One-channel time reversal focusing of ultra-high frequency acoustic waves on a MEMS

Time Reversal (TR) is based on the use of reciprocity and time reversal invariance of the wave equation.11. A. Parvulescu and C. S. Clay, “ Reproducibility of signal transmissions in the ocean,” Radio Electron. Eng. 29, 223–228 (1965). https://doi.org/10.1049/ree.1965.0047 In particular, time-reversed acoustics2,32. M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, “ Time-reversed acoustics,” Rep. Prog. Phys. 63, 1933–1995 (2000). https://doi.org/10.1088/0034-4885/63/12/2023. F. Wu, J.-L. Thomas, and M. Fink, “ Time reversal of ultrasonic fields. II. Experimental results,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 567–578 (1992). https://doi.org/10.1109/58.156175 (TRA) provides unprecedented possibilities for ultrasound (US) imaging,4–74. G. Montaldo, D. Palacio, M. Tanter, and M. Fink, “ Time reversal kaleidoscope: A smart transducer for three-dimensional ultrasonic imaging,” Appl. Phys. Lett. 84, 3879–3881 (2004). https://doi.org/10.1063/1.17381865. F. Ma, Z. Huang, C. Liu, and J. H. Wu, “ Acoustic focusing and imaging via phononic crystal and acoustic metamaterials,” J. Appl. Phys. 131, 011103 (2022). https://doi.org/10.1063/5.00745036. V. Preobrazhensky, P. Pernod, Y. Pyl'nov, L. Krutyansky, N. Smagin, and S. Preobrazhensky, “ Nonlinear acoustic imaging of isoechogenic objects and flows using ultrasound wave phase conjugation,” Acta Acust. Acust. 95, 36–45 (2009). https://doi.org/10.3813/AAA.9181257. N. Quieffin, S. Catheline, R. K. Ing, and M. Fink, “ Real-time focusing using an ultrasonic one channel time-reversal mirror coupled to a solid cavity,” J. Acoust. Soc. Am. 115, 1955–1960 (2004). https://doi.org/10.1121/1.1699396 medical ultrasound,8,98. W. S. Gan, “ Application of time-reversal acoustics to medical ultrasound imaging,” in Time Reversal Acoustics, edited by W. S. Gan ( Springer, Singapore, 2021), pp. 101–107.9. J. Rufo, P. Zhang, R. Zhong, L. P. Lee, and T. J. Huang, “ A sound approach to advancing healthcare systems: The future of biomedical acoustics,” Nat. Commun. 13, 3459 (2022). https://doi.org/10.1038/s41467-022-31014-y communications in complex media,10–1210. G. Montaldo, G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink, “ Telecommunication in a disordered environment with iterative time reversal,” Waves Random Media 14, 287–302 (2004). https://doi.org/10.1088/0959-7174/14/3/00611. G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, “ Time reversal of electromagnetic waves and telecommunication,” Radio Sci. 40, RS6S12, https://doi.org/10.1029/2004RS003193 (2005).12. G. Lerosey and M. Fink, “ Wavefront shaping for wireless communications in complex media: From time reversal to reconfigurable intelligent surfaces,” Proc. IEEE 110, 1210–1226 (2022). https://doi.org/10.1109/JPROC.2022.3187339 and nondestructive evaluation (NDE).13–1613. N. Chakroun, M. Fink, and F. Wu, “ Time reversal processing in ultrasonic nondestructive testing,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 1087–1098 (1995). https://doi.org/10.1109/58.47655214. C. H. Wang, J. T. Rose, and F.-K. Chang, “ A synthetic time-reversal imaging method for structural health monitoring,” Smart Mater. Struct. 13, 415 (2004). https://doi.org/10.1088/0964-1726/13/2/02015. N. Smagin, A. Trifonov, O. Bou Matar, and V. Aleshin, “ Local damage detection by nonlinear coda wave interferometry combined with time reversal,” Ultrasonics 108, 106226 (2020). https://doi.org/10.1016/j.ultras.2020.10622616. T. J. Ulrich, A. M. Sutin, T. Claytor, P. Papin, P.