Active and Tunable Acoustic Metamaterials

As the study of acoustic metamaterials has progressed over the past couple of decades, research has shifted from focusing on the creation of materials with fixed structures to ones that are active or tunable. In this episode, we talk to the guest editors of the recent special issue on Active and Tunable Acoustic Metamaterials, Michael Haberman (University of Texas at Austin), Christina Naify (University of Texas at Austin), Bogdan Popa (University of Michigan), and Serife Tol (University of Michigan), about some of the latest research in the area. 

Find all the articles in the special issue here!

Read more from The Journal of the Acoustical Society of America (JASA).
Learn more about Acoustical Society of America Publications.

Music Credit: Min 2019 by minwbu from Pixabay. 

Transcript

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ASA Publications (00:25)

Today we're touching on a popular topic in the acoustics community, acoustic metamaterials. Specifically, I'll be talking with the guest editors of the recent joint special issue for JASA and JASA-EL on active and tunable acoustics metamaterials. With me are Christina Naify, who you may remember from a previous episode we did on what metamaterials are, Bogdan Popa, Serife Tol, and Mike Haberman. Thanks for taking the time to speak with me today. How are you?

Mike Haberman (00:49)

Doing well.

Bogdan Popa (00:50)

I'm doing great, Kat.

Serife Tol (00:52)

Great, thanks so much for having us. It's great to be here and talk about this special issue.

ASA Publications (00:59)

I've been looking forward to doing this recording since the special issue I think even opened. So first tell us about your research backgrounds.

Mike Haberman (01:06)

Right, this is Mike Haberman. I’m in the Mechanical Engineering Department at the University of Texas at Austin. And I work primarily in metamaterials and have done so for, I don't know, I guess a little over 15 plus years, and also work in like ultrasonic nondestructive testing.

Christina Naify (01:22)

I'm Christina Nafey. I'm also at the University of Texas at Austin, specifically at the Applied Research Labs, which is a sort of department of the university. I've been working on acoustic metamaterials for almost 15 years as well. Abd my research is really on materials in general for acoustics. And I do a lot of work with 3D printing.

Bogdan Popa (01:42)

I'm Bogdan Popa. I'm an associate professor at the University of Michigan in the Mechanical Engineering Department. I worked on metamaterials for more than 20 years now, and I've always been interested in how waves, for example, sound interacts with materials. On the acoustic side, I'm very interested in using metamaterials for better noise mitigation, acoustic imaging, and robotic perception.

Serife Tol (02:09)

Hello everyone, I'm Serife Tol, Associate Professor of Mechanical Engineering at the University of Michigan. My research focuses on metamaterials and metasurfaces, and more broadly on designing architected material systems to control acoustic and elastic waves. I'm interested both in fundamental science and applications. So I explore how these engineered systems can enable new physical properties, as well as how they can be used in areas like sensing, energy harvesting, and space structures.

ASA Publications (02:46)

Okay, okay, very cool. So what are acoustic metamaterials?

Bogdan Popa (02:50)

At the general level, these are structures with engineered microstructure designed to achieve a set of desired properties. If I can anthropomorphize sound, sound doesn't see very well extremely fine features. So if you can control these fine features, you can control the blur that sound sees as it propagates through these materials.

ASA Publications (03:13)

That's really cool.

Mike Haberman (03:13)

Yeah, and so, just going add to a little bit. I mean, Christina and I wrote with Alexei Titovich, wrote a little kind of POMA paper on this a couple of years ago. And I know Christina, you talked about this. So there's actually, it's a nice little write up, kind of high-level description. But the main point, of course, is just try to control acoustic wave propagation through structural design, as opposed to just materials. And so that's the main objective of metamaterials research. And also trying to understand, you know, kind of extend concepts from basic physics in order to improve sound control.

Christina Naify (03:48)

And the main thing I would add to that, just that came out of that other, the Poma and other episode that we did ,is that there's no consensus on what they are. So if you ask ten people, you'll get ten different answers. But I think the common themes that Bogdan and Mike explained cover what the general field or the consensus of the field is.

Mike Haberman (04:11)

One little funny highlight about that is that actually there's a little kind of ongoing joke that in every single metamaterial session, almost every single speaker tends to highlight the question of what is a metamaterial, which is funny given the duration of how long this has been in existence, it's actually kind of comical.

ASA Publications (04:27)

Right.

Christina Naify (04:27)

It's actually much more noteworthy when people don't do that. It's like, “Oh!”

Mike Haberman (04:30)

That's right.

ASA Publications (04:33)

We still don't know what they are, but we're still researching them. ⁓

Mike Haberman (04:37)

Yes.

Christina Naify (04:37)

Right.

ASA Publications (04:38)

So we've actually done a number of issues on metamaterials before this. How did this special issue come about?

