Active acoustic metamaterials reconfigurable in real-time
Bogdan-Ioan Popa, Durvesh Shinde, Adam Konneker, Steven A. Cummer
aa r X i v : . [ phy s i c s . c l a ss - ph ] M a y Active acoustic metamaterials reconfigurable in real-time
Bogdan-Ioan Popa, ∗ Durvesh Shinde, Adam Konneker, and Steven A. Cummer † Department of Electrical and Computer Engineering, Duke University, North Carolina 27708 (Dated: May 5, 2015)A major limitation of current acoustic metamaterials is that their acoustic properties are eitherlocked into place once fabricated or only modestly tunable, tying them to the particular applica-tion for which they are designed. We present in this paper a design approach that yields activemetamaterials whose physical structure is fixed, yet their local acoustic response can be changed al-most arbitrarily and in real-time by configuring the digital electronics that control the metamaterialacoustic properties. We demonstrate experimentally this approach by designing a metamaterial slabconfigured to act as a very thin acoustic lens that manipulates differently three identical, consecu-tive pulses incident on the lens. Moreover, we show that the slab can be configured to implementsimultaneously various roles, such as that of a lens and beam steering device. Finally, we show thatthe metamaterial slab is suitable for efficient second harmonic acoustic imaging devices capable toovercome the diffraction limit of linear lenses. These advantages demonstrate the versatility of thisactive metamaterial and highlight its broad applicability, in particular to acoustic imaging.
Acoustic metamaterials significantly expand our abil-ity to manipulate sound by enabling material parametersthat are not easily available in natural media, such asnegative mass density, bulk modulus, and refractive in-dex [1–7], as well as highly anisotropic [8–11] and evenunidirectional acoustic properties [12–15]. Most impor-tantly, they allow rigid materials to behave as regularfluids and are consequently suitable for robust devicesfor sound control. As a result, recent years have seena remarkable development of new classes of metamateri-als that are suitable for numerous applications, such asexotic sound cancellation [16–18] and improved acousticimaging devices [19–22].One of the drawbacks of most reported metamateri-als is that their functionality is locked into place oncethey are fabricated. There are scenarios where it is de-sirable to tune their properties dynamically as neededrather than building a new device for each particular ap-plication. There are currently only a few designs thatpromise to address this limitation [14, 23–26]. Thus, re-cent advances on active metamaterials employing elec-tronic circuits in their structure provide a natural pathtowards tunable metamaterials [14, 23–25]. Other ap-proaches involve the use of variable magnetic fields tocontrol the properties of pre-stretched membranes [26].However, these designs merely tweak a particular mate-rial parameter in a relatively narrow range. It would beadvantageous to change entirely the metamaterial func-tionality in a dynamic manner.We show in this paper that active acoustic metamate-rials provide an ideal platform to design versatile mediawhose acoustic properties are easily configured dynami-cally. To demonstrate this concept, we fabricate a meta-material slab and demonstrate the following two features.First, its functionality can be set in real-time withoutchanging the physical structure of the slab. Second, it ∗ [email protected] † [email protected] can implement acoustic properties not easily available inmetamaterials designed through other methods. Acous-tic imaging is a promising area of application for acousticmetamaterials [19–22], therefore the experimental illus-tration of the benefits of our design method will havethese applications in mind. More specifically, to provethe first point we send a plane wave consisting of threemodulated Gaussian pulses coming in quick succession,and configure the slab to act as an acoustic lens whoseproperties are changed rapidly so that each pulse is ma-nipulated differently.To