-Y. Le Bas, and J. A. TenCate, “ The time reversed elastic nonlinearity diagnostic applied to evaluation of diffusion bonds,” Appl. Phys. Lett. 93, 151914 (2008). https://doi.org/10.1063/1.2998408 Initially, TR focusing (TRF) was considered with the use of multi-element phased array transducer able to record an acoustic field over extended spatial regions. Later, a one-channel TR was introduced as a low-cost technique able to focus acoustic energy anywhere17,1817. A. M. Sutin, J. A. TenCate, and P. A. Johnson, “ Single-channel time reversal in elastic solids,” J. Acoust. Soc. Am. 116, 2779–2784 (2004). https://doi.org/10.1121/1.180267618. C. Draeger and M. Fink, “ One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997). https://doi.org/10.1103/PhysRevLett.79.407 even on a 3D domain,1919. G. Montaldo, D. Palacio, M. Tanter, and M. Fink, “ Building three-dimensional images using a time-reversal chaotic cavity,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1489–1497 (2005). https://doi.org/10.1109/TUFFC.2005.1516021 with a spatiotemporal resolution comparable to that of multiple transducer array.4,20–224. G. Montaldo, D. Palacio, M. Tanter, and M. Fink, “ Time reversal kaleidoscope: A smart transducer for three-dimensional ultrasonic imaging,” Appl. Phys. Lett. 84, 3879–3881 (2004). https://doi.org/10.1063/1.173818620. B. Van Damme, K. Van Den Abeele, Y. Li, and O. B. Matar, “ Time reversed acoustics techniques for elastic imaging in reverberant and nonreverberant media: An experimental study of the chaotic cavity transducer concept,” J. Appl. Phys. 109, 104910 (2011). https://doi.org/10.1063/1.359016321. P. Roux, B. Roman, and M. Fink, “ Time-reversal in an ultrasonic waveguide,” Appl. Phys. Lett. 70, 1811–1813 (1997). https://doi.org/10.1063/1.11873022. A. P. Sarvazyan, L. Fillinger, and L. R. Gavrilov, “ A comparative study of systems used for dynamic focusing of ultrasound,” Acoust. Phys. 55, 630–637 (2009). https://doi.org/10.1134/S1063771009040198 Implementation of this technique requires a multi-reverberating regime that could be obtained by confining an ultrasonic field in an ergodic structure called a chaotic cavity.1818. C. Draeger and M. Fink, “ One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity,” Phys. Rev. Lett. 79, 407–410 (1997). https://doi.org/10.1103/PhysRevLett.79.407 Thus, the loss of spatial information is compensated by increased temporal information.The reported TRA devices operate in the medical or the NDE frequency range (0.1–10 s MHz), and their spatial resolution is of the order of wavelength. Additionally, TR sub-wavelength focusing and super-resolution imaging could be achieved using phononic crystals and acoustic metamaterials.55. F. Ma, Z. Huang, C. Liu, and J. H. Wu, “ Acoustic focusing and imaging via phononic crystal and acoustic metamaterials,” J. Appl. Phys. 131, 011103 (2022). https://doi.org/10.1063/5.0074503 For homogeneous media, exploiting TRF capabilities in the micrometric scale necessitates shifting the operating frequency toward the ultra-high frequency (UHF) range.This Letter reports a feasibility of one-channel TRF of UHF (0.2–2 GHz) acoustic waves in the MEMS context. The overall device size is about 2 × 2 mm2; an acoustic reverberating medium was obtained by micromachining a standard silicon wafer. Integrated Zinc oxide (ZnO) transducers were used as emitters/receivers. The presented MEMS prototype is intended to provide a space-resolved measurement option for characterization techniques in the microfluidics domain, such as measurement of microdroplets viscosity,2323. I. Zaaroura, M. Toubal, J. Carlier, S. Harmand, and B. Nongaillard, “ Nanofluids dynamic viscosity evolution using high-frequency acoustic waves: Application applied for droplet evaporation,” J. Mol. Liquids 341, 117385 (2021). https://doi.org/10.1016/j.molliq.2021.117385 mixture concentration,2424. P. Chen, M. Toubal, J. Carlier, S. Harmand, B. Nongaillard, and M. Bigerelle, “ Evaporation of binary sessile drops: Infrared and acoustic methods to track alcohol concentration at the interface and on the surface,” Langmuir 32, 9836–9845 (2016). https://doi.org/10.1021/acs.langmuir.6b02564 wetting,2525. A. R. Salhab, J. Carlier, P. Campistron, M. Neyens, M. Toubal, B. Nongaillard, and V. Thomy, “ Polydimethylsiloxane micro-channels application for the study of dynamic wetting of nano-etched silicon surfaces based on acoustic characterization method,” Solid State Phenom. 314, 143–149 (2021). https://doi.org/10.4028/www.scientific.net/SSP.314.143 and others. As the authors are aware, this is the first implementation of acoustic UHF TR of acoustic waves. Earlier, the UHF range has been explored for TRF of electromagnetic waves.2626. M. Davy, J. de Rosny, J.