Mike Haberman (04:45)

Yeah, so on this front, I'll let Christine follow up a little bit. But, you know, the main thing is we did the previous special issues were either specifically just generic metamaterials topics, which were a while ago, over 10 years ago. And those were really kind of when acoustic metamaterials became a little bit more widespread, the study of them, the research that had been going on for a while. But, you know, they were very broad and open calls. Through time we refined them a little bit. There were a couple others on like topological acoustics, nonreciprocity, which we'll talk about actually here, but then also another special issue where we looked at additive manufacturing in acoustics, which is obviously slightly different, but a lot of the motivation for additive manufacturing, is actually to create very customized and fine-scale structure, which is very relevant to meta materials. Christina, do you want to talk about why we decided to put this one together?

Christina Naify (05:39)

Yeah, I think I agree completely with what you said. And from my perspective, you know, those early issues were fairly general. In seeing where the field has come in the last 10 to 15 years, the prevalence or the idea of trying to tune or have tunability or incorporating active materials into metamaterials has grown. Ten or 15 years ago-- actually Bogdan was probably one of the first people to look at active metamaterials. But obviously you can't have a special issue with one researcher. So, kind of watching the field and seeing what directions it was going in, this was a key direction, right? Where people are really interested in being able to incorporate active components or tunability into their structure. So it just seemed like the time was right to really highlight this new phase of acoustic metamaterials research. And maybe, Bogdan, you were one of the pioneers in this area, so I don't know if have anything you want to chime in on.

Bogdan Popa (06:42)

Yeah, we started with materials with fixed structure and from the beginning we figured out that those have all kinds of problems. So how about we solve those problems by enabling tuning of, you know, like the structure of the material. And from there one thing leads to another. And, oh, what if we put, you know, like a source inside the material? What happens then? What kind of new functionality would we be able to achieve? So that started the ball rolling.

Christina Naify (07:16)

I'll add too, just quickly, that I think that there's a little bit of right place, right time with some of this and that having, especially when you think about the active component, which I know we haven't gotten into what that means yet, but when you think about that component, having electronics that are affordable and easy to access makes incorporating those components into your design much easier.

ASA Publications (07:39)

So good segue then: What are active or tunable metamaterials, and what are the benefits of using these types of metamaterials compared to their static counterparts?

Bogdan Popa (07:48)

Yeah, so what I was saying earlier, people started with these fixed structures that had a fixed set of properties and functionalities. And they were not very happy with that because, for example, one problem was you had all kinds of tolerances, fabrication tolerances, and very often you would not be able to hit the right performance in the material and you would just like to tweak those materials, those structures. And so this led to the idea of tunable metamaterials. Let's build this tunability, if you wish, into the material structure so that after you fabricate it, you can still change it. And that solved some problems, but not all of them. And then people thought about, well, these, you know, like tunable metamaterials, these fixed metamaterials, at the end of the day, they are really passive structures. Can we overcome the fundamental limitations of these structures, such as, you know, the narrow behavior that they tend to have? And one of the ideas was to insert some active elements in the fabric of the material itself. So these active elements would be, for example, speakers, arrays or arrangements of speakers. And with these speakers, you could inject or extract energy from the incoming sound, and thus you have more freedom to control what the sound is doing, maybe guide it in new ways, maybe absorb a lot of energy using that.

Serife Tol (09:25)

Maybe I can add on to what Bogdan has mentioned. With these active approaches, we can adapt the response of metamaterials in real time. As he mentioned, this can be achieved either by inputting energy to system, for example, through piezoelectric actuation, or we can modify properties through external stimuli, for example, applying electric or magnetic fields, or mechanically reconfiguring the structure, like with inflatable or shape-morphing designs we have seen in this special issue. And in the special issue, also, what really came through is much broader design space where systems can switch functionality, responding to changing environments and achieving behaviors that are impossible in passive materials. So overall in our field, now we are seeing a shift toward adaptive and programmable acoustic systems, which opens a wider domain for new applications and devices.

ASA Publications (10:31)

Okay, so question. So that would be like,  you need a material that would do noise absorption, right? Would that mean that the material would adapt or change based on, like, your frequency needs for the material?

Serife Tol (10:42)

Exactly. So the metamaterial system can sense the noise and the bandwidth, and then it can adapt itself to tune or to absorb specifically those frequencies. So this is what active metamaterial system is, as an example.

Bogdan Popa (11:00)

And another example would be something similar to noise cancellation. Think of the noise cancellation headphones. These have an embedded microphone that senses the incoming noise and then tries to cancel it by playing it with reverse polarity. And these noise cancellation are really controlled. They use controls methods. So there is an adaptive change of the transfer function between that microphone that you add and the additional speaker. And because of that adaptability, you can cancel a lot more noise that you would be able to do just passive methods. But this comes at a cost. You have to include some electronics. Also these controls methods tend to converge to the optimal transfer function quite, you know, they need some time. And unfortunately, sound is very fast, travels very fast. So in the metamaterial world, people try to avoid controls methods, and try to compute, pre-compute that transfer function. And by doing so, make these materials react a lot faster, and by doing so, extend the range of frequencies that you can cancel out. And there are several papers in this special issue that touch upon this approach.

