We are surrounded by waves. Tiny vibrational waves carry sound to our ears. Light waves stimulate our retinas. Radio, television, and endless streaming content are all brought to us by electromagnetic waves. All these waves are controlled by the same basic physical principles, which is quite remarkable. These waves can be controlled using nanoscale materials known as metamaterials. This revolution has occurred in the last few years.
The Greek prefix meta means “beyond.” These engineered materials let us move beyond the traditional ways in which waves and matter interact, creating technologies where light and sound appear to disobey conventional rules. The “invisibility cloth” is a metamaterial coating that hides an object from plain sight. It is the most prominent example of this new type of materials. Many research teams around the globe, including mine, have created metamaterial coatings that can redirect light that hits them. This effectively prevents light from bouncing off of the object and reaching our eyes, and even from creating shadows. These inventions are not perfect, but they interact with light in a way that is almost magical.
Cloaks is just one example. Other metamaterials allow light travel in one direction but not the other, making them useful for communication and detection. Modern nanofabrication tools, combined with a better understanding about how light and matter interact, allow us to structure metasurfaces in any way we like.
Scientists have been trying to control the properties light and sound through their interaction with our sensory systems for centuries. The invention of stained glass was a breakthrough in this endeavor. Ancient Romans and Egyptians were able to melt metallic salts into glass to tint it. The tiny metal nanoparticles in glass absorb certain wavelengths and let other colors through, creating stunning masterpieces that we still enjoy today. In the 17th century Isaac Newton and Robert Hooke recognized that the hue and iridescence of some animals are created by nanoscale patterns on the surface of their body parts–another example of how nanostructured materials can create surprising optical effects.
Human eye are skilled at detecting two fundamental properties in light: its intensity (brightness), and its wavelength (that is, its colour). The third property of light is its Polarization. This describes the path that light’s electromagnetic field trace in space over time. Although we cannot see the difference between polarizations with our eyes, many animal species have polarization sensitivities, which allows them to see more, better understand their surroundings, and communicate with other creatures.
In the late 19th century, a few years after James Clerk Maxwell’s discovery of the equations of electromagnetism, Jagadish Chandra Bose built the first examples of what we could call a metamaterial. He demonstrated that linearly-polarized electromagnetic waves, which are light whose electric and magnet fields oscillate along straight lines, can rotate their polarization when they travel through the jute structures. Bose’s twisted Jute demonstrated that artificial materials can be controlled in new ways.
The modern era of metamaterials can be traced back to 2000, when physicists David R. Smith of Duke University, the late Sheldon Schultz of the University of California, San Diego, and their colleagues created an engineered material unlike any seen before–a material with a negative index of refraction. A beam of light moves from one medium to the next, such as air to glass. As a result, the angle of the bending occurs.
Refraction phenomena is the basis of most modern optical devices including lenses and displays. They explain why a straw looks broken in a glass. The index of refraction for all known natural materials is positive. This means that light always bends on one side of the interface with a smaller or larger angle depending on the index change. A medium with a negative index would cause light to bend backwards, creating unexpected optical effects such as a straw appearing to be leaning in the wrong direction. Scientists have long believed that it was impossible for a material to support negative refraction to be found or created. Some even suggested that it would be contrary fundamental physical principles. Schultz, Smith, and their colleagues demonstrated that a microwave beam passing through the engineered material experiences negative refraction when they combined tiny copper rings with wires on stacked circuit board substrates. This remarkable discovery showed that metamaterials can produce a wider range of refractive indexes, than what nature provides. It opens up new technological possibilities. Researchers have since created negative-index materials that can be used for visible light and other frequencies.
After this breakthrough, a lot of metamaterial research was focused on cloaking. Around 15 years ago, while I was working with Nader Engheta of the University of Pennsylvania, we designed a metamaterial shell that would make an object undetectable by causing the light waves bouncing off the shell to cancel out the light waves scattered from the cloaked object. The cloak would redirect any wave that hits the structure, regardless of its direction. This would cancel the wave scattered from the object. The cloaked object would not be visible to the naked eye, and would not appear to exist from an electromagnetic perspective.
Around this time, John B. Pendry of Imperial College London, and Ulf Leonhardt (now at the Weizmann Institute of Science, Rehovot in Israel) proposed other ways to use metamaterials as cloaks. These ideas became a reality after a few years of experimental demonstrations. My group developed a three-dimensional cloak, which can dramatically reduce radio waves that scatter off a cylindrical, making it difficult for radar detection. Metamaterial cloaks are better than existing stealth technologies. They don’t just block the reflected waves but also redirect the incoming waves to eliminate scattering. This makes the cloaked object invisible to radar. Other groups have also extended cloaking to sound waves, creating objects that are impossible to detect by sonar devices. Others have also created cloaks to detect seismic and thermal waves.
There is still a lot to be done before these devices can become invisible cloaks, like those seen in movies. These cloaks allow the object’s multiwavelength background to shine through. Our real-life cloaks have limited capabilities. The fundamental problem is the competition against the principle o causality: information cannot travel faster than the speed light in free space. It is impossible to restore the background electromagnetic field as if they were traveling through an object, without slowing them down.