demonstrate the second point, we configure the slabto play simultaneously two different roles, namely thatof a beam steering device and focusing lens. In addi-tion, we show how very small F-numbers of less than 0.5are possible in a very thin lens whose thickness is lessthan a tenth of the wavelength. Moreover, we use thisopportunity to demonstrate experimentally an idea firstpresented in the context of electromagnetic metamateri-als, namely that imaging using higher order harmonics ofthe incident field can beat the diffraction limit associatedwith linear devices.The metamaterial unit cell follows the general archi-tecture described in Refs. 14 and 24. It consists of athree terminal piezoelectric membrane produced by Mu-rata Inc. augmented by electronics, as illustrated in Fig.1a. The incident sound is sampled by the membrane’ssensing terminal, which creates an electric signal propor-tional to the acoustic excitation. The signal is ampli-fied in a pre-amplifier of gain G S and passes through abandpass filter of bandwidth 20% centered on frequency f = 1500 Hz. It then enters a block of reconfigurableelectronics that essentially determines the metamaterialfunctionality. Since the focus here is on second harmonicimaging applications, one of the functions of this stageis to create the second harmonic. The resulting signalpasses through a second bandpass filter of bandwidth20% centered on 2 f = 3000 Hz, and it is further amplified(gain G D ) and drives the main terminal of the piezoelec-tric membrane, thus creating the acoustic response of the DrivenGroundSensingGBandpass (f) GBandpass (2f)
S D
Reconfigurable electronics a bc
FIG. 1. Reconfigurable metamaterial unit cell. (a) The unitcell consists of a piezoelectric membrane controlled by elec-tronics. The cell acoustic response is controlled by a digitalelectronic circuit that can be reconfigured in real-time. (b)Photograph of fabricated unit cell. (c) Metamaterial slab con-sisting of ten unit cells. cell. To increase cell repeatability and the overall flex-ibility of the system, the bandpass filters together withthe reconfigurable electronics are implemented digitallyin a digital signal processor (DSP) produced by Atmel(SAM3X8E). The cell functionality is thus set by up-loading various programs into the DSP.To better match acoustically the piezoelectric mem-brane to the surrounding environment, the membrane ismounted between two identical Helmholtz cavities madeof Plexiglas and designed according to the membranemanufacturer recommendations. Thus, each cavity hasa height 3.2 mm, a circular cross section of diameter 33mm, and end with an opening whose diameter is 6 mm.Figure 1b shows a photo of the metamaterial unit cell,and Fig. 1c presents a metamaterial slab composed often identical unit cells.The goal of this paper is to leverage the flexibil-ity afforded by the reconfigurable electronics block andchange the metamaterial functionality without changingits physical structure. The first application is to con-figure the slab to act as an acoustic metamaterial lens(AML) that images a distant object by focusing the planewave incident on it into a focal spot in the lens vicinity.This has been done using passive materials and varioustechniques [20–22, 27, 28]. Here we emphasize the config-urability feature of this design method by changing thelens parameters, namely focal length and direction of thefocused beam, in real-time as the incident wave hits thelens.The acoustic behavior of the AML is characterizedexperimentally inside a two-dimensional (2D) acousticwaveguide composed of two square parallel plastic sheets a I n c i d e n t w a v e ( a r b . u n i t s ) b Time [ms]10.5-0.5
FIG. 2. Experimental setup. (a) Top view sketch of the 2Dacoustic waveguide showing the metamaterial slab positionedin the middle of the waveguide. The incident sound consists ofa series of three identical, closely spaced pulses. The acousticfield is measured in the highlighted waveguide region behindthe metamaterial in which the metamaterial response to thefirst pulse is shown. (b) Time domain variation of the incidentsound field.