ASA Publications (12:21)

Well, so let's get into the special issue, which was quite expansive. And so there are a lot of themes that popped up. Can you give a brief overview of the topics that came up?

Mike Haberman (12:31)

So, as you said, it was pretty expansive. There were 25 individual articles that were finally put into the collection, covered a really wide range of topics, even though obviously we did, as we said earlier, tried to narrow down the focus so that it wasn't completely wide open. That being said, we tried to classify them a little bit into a few different areas, which I think we'll talk about probably later. And those topics were, I'll just kind of list them, because I think we'll want to go through and define in a bit. First there are metasurfaces and metagreatings, the idea here being interfaces that interact with waves propagating in some medium and scatter or reflect and transmit through them. General noise control, like very applied concept, you know, hopefully that's going to be useful in the future. Dispersion engineering, so designing something to have certain frequency-dependent response. Nonlinear metamaterials and phenomena, so designing material to behave differently at different amplitudes of excitation. Nonreciprocity, which is this idea of being able to, you know, hear without being heard, kind of the acoustic analog of at least what we think of as

one-way glass, although that's more of an optical trick, but you can hear something when somebody cannot hear you. Topological acoustics, which is emerging and quite interesting area. Time- and space-modulated metamaterials—these are materials whose properties change as a function of time and space, and how waves interact with them. And Wiills coupling, which is a very specific type of constitutive response that links momentum and strain in unique ways. But yeah, I just want to add there. So those are the quick rundown. I think we'll go through each of the topics. But I just wanted to say that we tried to characterize these things to a certain extent within the collection. Many of them are linked together, right?  So the nonreciprocal systems are often, you know, maybe either nonlinear or have time-and-space-modulation properties, et cetera, et cetera. Maybe the way that we try to categorize them is associated with the primary focus or intent of the research that's summarized in the article.

ASA Publications (14:36)

Thank you for that rundown, that was great. So the first theme you mentioned was research related and metasurfaces and metagratings. I know you already said a little bit about what those are, but what are they? And what was some notable research related to these types of metamaterials that showed up in the special issue?

Serife Tol (14:52)

So metasurfaces and metagradings are both approaches for controlling sound using engineered materials rather than bulky counterparts. More specifically, metasurfaces typically consider an array of sub-wavelength unit cells that imposes a design phase shift on waves, which allows us to do things like steering, focusing, or shaping wavefront in a very compact structure. On the other hand, metagrating is very closely related, but instead of continuously shaping the wavefront, they are used to engineer deflection to direct energy into specific directions. And they're often more efficient, and they often come with simpler designs. So in this special issue, we are seeing a shift toward more compact and reconfigurable wave control devices, which is really exciting for their deployment in real world applications. Maybe, Christina, do you want to expand on some of the specific examples or applications from the special issue?

Christina Naify (16:05)

Sure. The applications for acoustic megtasurfaces and metagratings, I think when I look at ones that we sort of categorized, they focus pretty heavily on the idea of, sort of, wave steering or wave manipulation. There were a couple of different approaches used in order to sort of tune or activate the sort of varying response of the different designs. For example, changing arrangement of plates relative to each other in order to manipulate phase. And there was a paper that looked at hydraulic control of a metasurface lens. But in general, all of the papers in this group were looking at things like lensing or wave steering. I think, you know, when you're looking at metasurfaces and metagratings, phase manipulation is a really common application. And so I guess that wasn't too surprising that those, that was the direction of the general research, but each of the different papers employed the attunability in a different method and was looking to exploit different phenomena, like changing the focus or the focal length of a lens or moving beams around in space.

ASA Publications (17:15)

Okay, okay. The next theme you discussed in your introduction was a topic that I know I think of whenever I hear metamaterials, which is noise control. How can active and tunable acoustic metamaterials help with noise control?

Christina Naify (17:28)

Bogdan touched on this a little bit earlier, but the main reason to use active or tunable metamaterials for noise control is that, a lot of times, when you design your metamaterial, it has a specific frequency response that's designed into the microstructure that you've sort of architected across your structure. And if that is fixed and the conditions change, you might not get any benefit from your structure. So the idea of being able to, if there's a different frequency or even being able to adapt your structure to a different location for noise control, that might have a different, you know, different noise, different amplitude or frequency content. I think that's probably one of the reasons that you would want to use active or tunable metamaterials for noise control.

Bogdan Popa (18:16)

Yeah, exactly. And there are some examples in this special issue that targets applications of reducing sound in buildings, in rooms, in ducts. So for architectural acoustics, basically applications. For example, they came up with this drawer-based structure where they would open and close this drawer in order to change the geometry of a resonator, and by doing so they were able to change the frequency at which these absorber absorbed acoustic energy. This is one approach that is represented in this special issue. There is another approach that uses these combinations of microphones and speakers connected through some electronics. And in this approach they were able to reduce, again, sounding ducts at a impressive level.