-C. Joly, and M. Fink, “ Focusing and amplification of electromagnetic waves by time reversal in a leaky reverberation chamber,” C. R. Phys. Propag. Remote Sensing 11, 37–43 (2010). https://doi.org/10.1016/j.crhy.2009.12.008Figure 1(a) gives an overall schematics of the MEMS for TR imaging. The main structural element of the device is a 400 μm thick double-side polished silicon wafer of (110) crystalline orientation. The ergodic and chaotic ultrasound propagation was obtained by introducing irregularities using anisotropic wet etching [Fig. 1(b)]. The etched structures were represented by 220 μm height truncate pyramids whose lateral sides were inclined by 54.7° relative to their base (base dimensions are of order 1000 × 1000 μm2). Such an approach gave a possibility to obtain a diffused acoustic field in the partially confined region (leaky cavity)22,2722. A. P. Sarvazyan, L. Fillinger, and L. R. Gavrilov, “ A comparative study of systems used for dynamic focusing of ultrasound,” Acoust. Phys. 55, 630–637 (2009). https://doi.org/10.1134/S106377100904019827. B. Arnal, M. Pernot, M. Fink, and M. Tanter, “ Tunable time-reversal cavity for high-pressure ultrasonic pulses generation: A tradeoff between transmission and time compression,” Appl. Phys. Lett. 101, 064104 (2012). https://doi.org/10.1063/1.4742930 surrounded by etched volumes [shown with red highlighting in Figs. 1(b) and 1(c)]. Due to the partial confinement, the diffused acoustic field could be observed in the region of the mentioned leaky cavity as well as outside of it. Two receiving transducer arrays referred to as Ri,j and Rk were placed on the opposite side of the wafer, in the regions inside and outside the confined zone, respectively. The emitter E was situated in front of the inclined mirror to enhance multiple reflections [Figs. 1(a) and 1(b)]. The piezoelectric transducers were made of Zinc Oxide (ZnO). They had a diameter of 100 μm and a thickness of 2 μm. The receiving transducers Ri,j and Rk were spaced with a 190 μm pitch.The starting phase of the MEMS fabrication consists in introducing irregularities in ultrasound propagation media.2828. M. Hoffmann and E. Voges, “ Bulk silicon micromachining for MEMS in optical communication systems,” J. Micromech. Microeng. 12, 349 (2002). https://doi.org/10.1088/0960-1317/12/4/301 In the first step of the anisotropic wet etching [1 in Fig. 1(d)], two 1600 nm layers of silicon oxide (SiO2) were produced by thermal oxidation on both sides of the Si wafer. The oxidation was carried out at a high temperature (900–1000 °C) in water vapor (H2O). After step 2 in Fig. 1(d), the SiO2 layer was locally etched with hydrofluoric acid (HF) via a 2 μm thick positive photoresist mask (PMGI SF19 from Microchem Corporation and S1828 from Shipley Corporation) aligned in the ⟨110⟩ direction. The photoresist was then eliminated with acetone. Furthermore, in the third step, the silicon patterns were etched through the SiO2 mask with 20% potassium hydroxide (KOH) at 80 °C. The etching is performed in the plane at approximately 73 μm/h. Since the KOH wet etching is anisotropic, the etching rates are not equal for different crystal directions resulting in 54.7° lateral flanks inclination relative to the ⟨110⟩ Si plane2929. J. Gao, J. Carlier, S. Wang, P. Campistron, D. Callens, S. Guo, X. Zhao, and B. Nongaillard, “ Lab-on-a-chip for high frequency acoustic characterization,” Sens. Actuators B 177, 753–760 (2013). https://doi.org/10.1016/j.snb.2012.11.037 [step 4 in Fig. 1(d)]. This inclination is visible in the SEM image in Fig. 1(b). Figure 1(c) presents several neighboring etched pyramids dedicated to acoustic propagation confinement. Low intrinsic acoustical attenuation of silicon and high reflectivity of etched walls contribute to establishing long propagation paths and multiple reflections of acoustic waves.3030. V. B. Thati, N. Smagin, H. Dahmani, J. Carlier, and I. Alouani, “ Identification of ultra high frequency acoustic coda waves using deep neural networks,” IEEE Sens. J. 21, 20640–20647 (2021). https://doi.org/10.1109/JSEN.2021.3099078The MEMS fabrication's second phase consists of integrating the ZnO piezoelectric transducer array on the rear face of the substrate [Fig. 1(e)]. The process began with the deposition of the lower electrode, consisting of two layers: 10 nm of the titanium adhesion layer and 80 nm of the platinum conductive layer [step 1 in Fig. 1(e)]. A photolithography process was then performed to make the transducer's pattern, where a thick 8 μm layer of PMGI SF19 was dispensed by spin coating on the lower electrode. Furthermore, a layer of 1.5 μm of S1828 was appended (step 2). After ultraviolet exposure using a mask (step 3), a commercial developer MF 319 (Microposit) was used to obtain a pattern of 100 μm diameter circular transducers in the PMGI layer (step 4). Next, a 2 μm thin ZnO layer was deposed (step 5). Finally, 10 nm of titanium adhesion layer followed by 400 nm of gold was deposited. The last step is the lift-off process using SVC 14 (Shipley Corporation), where the UV-exposed resin is removed.Photography of the micromachined transducer array can be seen in Fig. 1(f). The transducer electrical response was measured with a manual radio frequency (RF) probe station connected to a Vector Network Analyzer (VNA) Tektronix TTR 503. The used RF probes (|Z|-Prob from Cascade Microtech with a 1250 μm pitch) were flexible enough to assure simultaneous electric contact with the transducer's top and bottom electrodes. The characterization measurement was carried out on a silicon wafer with no etching to reveal the response features related to the transducers only. Figures 1(g) and 1(h) reveal the S11 parameter measurement performed for one of the transducers in the time and frequency domain, respectively. In a frequency domain, it can be decomposed into two contributions as follows: S11=S11 el+K11S11 ac. Here, S11 el is the reflection of the electromagnetic wave on the transducer due to a non-perfect electrical matching, S11 ac represents all the acoustic wave reflections on the opposite side of the substrate converted into an electrical signal, and K11 is the electro-acoustic-electrical coupling coefficient of the ZnO transducer.In the time domain, S11 signal is obtained with inverse Fast Fourier Transform (FFT). The electrical term S11 el response appears shortly after the transducer's excitation. In contrast, the group of acoustic terms arises later [Fig. 1(g)]. The crystal orientation of the ZnO was intentionally set to be not perfectly vertical. That favored the generation of acoustic shear waves (SS), seen in the waveform among the longitudinal wave echoes (LL).3131. H. Dahmani, I. Zaaroura, A. Salhab, P. Campistron, J. Carlier, M. Toubal, S. Harmand, V. Thomy, M. Neyens, and B. Nongaillard, “ Fabrication and optimization of high frequency ZnO transducers for both longitudinal and shear emission: Application of viscosity measurement using ultrasound,” Adv. Sci. Technol. Eng. Syst. J. 5, 1428–1435 (2020). https://doi.org/10.25046/aj0506173 The acoustic-only transducer response can be obtained by gating the time domain signal after approximately 25 ns and performing the FFT. The resulting curve of real S11 part in Fig. 1(h) also reveals the presence of the transversal mode. The observed echoes correspond to the different acoustic signals traveling back and forth in the silicon wafer. They are separated by periods of 10.5 MHz for longitudinal waves and 7.4 MHz for shear waves [inset in Fig. 1(h)], defined by the Si wafer's double thickness (800 μm) and propagation velocity of the corresponding wave component (VL = 8432 and VS = 5843 m/s, respectively). In conclusion, the ZnO transducer's response shows that the latter can produce both longitudinal and shear waves in the ≈2 GHz range with a central frequency of 0.9 GHz for longitudinal waves.The magnitude of mechanical displacement provided by ZnO transducers was measured by a Polytec UHF-120 laser Doppler vibrometer (LDV). The transducer was driven with a continuous sinusoidal signal by a Marconi 2030 RF generator connected to a power amplifier (Amplifier Research 50W1000A). The power of