was eventually constructed. To minimize the nonlinearity effect near the interface, a layer of water was left between the superlattice and the NLM samples. In general, the AD’s ‘positive’ and ‘negative’ directions are defined as the propagation directions of acoustic waves incident from the sides of the NLM and the superlattice, respectively. The experiments were conducted in a water tank (60 cm × 40 cm×40 cm) that should be large enough to neglect the reflection from its walls. For each measurement, two broadband ultrasonic transducers were used, one as a transmitter and the other as a receiver. Two series of studies were carried out to measure the frequency dependencies of acoustic transmissions for the superlattice (series 1) and the AD device (series 2). In series 1, owing to the bandwidth limitations, two pairs of ultrasonic transducers were used to fully cover the interested frequency range from 0.5 to 2.3 MHz. One pair worked at 1-MHz central frequency and 1.1-MHz bandwidth, and the other pair worked at 2.25-MHz central frequency and 2.5-MHz bandwidth. In series 2, a 1-MHz transducer was used as a transmitter, and the receiver worked at 2.25-MHz central frequency. The driving electronics consisted of 990
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Figure 2 | Measured frequency dependence of acoustic transmission for the superlattice. The green regions denote two theoretically predicted ERBs (ERB 1 or 2), in which the frequencies of the incident waves fall in the stop bands of the superlattice and their corresponding doubled frequencies sit in the pass bands (gold regions).
a waveform generator and a radiofrequency power amplifier. The waveform generator provided sinusoidal driving pulses, which were then amplified (with a fixed gain of 50 dB) and used to drive the transmitter. Unless otherwise stated, the incident acoustic pressure was kept at 5 kPa, sufficiently small for neglecting the acoustic nonlinearity of media I and II. The transmitted waves were detected by the receiver before being digitized by an oscilloscope. The oscilloscope was triggered synchronously with the driving pulses, and the detected waveforms were stored in a PC using the GPIB interface for post-processing. The acquired signals were averaged for every 16 consecutive pulses to improve the signal-to-noise ratio. In the experiments, the transmission is defined as T = Et /Ei , where Et is the total acoustic energy transmitting through the whole system, and Ei refers to that emitted from the transmitter, which is assumed to be approximately of a single frequency. Without the NLM, only the fundamental wave contributes to Et . In the presence of the NLM, however, the acoustic nonlinearity is no longer negligible and Et refers to the total energies of all frequency components acquired by the receiver. That is, Et primarily consists of the energies of the fundamental wave and the SHW. The measured transmission property of the superlattice is plotted as a function of the driving frequency in Fig. 2. Within the considered frequency range, there are four pass bands centred approximately at 0.6, 1.2, 1.8 and 2.1 MHz, respectively, consistent with the numerical results predicted using a transfer-matrix method (see Supplementary Fig. S2). It should be mentioned here that, as a significant difference between an AD and its counterparts (for example, an electric diode or a thermal diode), acoustic rectification can be achieved only when the fundamental-wave frequency falls in the stop bands of the superlattice while the SHW sits in the pass bands, and the corresponding incident wave frequencies satisfying the above condition are defined as the effective rectifying bands (ERBs). In the present study, considering the dispersion characteristics of the superlattice5 , two ERBs were analytically predicted to be located at (850 KHz, 930 KHz) and (1 MHz, 1.09 MHz). The green regions marked in Fig. 2 represent the predicted ERBs, and the yellow regions show the corresponding SHW frequency bands. It could therefore be expected that the acoustic rectification should occur within these two ERBs where the fundamental wave will evanesce but the SHW can pass. Figure 3 illustrates the frequency dependencies of the acoustic transmissions for AD devices formed with three different NLM samples, which were produced using SonoVue microbubble suspensions with different volume concentrations of ∼0.025%,
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NATURE MATERIALS DOI: 10.1038/NMAT2881 100
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Figure 4 | Comparison of the rectifying ratios for the AD models formed with three different NLM samples. Results for NLM samples produced using SonoVue microbubble suspensions with volume concentrations of ∼0.025% (blue line), 0.05% (red line) or 0.1% (black line), respectively, corresponding to the three cases in Fig. 3.
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Figure 3 | Comparison of the measured frequency dependence of acoustic transmissions along two opposite directions for the AD models formed with three different NLM samples. a–c, Results for NLM samples produced using SonoVue microbubble suspensions with volume concentrations of ∼0.025% (a), 0.05% (b) or 0.1% (c). The solid and the dashed lines refer to transmissions along the positive and the negative directions, respectively.