ASA Publications (19:09)

The drawer idea is really interesting. Another topic that came up was dispersion engineering. What is it ,and how can it be used?

Christina Naify (19:16)

So dispersion describes a changing of your propagating wave with frequency. And metamaterial designs often rely on dispersion via resonances or other types of phenomena. One of the ways that we can implement the controllability that we get in general with metamaterials is to control that dispersion. And in the similar vein to being able to control for noise control, being able to incorporate tunability into that dispersion just gives you another sort of knob to turn when you're designing your structure.

Mike Haberman (19:50)

Right, yeah, So one of the contributions in dispersion engineering was actually on the topic of a leaky wave antenna. I almost feel a little funny having me describe it because Christina did a whole bunch of work on this from the beginning of when she started working in metamaterials. So hopefully I do it right, and you can correct me if I'm wrong, Christina.

But a leaky wave antenna was looked at, which is, let me kind of describe it really quick. The idea being that if you placed wave guide, a system that, you know, where waves propagate in it, that is coupled to an external medium, right? So just imagine you literally have like a duct and inside the duct, the wave propagates, and then some of the energy radiates out from the duct, which, you know, we're all used to hearing. And it does that in a specific way based on how the waves propagate within the duct. It's a frequency dependence on how fast the waves go in the duct. And then the direction in which the sound radiates out is dependent on the speed with which it propagates through that duct or that waveguide. 

So a group at Penn State actually went in designed this leaky wave antenna using internal resonators, like internal membranes, in order to control the dispersion within that wave guide, the sound speed with which it propagates as a function of frequency, in order to control the direction at which energy radiates out from this antenna, quote unquote leaky wave antenna. And the tunability that they added, because if you just have those little resonators in there, they will, you know, kind of have a fixed response. What they did is they looked at the case where they could tune the resonance of those resonators in order to adjust that dispersion, in order to tune the frequency range, the direction at which you radiate off as a function of frequency just by tuning the resonators a little bit more at will. So it's a nice, interesting demonstration of some of these principles used in metamaterials.

Christina Naify (21:37)

And that was a case where they were doing that tuning via electronic control, right? Yeah, so.

Mike Haberman (21:43)

Correct. Yes.

Christina Naify (21:44)

Yeah, so.

Mike Haberman (21:45)

Yeah, which is a pretty consistent theme as was mentioned earlier. It's one of the valuable aspects of relatively low-cost electronics.

ASA Publications (21:53)

Very neat. So what did research in the special issue show about nonlinear metamaterials and phenomena?

Mike Haberman (21:59)

So there were a couple of contributions in this area. This stuff gets a little bit involved, some of the nonlinear metamaterials work, but there were two in particular that were interesting. So in general, we could just say that nonlinear materials, metamaterials, nonlinear phenomena in general ,are characterized by an amplitude-dependent response. So, you know, if the acoustic wave is a high amplitude, then it will actually propagate in a different way than if it's low amplitude. In general, it's worth saying all systems behave this way, but often in acoustics in particular, we don't have to worry about that. Here they're designed kind of specifically to have a nonlinear response for some advantageous aspect. 

One of them in particular, there was a group in Paris that were actually motivated by hearing, the hearing mechanism, right? If you think of our, you know, the inner ear behaves as basically a bunch of coupled resonators. And they were kind of curious to know, or kind of wanted to, were motivated by knowing if I have, you know, two resonators side by side that have slightly different resonances, but they're coupled together in some way. And their delay between them, between the excitation of both of them, is what, kind of is a tunable factor, is a factor that changes. So all they did is they just basically put together two cavity resonators, literally, you know, volumes filled with air, and then they coupled them together via a sensor and source and could tune the delay of the pressure inside one cavity and the driving in the other. And effectively what they showed is that they could tune them such that at specific delays between the two, and specific delays at low amplitudes, they could get that the two resonances would actually synchronize. And then on the other hand, they could tune via the delay, the amplitude at which their resonances bifurcate, they become unique and distinct. And so this was a study that, you know, kind of hopefully would inform an ability to tune coupled resonators in a way where you can get them to selectively distinguish sensing capabilities for one frequency versus another, even if the resonators are coupled together. 

The other one, which is a little bit more specific to nonreciprocity, was a work out of a group in Canada that was actually interested in just this idea of nonreciprocity through non-linearity. And they did a fundamental study that basically said you can characterize non-reciprocal wave propagation by both the amplitudes of the waves that can travel in one direction versus another. So if you interact with this medium, in their particular case, it was more of a vibrational system. If you come from one direction, you get a certain output. You come from another direction, you get a different output that is in amplitude only, and that's sort of an energetic description. But they showed that you might be able to have non-reciprocal behavior in amplitude, a reciprocal response in phase. So the shape of those things as a function of time may be similar, but the amplitudes will be different. So that was a very interesting contribution from a more fundamental standpoint.