the electrical signal applied to the transducer was about 10 W. It was determined by the electrical breakdown limit of the 2 μm thick ZnO. The excitation signal was swept around a central frequency of 0.9 GHz with a 105 MHz span. Optical measurements were carried out in the frequency domain using the “peak hold” mode. As a result (Fig. 2), the measured displacement magnitude is about 25 pm. The mechanical behavior exhibited by the transducer is wideband and relevant to its electrically measured S11 ac response [Fig. 1(h)]. The noise level of the vibrometer acquisition for time domain measurements is of the same order (20 pm) as the response for quasi-continuous excitation detected in a frequency mode. Furthermore, the displacement level provided by the ZnO transducer is considerably lower using pulsed excitation necessary for TRF. For this reason, time domain measurements with pulsed excitation (0.2–2 GHz linear chirp) were unsuccessful as the signal amplitude stayed below the mentioned noise level. In summary, the obtained displacement level was insufficient for TRF using vibrometer measurement, and the TR results reported below were obtained by electrical acquisition with arrays of receiving transducers.One of the micromachined regions allowing acoustic field confinement is shown in Fig. 3(a). The central part possessing the initial layer thickness of 400 μm is surrounded from four sides with etched volumes. An emitter E is placed in front of the lateral mirror to reinforce multiple reflections. The internal volume of the leaky cavity is referred to as “Zone A” in Fig. 3(a) and in the sectional view S in Fig. 3(b). The “Zone A” area is 1480 × 720 μm2; it contains an array of receivers Ri,j (i=1,2; j=1…6) placed to characterize the acoustic wave propagation. Another receiver array Rk (k=1…4) is placed in one of the zones outside the leaky cavity referred to as “Zone B” in Figs. 3(a) and 3(b).The impulse responses between the emitter and receivers were obtained with inverse FFT of the S12(f) measurements carried out on the RF probe station mentioned above [Fig. 1(f)]. As an example, the S12(f) signal between the emitter and the R2 receiver from the “Zone B” is presented in Fig. 3(c). The observed features reveal the presence of diffused field: several ballistic arrivals at the beginning of the signal, increasing wave mixture, and exponentially decaying coda “tail” starting at t0 = 0.83 μs. The estimated decaying rate linked with the attenuation in bulk Si is of 22 dB/μs. Thus, the coda signal is observable during approximately 1 μs, which contains about 900 periods at the central transducer frequency of 0.9 GHz. Such attenuation level might be sufficient for one-channel TR.77. N. Quieffin, S. Catheline, R. K. Ing, and M. Fink, “ Real-time focusing using an ultrasonic one channel time-reversal mirror coupled to a solid cavity,” J. Acoust. Soc. Am. 115, 1955–1960 (2004). https://doi.org/10.1121/1.1699396Ergodic properties of the media could be verified using cross correlation analysis. Figure 3(d) presents the matrix of normalized cross correlation coefficients between all considered receivers. The correlation between noisy-like coda signals propagating in zones “A” and “B” is rather low, being within the range from −30 to −20 dB. Additionally, the correlation between the signals received in zone “B” is rather low as well, staying within limits from −25 to −15 dB. On the contrary, several elevated values of the coefficient (from −10 to −5 dB) could be observed for adjacent receivers in zone “A.” This observation indicates that using zone “B” external to the leaky cavity could be preferable due to better ergodicity.The presented MEMS allowed one-channel TR focusing of UHF ultrasonic waves. This goal has been achieved with the experimental setup presented in Fig. 4(a), which consisted of excitation (arbitrary waveform generator Tektronix AWG 70002A) and acquisition (digital phosphor oscilloscope Tektronix DPO 71254C) units connected via Ethernet to a personal computer (PC). To improve the quality of spatiotemporal energy focusing, we used a linear chirped signal S(t) for emitter