120 cm long and separated by 5 cm. The latter dimen-sion coincides with the metamaterial unit cell size. Atop-view schematic of the waveguide showing the lensplaced in the middle is presented in Fig. 2a. A planewave is obtained inside the waveguide using an array of12 in-phase speakers placed on the left edge of the waveg-uide. The plane wave consists of three identical Gaussianpulses modulated by a sinusoid at 1500 Hz separated by13 ms. The spatial distribution of the wave is sketched inFig. 2a, and its time domain evolution at the AML po-sition is given in Fig. 2b. Our purpose is to reconfigurethe lens in between the pulses so that the lens behavioris different for each pulse. More specifically, the targetAML parameters for the three pulses are given by thepairs (30 cm, 30 ◦ ), (20 cm, -30 ◦ ), and (30 cm, 0 ◦ ), re-spectively, where the first parameter of the pair is thefocal length, and the second is the angle that the focusedbeam makes with the horizontal.The fields on the transmission side of the AML aremeasured using a microphone that scans the waveguideinterior on a square grid of points separated by 2 cm inboth the horizontal and vertical directions. To obtain avisually more pleasing image of the fields, the measure-ments are spatially interpolated to double the number ofsampled points in each directions. A typical measure-ment is shown in Fig. 2a to illustrate the scanned arearelative the the lens position.Acoustic lenses can be realized in several ways. Forexample, curved surfaces [29] could be used to trans-form the incident acoustic field into a converging field.Gradient-index metamaterials could achieve the same ef-fect by varying the delay of the acoustic wave as it prop-agates through various parts of a flat lens [20–22, 27, 28].We employ here the latter idea. However, instead of de-laying the incident wave inside the material itself we en-gineer the delay in electronics. This approach addressestwo inherent limitations of passive designs, namely lensescan be made much thinner than through other methodsand the focal distance and, consequently, their F-numbercan be made remarkably small.The functionality of the reconfigurable electronicsblock is shown in Fig. 3. A rectifier block generates thesecond harmonic used in the imaging process. The result-ing signal is delayed in a delay line implemented in theDSP as a first-in-first-out queue. The amount of delay isproportional to the length of the queue, and is changed inreal-time to implement the target functionality specifiedabove. For the particular application described above,the phase delay for each metamaterial element indexedby variable i = 0 , ω , and it is given by φ i ( f, α ) = φ − f ω v s (cid:20) tan( α ) − (cid:18) i − (cid:19) ∆ xf (cid:21) , (1)where f is the focal length, α is the angle of the focusedbeam, φ is a constant big enough to make all φ i positive, v = 343 m/s is the speed of sound, and ∆ x = 5 cm is themetamaterial periodicity.The supplemental movie [30] shows the acoustic re-sponse of the slab to the three-pulse plane wave presentedin Fig. 2. Figure 3b-d shows three representative framesseparated by 13 ms that highlight the response of the lensfor each pulse. In each case, we note the clear convergentfields emerging from the lens, the focal spot marked oneach panel, and the focused beam leaving the scene in thedesigned direction, which confirm the desired functional-ity. The only deviation from the expected theoreticalbehavior is the side lobe visible in Figure 3d and causedby the multiple reflections of the incident wave in thearea between the lens and the speaker array.These measurements emphasize the advantage of usinghigher order harmonics in imaging systems, namely thefocal spot is considerably smaller than what can be ob-tained with regular, linear systems. To quantify the sizeof the focal spot, we present in Fig. 4a the field amplitudeat the second harmonic frequency of 3000 Hz measuredfor the lens’ response to the second plane wave pulse. Thefield amplitude measured along the focal plane is plottedin Fig. 4b as the circles marked curve and matches verywell the theoretical prediction (dotted curve). Moreover,the image at the frequency of the incident field producedby an ideal linear lens having the same size and focal dis- Rectifier Phase Delay (t)Reconfigurable electronics ab c d P o s i t i o n [ c m ] Position [cm]0 20 40 60From inputbandpassfilter To output bandpass filter
FIG. 3. Lens acoustic response to three closely spaced identi-cal pulse. (a) Functional diagram of the reconfigurable elec-tronics block. The rectifier generates the second harmonic,and the phase delay line configures the metamaterial to be-have as a lens. (b-d), Time instances of the acoustic responsesto each one of the three pulses. For each pulse the metama-terial slab behaves as a lens whose parameters are reconfig-ured in-between pulses. The time instance, focal spots, andthe direction of propagation of the beam leaving the lens arespecified on each plot.
20 40 6020406080100
Position [cm] P o s i t i o n [ c m ] Field amplitude [arb. units] a P o s i t i o n [ c m ] Theory, fundamentalMeasurement, 2nd harmonicTheory, 2nd harmonic b FIG. 4. Second order harmonic lens performance. (a) Com-plex amplitude of the lens’ second harmonic response (3000Hz) to the third pulse shown in Fig. 3d. The dotted linemarks the focal plane. (b), Comparison between the fieldmeasured on the focal plane (circles) and an ideal lens imagingat the second harmonic (dotted curve) and the fundamental(solid curve). The second harmonic image is twice narrowerthan the image at the fundamental frequency.
