Shedding Light on Wave Physics in Dynamical Metamaterials

By exploring how waves move through artificially engineered metamaterials, structured in space and modulated in time, physicist and first-year Simons Junior Fellow Emanuele Galiffi is obtaining fundamental new insights about wave dynamics.

Emanuele Galiffi is a Junior Fellow with the Simons Society of Fellows.

When you throw a pebble into a pond, waves will ripple out along the surface. They might bounce back (reflect), change their shape (disperse) and interfere with one another, before ultimately dissipating as their energy fades over time. These waves, like all waves, are essentially disturbances mediated by the host medium — in this case, water — across space and time. And while these waves are visible to the naked eye, many types of waves are not.

Over the past two centuries, physicists have proven that light, as well as matter, exhibits wavelike behavior. The quantum physics underpinning the behavior of semiconductors, which has fueled our current digital revolution, describes electrons as dynamic waves, not pointlike particles. Similarly, optical communication systems (e.g., the fiber cable that grants us wonderfully fast internet connections) are governed by the wavelike behavior of light. Much of the wave physics that governs quantum mechanical systems finds analogues among more well-known wave phenomena, such as the electromagnetic waves that we experience as light, the seismic waves that we call earthquakes and the water waves that form tsunamis. But there’s a lot we still don’t understand about wave dynamics.

Simons Junior Fellow Emanuele Galiffi, a postdoctoral fellow in Andrea Alù’s lab at the City University of New York’s Advanced Science Research Center, studies synthetic and complex materials called “metamaterials.” His current research focuses on how ultrafast dynamical modulations induced in such materials may be used to engineer new wave effects that, among other possibilities, could help us harness hard-to-reach parts of the electromagnetic spectrum for telecommunications, and manipulate waves in completely new ways.

Galiffi earned his doctorate from Professor Sir John Pendry’s group at Imperial College London. Our conversation has been edited for clarity.


What is a “metamaterial”?

When a wave — such as a light wave — impinges on a material, its interaction with the material’s electrons and ions controls how much light across the color spectrum is reflected, in which direction, and so forth.

In a conventional, naturally occurring material — such as gold, silver or silicon — this occurs primarily because of the material’s chemical composition, what atoms it is made of, and how these are arranged to form a periodic crystalline structure. When light reflects off of, or propagates through these materials, its wavelength is hundreds of times longer than the spacing between atoms forming the crystal, so that its interaction with the material cannot probe any individual atom or molecule. Instead, the optical response is collective, or “emergent.”

By contrast, instead of relying solely on chemistry, metamaterials are engineered artificial materials formed by periodic arrangements of nanostructures, often called “meta-atoms,” whose collective response can be tailored to produce wave-matter interactions that differ substantially from those found in nature. The landmark example of this is the negative refractive index. A refractive index describes how fast a wave’s phase travels in a material. In a natural material, this phase evolution always follows the direction of propagation of the entire wave pulse. In a negative-index material, the wave’s phase evolves backwards, even though the pulse travels forward. This exotic phenomenon is not supported by any currently known natural material, but metamaterials have achieved this in several different wave realms. One key application of these negative-index materials is the possibility to use them to build a perfect lens, i.e., a lens with potentially infinite resolution, as Sir John Pendry discovered at the very end of the past century. This is impossible with conventional optics.

In my view, the consequent rise in popularity of metamaterials — sparked 20 years ago by the quest for negative refraction — has in some sense united the wave-physics community. Metamaterials have provided a common ground for distinct wave-related fields, from quantum mechanics to elasticity, photonics, acoustics and other fields, in which new concepts can be smoothly translated across different wave realms. This provides opportunities not only for fundamental advances in wave theory and proof-of-concept experiments, but also a pathway towards technological impact for these new ideas. This universal vision of wave physics is what drew me to this research field.


Tell me more about your doctoral research.

During graduate school, I studied the behavior of hybrid electron-photon waves — called “plasmon polaritons” — in graphene metamaterials. I was interested in finding out what happens when the density of electrons that conduct these waves is periodically suppressed by external electrostatic fields. We call these suppression points “singularities.” Our observations revealed that when this occurs, an enormous amount of energy is trapped near these singularities — but why?