ASA Publications (25:06)

Okay, okay. And so nonreciprocity is something also that you said came as well, in general. So what is nonreciprocity and what was found in the research?

Bogdan Popa (25:16)

Nonreciprocity probably is better introduced through one example. So suppose you have a speaker and a microphone that records what the speaker is doing. If you switch the speaker position with the microphone, then you should get the exact same recording. And this is a fundamental property. It's true in air, it's true in water, it's true almost everywhere. So people, you know, like try to build materials that, well, doesn't follow this property. Can we do it? And how would we go about doing it? And this, as you said, Kat, launched an entire area of research. So there are several papers in this special issue that discusses this, and these papers can very easily be part of any of those, you know, sections that we identified and talked about today. And maybe Mike can speak more about some specific examples.

Mike Haberman (26:18)

Yeah, of course. I mean, the main differences that were, or the main cases of the contributions that I think are worth highlighting, most of these relied on active elements embedded in the system, okay? So either through sensor and a source that were not necessarily co-located and such that you get a non-local, so in other words, when the sensing and the actuation are not at the exact same point in space, we call that a “non-local” behavior. So the field at one position depends on the field at another position in some instantaneous way. And the way that it was used, there was group in, where were they at? Ah, in Le Mans in France. There's a group that actually used little speaker microphone group or speaker microphone combination in a series. And they showed that effectively what they could do is by tuning the specific source receive or sense actuate pairs, they could generate, maybe not unsurprisingly, a unique type of nonreciprocity that could engineer phase of that non-reciprocal response while preserving it in another—so making it different in one direction and the same another direction. 

There was also a group in the UK, at The Institute for Sound and Vibration, that actually looked at PT symmetric materials or non-Hermitian materials, and these are materials who basically contain active elements where there's dissipation in one element and a source in another element, and they showed strong control of the non-reciprocal behavior that actually mimicked quantum mechanic behavior. This one was related to quantum mechanical tunneling, which was super interesting. So you got quantum mechanical analog tunneling in one direction and isolation in the other.

And in the last one that was interesting, there a group in France that actually studied piezoelectric metamaterials, where instead of actually injecting energy through sources and sensing and actuating, they actually just changed the electrical boundary conditions, piezoelectric elements, for a elastic waveguide, such that you could get nonreciprocity by altering the local effective stiffness as a function of space and time.

So these were pretty involved studies, and they're all kind of playing on different components of sensing and actuation and injecting energy in order to generate non-reciprocal response.

ASA Publications (28:48)

Okay, okay. So this is kind of a more basic question, but what is the use of nonreciprocity? Like why… Why do you want it? How is it useful?

Mike Haberman (28:56)

I mean, there's a couple different cases. I mean, a really easy one is like, you know, almost like a spy movie, right? I want to sit somewhere and eavesdrop on somebody and not have them hear me, right? So can sit there and listen, and I can move around and talk with my friends and they can't hear me. So I mean, so that’s sci-fi, right?

There can be other things though that are interesting that are analogous, which is, you know, maybe you want to monitor behavior in a structure. So imagine, this more of a vibrational example, but imagine I have a structure, a plate-like structure for example, and I've got vibratory motion, excitation in one place, and I want to sense it, but I don't want whatever's happening near my sensor to influence the behavior at the place that I'm trying to measure, right? I'm pushing over here on one component of the structure. I observe it at a different location. But the presence of my sensor, I would prefer to not have interfere or influence in only a minor way, what's happening at the thing I'm trying to monitor. 

Bogdan Popa (29:54)

And there are also other examples, if I can jump in, Mike. 

Mike Haberman (29:59)

Of course.

Bogdan Popa (30:00)

So for example, imagine you're at a concert and you would like to be able to hear music coming to you, right? But it would be probably better if the people performing in front of you don't hear the random cell phone that turns on in the middle of a performance.

ASA Publications (30:18)

Right, right, that makes a lot of sense. Yeah.

Well, thank you for that. I appreciate that. So somewhat related to nonreciprocity, there was also research related to materials whose properties change as a function of space and time. Can you tell us about some of this research?

Bogdan Popa (30:33)

Yeah, this is another way of obtaining nonreciprocity by just changing in time, potentially really quickly, the acoustic properties of materials and modulate them by doing so. And there are several papers that touch upon this. One of them being even, you know, Mike is a co-author on that. What I liked about that paper is that, unrelated to nonreciprocity, they looked at flat diffusers. And these are elements that are typically placed in enclosed spaces such as rooms in order to make those rooms more comfortable acoustics. Without these diffusers, the sound can be very uneven; you can hear all kinds of echoes. And these diffusers are obtained by changing in time the impedance of those surfaces—and by changing the impedance of those surfaces, you change how the sound reflects from those surfaces. And you can sense sound that is initially incident in one direction in all directions by doing that. And of course, they also looked at how to make these reflectors non-reciprocal. 