0.05%, or 0.1%, respectively. Significant differences between the acoustic transmissions along two opposite directions can be observed within the ERBs (green regions) for all of the measurements. This may be reasonably interpreted as the important phenomenon of acoustic rectification. Outside the ERBs, the transmissions along the positive and the negative directions are almost identical as expected, except for slight discrepancies resulting from the measurement errors. In fact, relatively low UCA volume concentrations were adopted for all of the NLM samples so that the reflection resulting from the acoustic impedance mismatch between
the water and the adjacent NLM was kept at a low level, which could improve the acoustic rectification efficiency. The origin of acoustic rectification is briefly addressed here. For an acoustic wave that propagates along the AD’s negative direction, the acoustic energy penetrating into the NLM is determined by the transmission property of the superlattice. However, when the propagation direction is reversed, the acoustic wave hits the NLM first and the acoustic energy is therefore partially transferred from the fundamental wave to the SHW. Within the ERBs, the generated SHW can penetrate the superlattice while the original fundamental wave evanesces; therefore, only part of the incident energy flux would transmit through. As for the efficiency of rectification, it is highly determined by the generated SHW amplitude, which is dependent on the UCA concentration. Figure 3b shows that higher transmitted acoustic energy can be achieved with an appropriate UCA concentration. A possible explanation for this phenomenon lies in the tradeoff between the acoustic nonlinearity and the attenuation induced by the UCA microbubbles13,14 . The energy of the SHW could be greatly reduced as a result of either the weak acoustic nonlinearity caused by an insufficient UCA concentration or the high attenuation generated by an excessive UCA concentration. The quantitative rectifying ratio of the AD device is defined as σ = T+ /T− , where T+ and T− are the measured acoustic transmissions along the positive and negative directions, respectively. The frequency dependencies of the rectifying ratio are presented in Fig. 4 for the three cases mentioned above. At an appropriate UCA concentration, the highest magnitude of the rectifying ratio is ∼104 for the present AD device with the incident wave driven at a source frequency of 1.06 MHz. In Fig. 5, the acoustic pressure dependence of the transmitted acoustic energy flux is also shown. The results indicate that the proposed AD device allows more energy to penetrate as the amplitude of the acoustic wave propagating along the positive direction increases, but keeps insulating as the propagating direction is reversed. In fact, as the asymmetric acoustic transmission of the system results from the difference between the transmission properties of the fundamental wave and the SHW, the efficiency of the AD device is therefore determined by the extent to which the system is converted to a nonlinear one, which depends on both the acoustic amplitude and the wave propagation direction7 . The acoustic pressure dependence of the transmitted energy flux illustrated in Fig. 5 exhibits a strong similarity to the voltage–ampere relationship of an electric diode, which indicates that the present structure can be
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practical AD devices, further efforts should be made to delicately investigate the influences of NLM’s acoustical properties. Such efforts would benefit the optimization of the design strategy but are beyond the scope of the present Letter. Generally, the proposed AD device offers several advantages, for example, a simple fabrication procedure, low cost, high extensibility and compatibility with other instruments. Therefore, it is promising to fabricate effective AD devices that may be applied to various practical situations where the acoustic waves need to be specially controlled, for example, the significant medical application of ultrasound. In particular, the AD device is extremely robust against backtracking waves with quite large amplitudes. This is particularly meaningful for therapeutic applications of high-intensity focused ultrasound.
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Received 17 June 2010; accepted 15 September 2010; published online 24 October 2010
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Figure 5 | Comparison of the pressure dependence of the transmitted acoustic energy flux for the AD models formed with three different NLM samples. Results for NLM samples produced using SonoVue microbubble suspensions with volume concentrations of ∼0.025% (blue line), 0.05% (red line) or 0.1% (black line), respectively, corresponding to the three cases in Figs 3 and 4.
reasonably considered as an effective AD device. As a comparison, an electric diode may undergo the well-known ‘reverse breakdown’ characterized by the phenomenon that the insulator collapses and conducts in reverse as the reverse bias exceeds a threshold. However, an AD device exhibits an extremely high resistance to such a ‘reverse breakdown’ phenomenon because of the exponential attenuation of the fundamental wave within the stop bands of the superlattice. Another point that can be observed in Fig. 5 is that the transmitted acoustic energy flux along the positive direction might shrink as the amplitude of the incident wave becomes excessively large, probably because the UCA microbubbles collapse quickly when undergoing severe pulsation. It is therefore suggested that NLMs with a higher stability should be pursued to improve the reliability of acoustic rectification, which is a challenge for the design and fabrication of practical AD devices. With the first experimental realization of an acoustic rectifier, acoustic waves should no longer be considered to always travel easily in both directions in a given path, as perceived traditionally. Although it is well known that, for example, laser reflection can be conveniently prevented using polarization effects, there exists no analogous way to build a one-way mirror for acoustic waves that generally exhibit no polarization. Now, a realistic AD prototype device is constructed simply by coupling a superlattice with a NLM layer. The NLM layers are produced with commercial UCA (SonoVue) suspensions, which are easy to make and have been proved to be clinically safe. It should be stressed that the significance of the present work is to experimentally realize an acoustic rectifier for the first time. As the acoustical properties of UCA (for example, actual acoustic nonlinearity and dispersion and so on) are very complicated13,14 and indeed significantly affect the performance of
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Acknowledgements This work was financially supported in part by National Basic Research Program 973 of China (Grant No. 2011CB707900), the National Science Foundation of China (Grant Nos. 10804050, 10874086, 10974093, 10704037, 10774072, 11074123 and 10974095), the Ministry of Education of China under Grant No 20060284035 and No 705017 and the Research Fund for the Doctoral Program (for new scholar) of Higher Education of China (20070284070).
Author contributions B.L., X.S.G. and J.T. carried out the experiments and interpreted the data. J.C.C. and D.Z. conceived and supervised the study. All of the authors wrote the paper.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper on www.nature.com/naturematerials. Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should be addressed to J.C.C. or D.Z.
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