To solve this mystery, I deployed a beautiful mathematical technique called “transformation optics”. Using Maxwell’s equations, which describe electromagnetic phenomena, we can mathematically transform space to map the wave patterns produced by simple, easy-to-understand structures onto more complex structures like these “singular” graphene metamaterials. Provided that we follow certain rules in designing these transformations, fundamental symmetries in Maxwell’s equations guarantee that structures that are geometrically very different will nevertheless share the same resonance spectra.

In doing so, we discovered that the observed wave patterns in these peculiar graphene metamaterials were equivalent to those that would be found in the presence of an additional “hidden” spatial dimension.

Thus, we showed how we can use these geometrical singularities, which can also in principle be engineered in conventional metals like silver, to mimic wave dynamics in higher dimensions, effectively hiding that extra dimension from view, while retaining its physical effect on the propagation of waves. This idea is important, because it could allow us to use relatively simple tabletop experiments with photonic nanostructures to mimic the way that extra “hidden” dimension can affect the physics of a seemingly lower dimensional system. This is relevant in the context of testing predictions of higher dimensional field theories which postulate the existence of extra dimensions that are curled up or “compacted” in undetectably small portions of space.


How did that work lead into your postdoctoral fellowship?

The first part of my doctorate focused on tailoring extreme wave dynamics in space. Towards the end of graduate school, I became interested in understanding what happens when a wave propagates through a material that changes over time. This question is central to my current work.

Imagine a sound wave made of two pulses: The first one might sound like tick, the second like tock. If this two-pulse wave bounces off a wall, you would again hear that first tick, followed by tock. However, imagine that instead of encountering a normal, sound-reflecting wall, the properties of the entire host medium (say, the density of air surrounding you) were switched in value extremely fast — faster than a single period of the sound wave (for a 440-Hz sound, the “A” note you tune an orchestra with, this would have to happen within about less than a millisecond.) This process, pioneered by Professor Mathias Fink from ESPCI, Paris, is sometimes called an “instantaneous time-mirror,” and has the effect of partly reversing the propagation of waves. Instead of going forward and bouncing off the wall, they now simply turn backward. If we were to now listen to the time-reversed waves, we would now hear first tock, and then tick.

In addition, if we were to measure the frequency of the final waves in this scenario, and the total energy contained in the pulses, we would find that they have changed. This stands in contrast to a conventional scattering experiment, in which the frequency and the total energy must be conserved in space. Breaking apart the usual time course of a wave has many provocative implications. Whilst this is a well-known phenomenon, my work involves exploring more sophisticated time-modulation schemes to achieve similarly striking effects.


What are some applications of this work?

On one front, there are parts of the electromagnetic spectrum that are very hard to exploit right now. One example are THz frequencies, which lie between the infrared and the microwave frequency bands typically used for wireless communications such as 5G. Time-dependent systems, like the one I just described, enable frequency shifting and mixing. Harnessing them could therefore be a new tool in the future for manipulating frequencies to generate and detect THz radiation that could be used to expand our usable bandwidth for telecommunications.

Another application relates to the fact that time-dependent systems can amplify waves. In fact, two of the projects that I led towards the end of my Ph.D. with my advisers Sir John Pendry and Paloma Arroyo Huidobro explored new mechanisms for amplifying electromagnetic waves by exploiting wave propagation in temporally varying materials. These are inherently out-of-equilibrium systems, which require an external “pumping” mechanism to modulate their properties while the wave of interest is “probing” these changes in time and being amplified. Experimentally, this is a very young and challenging field, and some of my work entails collaborations with experimental groups that are attempting some of the very first demonstrations of such dynamically modulated materials and probing the resulting exotic wave dynamics. Another front of applications is that of nonreciprocal wave propagation, namely designing materials which enable efficient wave propagation in one direction but not the other.


Finally, what are your thoughts on the Simons Junior Fellowship?

Having three years of unrestricted funding is a real privilege, as it allows me to craft and pursue my long-term research direction, adjusting the course as the field evolves, without being necessarily rushed by short-term goals. I am truly grateful to the Simons Foundation for this opportunity. In addition, the Simons Society of Fellows is also a haven for scientists of all fields. Interacting with so many talented young and experienced scientists across such a diversity of research areas is inspiring, as well as mind-opening. Finally, attending foundation-hosted events has really helped me adapt from my time in London and settle in to New York City, a step that felt especially daunting after two years of isolation and uncertainty during the pandemic.