There is another notable paper, once again coming from Texas, from I think University of North Texas, if I'm not mistaken, where they use this arrangement of cylinders that are made of two materials and they push up and down those materials and they modulate them like that. And they showed that you have the opening of what's called a momentum band gap. Everybody knows what a phononic band gap is, when you have some frequencies that do not propagate with the material. With a momentum band gap, you can make it such that sound propagates in some directions, but it's completely blocked in some other directions. So you get this unique directional sound behavior in this way.

Mike Haberman (32:36)

And one other quick comment on the space-time modulation, or spatiotemporally modulated media, is that the distinction here is actually quite subtle with these types of media versus what is traditionally understood as active acoustical materials. In an active sense, it's usually literally kind of like the active noise control case that was mentioned earlier, which is to say, I have a sensor somewhere; I measure the sound there. I use that information to then drive a source at another location, maybe for example, to diminish the sound at some preferred spot. So noise canceling headphones are a perfect example of this. These space and time modulated materials are a little different in the sense that they are not energy conserving. Energy must be injected into these materials in order to change their effective properties. But in their idealized form, they actually don't literally move in any way, shape or form. There are no sort of moving parts, if you want, to an idealized, spatiotemporally modulated material. Rather, the effective stiffness of the medium changes due to some other type of stimulus, for example, or boundary condition. And the example that I mentioned earlier with the nonreciprocity and the elastic wave guides were this case where what they did is they used the electrical boundary conditions. They literally just change the electrical boundary conditions of an element, a piezoelectric element that produces a voltage in proportion of the strain, right, those kinds of materials. And they just, by changing the electrical boundary conditions, you can alter the effective or the perceived stiffness. And so by changing that rapidly as a function of time at one position in space, you effectively change the stiffness that's there and can alter that. Now that takes energy to change the boundary conditions, but it doesn't generate, at least in an idealized sense, any wave motion on its own. It is the interaction of the wave with medium that's changing in time that produces the effect of interest.

Bogdan Popa (34:49)

And in addition to that, this gives rise to very interesting effects. So for most materials, you have this conservation of mass that happens. With the approach that Mike just described, you can actually go around that and you can really literally build these materials that do not satisfy this mass conservation law, which is another very interesting thing that comes out of space-time modulated materials.

ASA Publications (35:19)

So what kind of work was done in the field of topological acoustics?

Mike Haberman (35:23)

Well, so first, I know that I think Serife has a few things to chat about with this, but before that, I was gonna give like a really quick summary at my sort of naive understanding of these things. But the one thing that is always a little tricky about topological materials is the idea here is like what are they? What does it really mean? Just from a high level, the term topological here comes from the mathematics, topology in a mathematical sense. And so this is just this idea that shapes or kind of generic objects are related in some way such that they are invariant under changes in shape. So changes like stretching and twisting and things like that. So in other words, like a donut, this is sort of a classic example, a donut has the same topology as a coffee mug. Because there's one surface and there's a surface and there's a hole in the middle, right? Similarly, a sphere and an ellipsoid are the same topology. So the reason this, part of the reason that this actually has this name is that topological wave transport, one example of it is what's called a topological isolator, which are materials that are structured so that waves can go around the outside of the material. They don't propagate through the material. They only propagate around the outside in certain frequency regions. And if you change the shape of that thing, it still goes around it, no matter what. And so that is one of the reasons that it has that particular name. And the trick from topological materials is actually to figure out how to structure the media to demonstrate these kind of unique behaviors. So I wanted to just provide a little bit of high-level description, at least as I understand it. And if anybody has anything to add there, feel free. 

Serife Tol (37:11)

Thank you, Mike, for that great overview of topological acoustics. So within the context of our special issue, what is really exciting in this area is how topological concepts are being combined with tunability and practical design strategies. So here we see several examples where researchers created structures that support robust edge or corner states, meaning waves propagate along boundaries without being affected by defects or disorder, which is the main usage of topological acoustics in our field. So, for example, there are designs of topological waveguides where the frequency range can be tuned by adjusting geometric features, like cavity dimensions, while the system still maintains robust edge-state propagation. There are also other studies covering[KS1]  topological edge or cornered states in engineered lattices, where breaking certain symmetries, like time reversal symmetry using gyroscopic effects, opens band gaps, which supports unidirectional and defective [KS2] wave transport. So in the current state, what we see is instead of just having robustness provided by topological metamaterials, now we are starting to see controllable robustness, which is important because if you want to use them in real world environments, we want robust systems and designs.