excitation.20,3220. B. Van Damme, K. Van Den Abeele, Y. Li, and O. B. Matar, “ Time reversed acoustics techniques for elastic imaging in reverberant and nonreverberant media: An experimental study of the chaotic cavity transducer concept,” J. Appl. Phys. 109, 104910 (2011). https://doi.org/10.1063/1.359016332. T. Misaridis and J. Jensen, “ Use of modulated excitation signals in medical ultrasound. Part I: Basic concepts and expected benefits,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 177–191 (2005). https://doi.org/10.1109/TUFFC.2005.1406545 The 0.2–2 GHz linear up chirp was synthetized at 12.5 Gs/s, had a duration of 0.5 μs, and an amplitude of 0.5 Vpp. The received signals R(t) were digitized by the oscilloscope at the same rate of 12.5 Gs/s during 4 μs.We implemented a reciprocal TR focusing using deconvolution33,3433. M. Tanter, J.-L. Thomas, and M. Fink, “ Time reversal and the inverse filter,” J. Acoust. Soc. Am. 108, 223–234 (2000). https://doi.org/10.1121/1.42945934. M. Tanter, J.-F. Aubry, J. Gerber, J.-L. Thomas, and M. Fink, “ Optimal focusing by spatio-temporal inverse filter. I. Basic principles,” J. Acoust. Soc. Am. 110, 37–47 (2001). https://doi.org/10.1121/1.1377051 (or inverse filtering) procedure consisted of (i) recording the response for the chirped excitation R(t); (ii) reconstructing propagation media impulse response (IR) by cross-correlating the chirp source S(t) with the received signal from the chirp: IR(t)=R(t)⊛S(t); and (iii) rebroadcasting by the emitter E of the time-reversed impulse response IR(−t). A full deconvolution comprising the acasual part has been used.35,3635. T. J. Ulrich, B. Anderson, P.-Y. L. Bas, C. Payan, J. Douma, and R. Snieder, “ Improving time reversal focusing through deconvolution: 20 questions,” Proc. Meet. Acoust. 16, 045015 (2012). https://doi.org/10.1121/1.476448736. B. E. Anderson, J. Douma, T. Ulrich, and R. Snieder, “ Improving spatio-temporal focusing and source reconstruction through deconvolution,” Wave Motion 52, 151–159 (2015). https://doi.org/10.1016/j.wavemoti.2014.10.001The corresponding time-compressed signal received by R2 is shown in Fig. 4(b) with the blue curve, while the red one depicts the rebroadcasted IR(−t). The peak amplitude for a 250 mV0−p excitation is 0.5 mV. Its width is 0.72 ns, which corresponds to ≈ 1.4 GHz. The presence of distinguishable periodic peaks on the impulse response and rather high sidelobes level (11.2 dB) indicate that the degree of the cavity's symmetry is still high.37,3837. C. Draeger, J.-C. Aime, and M. Fink, “ One-channel time-reversal in chaotic cavities: Experimental results,” J. Acoust. Soc. Am. 105, 618–625 (1999). https://doi.org/10.1121/1.42625238. T. Goursolle, S. Callé, S. Dos Santos, and O. Bou Matar, “ A two-dimensional pseudospectral model for time reversal and nonlinear elastic wave spectroscopy,” J. Acoust. Soc. Am. 122, 3220–3229 (2007). https://doi.org/10.1121/1.2799900 The peak-to-noise factor is 21.5 dB.The peak amplitude can be increased by implementing such procedures as 1-bit TR39,4039. A. Derode, A. Tourin, and M. Fink, “ Ultrasonic pulse compression with one-bit time reversal through multiple scattering,” J. Appl. Phys. 85, 6343–6352 (1999). https://doi.org/10.1063/1.37013640. G. Montaldo, P. Roux, A. Derode, C. Negreira, and M. Fink, “ Generation of very high pressure pulses with 1-bit time reversal in a solid waveguide,” J. Acoust. Soc. Am. 110, 2849–2857 (2001). https://doi.org/10.1121/1.1413753 or normalizing the IR(−t) by its envelope. We implemented the latter technique and achieved a ×6 enhancement up to 3 mV level [Fig. 4(c)]. In turn, this introduced some asymmetry and decreased the sidelobe ratio (8 dB), as well as peak-to-noise factor (14.8 dB). The duration of the retransmitted signal is 2 μs; the recompression peak appears almost at the end of the emission, preceded by an uncorrelated noise-like part (0.42 mV level). After the focal peak, the signal rings out within less than 2 μs.The best theoretically achievable spatial resolution is of the order of one wavelength.77. N. Quieffin, S. Catheline, R. K. Ing, and M. Fink, “ Real-time focusing using an ultrasonic one channel time-reversal mirror coupled to a solid cavity,” J. Acoust. Soc. Am. 115, 1955–1960 (2004). https://doi.org/10.1121/1.1699396 For the given central frequency of 0.9 GHz, the spatial resolution is of 10 μm order, which is significantly smaller than the spacing of the receivers (190 μm). As mentioned above, the ultrasound vibrations level was insufficient for optical measurement of the acoustic field on the MEMS surface, so the direct estimation of the spatial compression was not possible. However, the presence of spatial compression can be confirmed by simultaneous reception by the arrays Rij and Rk. To this end, Fig. 4(d) shows a 3D waterfall plot containing signals received by the Rk array and arbitrarily chosen R11 and R22 from Rij. The focalization is effectuated on R2 with normalized IR(−t). Only this channel exhibits a recompression peak. All other signals contain only the uncorrelated noise-like parts preceding the peak for R2. The distribution of the non-compressed field is uniform within the studied region.In order to characterize the amount of temporal focusing, we used the temporal compression ratio ξt=EF/ET, where EF is the energy in the main peak of the TR signal, and ET is the total signal energy.35,4135. T. J. Ulrich, B. Anderson, P.-Y. L. Bas, C. Payan, J. Douma, and R. Snieder, “ Improving time reversal focusing through deconvolution: 20 questions,” Proc. Meet. Acoust. 16, 045015 (2012). https://doi.org/10.1121/1.476448741. T. Strohmer, M. Emami, J. Hansen, G. Papanicolaou, and A. Paulraj, “ Application of time-reversal with MMSE equalizer to UWB communications,” in IEEE Global Telecommunications Conference, GLOBECOM '04 ( IEEE, 2004), Vol. 5, pp. 3123–3127. ξt shows the amount of energy that is within the focal region (referred to as “Focal Energy” in Fig. 5) as opposed to the amount of energy that remains outside of that time interval (“Total Signal” in Fig. 5). The ratio should approach 1 for perfect focusing. The double duration of the rebroadcasted IR is used (4 μs) to let the signal ring out and calculate ET.We consider the TR signals at R2 as in Figs. 4(b) and 4(c) to calculate ξt. For the time compression using deconvolution, ξt = 29.6%, which is relevant to other data found in the literature for a lower frequency range.3535. T. J. Ulrich, B. Anderson, P.-Y. L. Bas, C. Payan, J. Douma, and R. Snieder, “ Improving time reversal focusing through deconvolution: 20 questions,” Proc. Meet. Acoust. 16, 045015 (2012). https://doi.org/10.1121/1.4764487 As observed, ξt becomes lower for TR focusing using normalized IR, decreasing to 7.8%.In conclusion, we have shown the feasibility of focusing UHF (0.2–2 GHz) ultrasounds in the MEMS context with a single ZnO micro-transducer coupled to a silicon wafer and using the deconvolution TR process. Measurements revealed that TRF is stronger in the zone external to the leaky cavity [“Zone B,” Fig. 3(b)] compared to the internal cavity volume22,2722. A. P. Sarvazyan, L. Fillinger, and L. R. Gavrilov, “ A comparative study of systems used for dynamic focusing of ultrasound,” Acoust. Phys. 55, 630–637 (2009). https://doi.org/10.1134/S106377100904019827. B. Arnal, M. Pernot, M. Fink, and M. Tanter, “ Tunable time-reversal cavity for high-pressure ultrasonic pulses generation: A tradeoff between transmission and time compression,” Appl. Phys. Lett. 101, 064104 (2012). https://doi.org/10.1063/1.4742930 (“Zone A”). In this case, the latter acts as a resonator with a weak quality factor and a strong leakage. In the future work, we plan to introduce more complex geometries (such as circular patterns) to increase ergodicity and minimize the sidelobes.

The focusing “library” of impulse responses was recorded by an array of UHF transducers identical to the receiver. For imaging purposes, ideally, the formation of the “library” should be effectuated with LDV scanning. However, we used ZnO receivers because of the emitter limitation in provided vibrations level. Integrating an emitter with a higher electromechanical coeffi

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