Rectifier Phase Delay 1Reconfigurable electronics ab P o s i t i o n [ c m ] Position [cm]0 20 40 60 Position [cm]0 20 40 60+Position [cm]0 20 40 60 c d
Phase Delay 2From inputbandpassfilter To output bandpass filterDelay 1 Delay 2 Delay 1&2
FIG. 5. Metamaterial lens configured to multiplex functional-ity. (a) Diagram of the reconfigurable electronics showing twophase delay lines that implement the two desired behaviors.(b) The first functionality is that of a focusing lens identicalto the one shown in Fig. 3b. (c) Metamaterial configured tobehave as a beam steering device. (d) Metamaterial config-ured to behave as a focusing lens and beam steering devicesimultaneously. tance as the metamaterial lens, i.e. the diffraction limit,is shown using the continuous curve. We notice that thewidth of the measured image is approximately twice nar-rower than what is normally obtained in a linear system,in agreement with previous results reporting second har-monic imaging in the electromagnetic regime [31].In the above example, we showed how the active meta-material can change functionality in real-time. Next, weshow how it can be configured to serve multiple roles atthe same time. To illustrate this idea, suppose we havea beam steering device that takes an incident beam andsteers it to a different direction. Without disturbing thisfunctionality, we want to monitor the quality of the beamby focusing it and measuring its characteristics using amicrophone placed at the focal spot.The double functionality is implemented in the recon-figurable electronics blocks as shown in Fig. 5a. Thebeam steering and focusing behavior is implemented us-ing two delay lines implemented as before using first-in-first-out queues in the DSP. The signals leaving thequeues are added and drive the metamaterial cell piezo-electric transducer that generates the cell acoustic re-sponse.The functionality implemented in the first delay line is that of a lens characterized by parameters (30 cm , ◦ ),also used in the previous example. The beam steeringfunctionality is obtained using Eq. (1) and parameters( f, α ) = ( ∞ , − ◦ ). To verify the correct behavior ofeach individual delay queue, we activated them individu-ally and measured the acoustic response of the metama-terial slab to an incident plane wave. Figures 5a and5b show the intended behavior of a lens and, respec-tively, beam steering device. By activating both delaylines we obtain the linear superposition of the two be-haviors. More specifically, the plane wave and focusedbeams leaving the metamaterial slab are virtually iden-tical to the beams of the basic devices whose functional-ity is combined, and confirm the excellent ability of themetamaterial slab to behave as two different devices atthe same time.We presented an active metamaterial design approachin which the effective material properties are set in recon-figurable digital electronic blocks and demonstrated theapproach experimentally for a slab composed of ten unitcells. The design method features four main advantagesover other acoustic metamaterial design methods. First,the material properties can be changed instantaneouslyto the desired values, which implies that metamaterialscan be configured in real-time to have various behaviorsdepending on application without changing their physicalstructure. Thus, the slab was configured to individuallymanipulate three identical, closely spaced short pulses.Second, the metamaterial can be configured to play mul-tiple roles at the same time. To this end, the metamate-rial was configured to simultaneously behave as a beamsteering device and focusing lens. Third, the design ap-proach is suitable for non-linear imagining applications inwhich the device responds with higher order harmonics ofthe incident field. This is advantageous because it resultsin sharper images that do not obey the diffraction limitof linear systems. Finally, the metamaterial response iscontrolled almost entirely by electronics as opposed tothe metamaterial geometry, which implies that it is nowpossible to obtain imaging devices much thinner thanwhat is feasible with other methods. In one of the appli-cations, the fabricated metamaterial slab was configuredto behave as a lens a tenth of a wavelength thick andhad an F-number below 0.5. These advantages demon-strate the versatility of the active metamaterial designprocedure and recommend it to numerous applications. ACKNOWLEDGMENTS
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