Mike Haberman (38:49)

Right, yeah, because the main point of one of these things is they're actually, these are very often it's kind of like dancing, you know, being right on the head of a pin. You-- Very specific configurations gives you this unique behavior. So the tunability, as you said, is important because it allows it to still behave as we'd like when certain things change.

ASA Publications (39:11)

Okay, okay, yeah, that makes total sense. So, finally, some of the work focused on Willis materials. What are they and what was found?

Mike Haberman (39:19)

So the main thing here, just to provide some context, so Willis materials, they got their name from a guy named—a guy.  I shouldn't say it, so, a professor, John Willis, who in the 1980s actually just showed kind of a non-intuitive result, which is if you have just an arbitrary, medium that has scatters inside of it, so you've got a background with some scatterers, that the pressure and momentum of the field are related in non-intuitive ways. And what I mean by that is, for example, the pressure locally to the medium is usually just as I as I squeeze it, right, the pressure goes up and as I, you know, rarify the pressure goes down. And if I just take that whole medium and I just shake it back and forth, if it's just a little small point, the pressure actually doesn't change at all. Right? If I just grab a volume inside, you know, a jug of fluid, assume it's all perfectly confined, if I shake it back and forth without creating waves, the pressure is identical. But he showed that actually if you have a medium that is heterogeneous, that has scatterers inside of it, in general, when you accelerate it, as you're accelerating, under certain conditions you actually generate stress. And that stress originates from the fact that there's asymmetry, you break a spatial symmetry. So it doesn't look the same from the front as it does from the back, basically. So imagine just a material, a scatterer, an object that has one material on one side, a different material on another side, would potentially give this behavior.

And so that actually ends up being really interesting. Materials like this actually end up having a direction-dependant impedance, which gives you a lot of control for both sound absorption and reflection, transmit and reflection behavior. As a matter of fact, a good design or application of Willis materials are materials that can reflect from one side and absorb from the other, without being nonreciprocal or anything else.

So the one contribution I want to highlight from this, which is most of these things as usual are static. You know, once you build the thing, you get the given response. A group at Naval Research Laboratories actually showed a case where they used a certain geometry, it was sort of the spiral-shaped geometry, of two kind of plate-like materials or structures. And if you had a 1D wave propagating in one direction, you got a different response and reflection if you did incidence from one side versus the other. And then if you actually heated those particular coil shapes, you could switch the way in which that was observed. The Willis type of response can be tuned and selected for the direction of incidence, which was a really kind of unique demonstration. So these would happen on time scales a lot slower than the things like the space-time modulated materials, but this was a case where the tunability actually came from thermal excitation or really joule heating, right? So electrical behavior creating heat. And so it was unique to see that as opposed to sort of, you know, these other active elements that were primarily related to electronics and things like that.

Bogdan Popa (42:32)

If I may add, these Willis materials, from the point of view of a material designer,9 are just two other material properties in addition to these mass density, this stiffness tensor that you can use in order to control how waves propagates through them. And they have been used a lot, as Mike pointed out, for nonreciprocal wave behavior. And there are quite a few papers in this special issue that highlight how sensors and actuators connected together using some feedback loops generate these Willis material properties.

ASA Publications (43:11)

Okay, okay. Were there any surprising results within the special issue?

Christina Naify (43:16)

So one of the things that stood out to me, which actually this dovetails really nicely off of the previous conversation, I think in general, the diversity of the research, but specifically the diversity of the methods by which people were able to sort of employ tunability or active components into their systems. So we saw pressure, we saw electrical control, we saw heating. There was really a lot of different ways that people were able to control their system and tune their response. And that, to me, shows a lot of creativity. It also maybe points to being able to use different environments to control your system. So if you had different thermal environments or things like that. So generally, there was a lot of diversity in the phenomena that people were able to demonstrate, but there was the diversity in sort of the ways that people were able to manipulate things was really impressive to me. And I was really glad to see that diversity represented across different applications and things like that. So that was one of the things that really stood out to me.

Mike Haberman (44:24)

I don't know if I have too much else to add to that. I mean, I think, big picture, there was nothing that really jumped out as like surprising, per se. But yes, what I would say as an observation was there was a certain amount of commonality between them. Right? It was like all variations on themes. So like we said at the beginning, a lot of them had quite different primary objectives. Some were more applied, some were more theoretical. But regardless, they all kind of had certain aspects that were sort of at its core fundamentally similar and got really a wide range of kind of demonstrated phenomena and useful results.

Bogdan Popa (45:01)

Yeah, and the number of papers that we received, that was surprising to me personally, to be honest.

Serife Tol (45:10)

Yeah, I agree and well said, Christina and Mike, and I totally agree with Bogdan. So the attention and interest in the special issue was beyond overwhelming, but we are so excited and happy to have this collection.

ASA Publications (45:23)

Yeah, it is so exciting to see this collection, and both the diversity and similarities within all the research. So where do you see this field of research going in the future, and what are some of the challenges facing the field?

Bogdan Popa (45:35)

I can start with the challenges because we worked in this space for a long time, right? And we faced lots of problems and challenges, as you say, Kat. And I think the first one is scalability. And this is true about almost every branch of metamaterials. So people show these structures that are made of one, two, and anyway, few unit cells, right? And then scaling this up to very large structures is a very big problem that we would like to see being solved, right? When you, for example, scale up structures that are made of speakers, microphones, in order to obtain very large active metamaterials, then you can get into all kinds of problems, stability or instability being one of them. When you have, you know speakers and microphones connected to each other in close proximity you have all these feedback loops that can produce problems such as very loud noises. You probably know better than us, right? What happens if you put a microphone too close to a speaker in a podcast like this?

ASA Publications (46:45)

Right, right. 

Bogdan Popa (46:46)

So you need to solve this problem, right? And you need to solve this problem by maintaining the special properties of your structure. The whole range of material properties, of behaviors, that you showed for one or two unit cells. So scaling this up is not trivial. It's actually a hard problem.

And moreover, maintaining the broadband behavior of these devices while maintaining stability is especially complicated. And keep in mind that many applications, such as noise mitigation, acoustic imaging, acoustic diagnostics, they use a large range of frequencies, right? So they need broadband operation. How do you maintain that?

Mike Haberman (47:35)

So to reinforce a little bit with the challenges, I mean, I think there's like literally the things that Bogdan was bringing up with respect to the electronics and the sensing, the actuations and these kinds of things and consistency there. It applies equally well for either tunable or active metamaterials as it does to passive ones. The challenge of sort of a fabrication question, right?

How do you make many individual elements that are repeatable, have reliable structure, have consistent material properties? And this applies actually not to just acoustics. There are what are now often called mechanical metamaterials, you know, like lattices that you'll see inside helmets or other structures that require a fair amount of precision and robustness to variability. So that's really important. 

But with respect to where things are going, I mean, I have a big picture. A lot of this adaptable, any sort of adaptable, I tend to often think of the structures themselves or surfaces that interact with acoustic waves that are able to, you know, change the environment a little bit, you know, on demand. Almost the 0th order example of are what we used to call baffles in performance halls or curtains, right? You deploy the curtains or you don't deploy the curtains, right? Or you open up this thing or you close it. Sort of two states that you can have, but imagine something that's a little more continuously variable, kind of on demand, even maybe during the middle of a performance, as a simple example. And that idea is really interesting and intriguing and worth pursuing, I think.

And then I think, yeah, Serife had said that you had maybe something kind of even beyond that, which I think would be good to highlight.

Serife Tol (49:20)

Yeah, I think looking ahead, I think those challenges also point to some really exciting opportunities. We are moving towards systems that are not just engineered for a single function, but they're adaptive, multifunctional ,and programmable. And I think the field is really moving toward intelligent metamaterials, which are systems that don't just control waves, but can also sense, adapt, and even compute using waves. So at the moment while we definitely have these challenges in complexity, fabrication, implementation, these are also driving the field toward more impactful and deployable technologies.

Christina Naify (50:04)

One thing I'd like to add, too, is, you know, I think this is true for metamaterials generally, but certainly true for active or tunable ones. I think the field continuing to try to push the limits of what's possible. When you think of the sort of effective material properties that people are able to achieve, really continuing to try to push the limits. So make things even more extreme. Get even better performance. And I think that active and tunable metamaterials have the possibility to push us further than we would be able to get with sort of static systems. So there's the tunability part, but then in addition to that, really being able to exceed the metamaterial performance that we can get from the tunable, rather than just… just, for example, changing the frequency, which is an example that we kind of started with.

ASA Publications (50:54)

Yeah, it does seem like there are quite a few exciting opportunities and also challenges to overcome, I guess. Does anybody have any closing thoughts?

Christina Naify (51:02)

The only thing I would say is, we were really happy with the contributions to this special issue. And we'd like to thank the contributors, right? This wouldn't have been possible without people doing great research and submitting it to the special issue. So we're really grateful to the journal for having us, our special issue, and extremely happy with all of the contributions that we received.

Mike Haberman (51:26)

Yeah, that was the only thing I really wanted to add as well.

ASA Publications (51:31)

Thank you all for being our editors. We really appreciate it as well. And thank you again for taking the time to speak with me today. It was exciting to hear about all the latest advances in acoustic metamaterials. It’s sounding like they're becoming more and more versatile, which is, you know, like I said, exciting. And it'll be interesting to see what the future holds. And have a great day.

Christina Naify (51:51)

Yeah, thank you.

Bogdan Popa (51:51)

Thank you, and thank you for having us, Kat.

 [KS1]This word wasn’t transcribed, but I couldn’t quite make out what it was supposed to be from the audio.

 [KS2]This doesn’t seem like the right word, but I couldn’t make out what it was supposed to be.