Based on these principles, my group has demonstrated that we cannot completely suppress scattering from an object at more than a single wavelength (a single color of light) using a passive metamaterial coating. Even if we achieve partial transparency, there is a trade-off between the object’s size and the number of colors it can be cloaked for. It is impossible to cloak a large object at visible wavelengths. However, we can use metamaterials cloaks for smaller objects at longer wavelengths. This opens up exciting possibilities for radar, wireless communications, and high-fidelity sensors that do not disturb their surroundings. Cloaks that are used for other types of waves, like sound, have less limitations as these waves travel at slower speeds.
The concept of symmetry is a powerful tool for designing and applying metamaterials to various purposes. Symmetries are aspects of an object that don’t change when it is rotated, flipped or otherwise modified. Symmetries play an important role in all natural phenomena. According to a 1915 theorem by mathematician Emmy Noether, any symmetry in a physical system leads to a conservation law. One example is the link between energy conservation and temporal symmetry. If a physical system is described using laws that don’t explicitly depend on time, then its total energy must be preserved. Systems that obey spatial symmetries (e.g. periodic crystals) that are stable under translations and rotations, also preserve certain properties of light like its polarization. We can create metamaterials that can overcome and localize conservation laws in controlled ways. This will allow us to develop novel forms of light control, and transformation.
My group has developed an optical metamaterial that can efficiently turn the polarization light that passes through it. It is an example of how symmetries play a powerful role in metamaterial design. In some ways it is a nanoscale version Bose’s twist jute arrangement. The material is made up of several thin layers of glass that are embedded with rows upon rows of gold rods. Each row is tens of nanometers in length. First, we create a layer of nanorods that are oriented in a specific direction over the glass. Next, we stack a second layer. This is identical to the first except that all the rods are rotated at a certain angle. The next layer is decorated with nanorods, which are rotated at the same angle as the previous one. The stack is about one micron thick. However, it has a unique degree of broken spatial order compared to natural periodic crystals where all molecules are lined up in straight rows. The light that passes through the thin metamaterial interacts with the gold nanorods, slowing down electron oscillations. The twisted symmetry of crystal lattice allows for large rotations of the incoming light, which results in a wide range of wavelengths. This form of polarization control is useful for many technologies, such liquid-crystal displays or sensing tools used by the pharmaceutical industry. These technologies rely on polarization rotation, which is typically less efficient in natural materials.
The underlying rotational symmetries play a critical role in governing metamaterial responses. Pablo Jarillo Herrero’s group at Massachusetts Institute of Technology recently demonstrated that two layers of graphene, each with a single layer of elements, were carefully rotated by an exact angle to produce superconductivity. This feature, which neither of the layers individually possess, allows electrons flow along the material with zero resistance due to the twist-induced broken symmetry. The new electronic response is created by the interactions between neighboring atoms within the two layers for a particular rotation angle.
Inspired by this demonstration, in 2020 my group showed that a somewhat analogous phenomenon can occur not for electrons but for light. We used a stack of two thin layers of molybdenum trioxide (MoO3) and rotated one with respect to the other. Each layer is a periodic crystalllite, which means that the underlying molecules are arranged in an orderly fashion. The molecules can vibrate when light passes through this material. Some wavelengths of light can cause strong lattice vibrations when polarized in a direction that is aligned with the molecules. This phenomenon is called a “phonon resonance”. However, light with the same wavelength and perpendicular orientation produces a weaker material response since it doesn’t drive these vibrations. This strong asymmetry in optical response can be exploited by rotating one layer relative to the other. The twist angle controls and modifies the optical responses of the bilayer in dramatic fashions, making them very different from those of a single layer.
Light emitted from a molecule placed on a surface of a traditional material like glass or silver flows outwards in circular ripples, just as a stone hits a surface of water. But when our two MoO3 layers are stacked on top of each other, changing the twist angle can drastically alter the optical response. The crystal lattices have a specific twist angle that forces light to travel in a single direction. This is the analog of superconductivity for photons. This phenomenon allows for the creation of nanoscale images beyond the resolution limits conventional optical systems. It can transport subwavelength details of an imaging without distortion and efficiently guides light beyond the limits of diffraction. These materials are so strongly linked with material vibrations that light in them forms a single quasiparticle, a polariton. This allows for quantum technologies to flourish.
Symmetries in Time
The role of symmetry within metamaterials goes beyond spatial symmetries like the ones caused by geometric rotations. It’s even more fun to break time-reversalsymmetry.
Wave phenomena are often reversible in terms of time. If a wave travels from A to B with the same features, it can also travel back to A. Time-reversalsymmetry is the reason we have the common belief that if someone can hear or see us, they can also hear and see us. This symmetry in wave transmission, also known as reciprocity, can be crucial for many applications. Nonreciprocal transmission of radio waves, for instance, can enable more efficient wireless communications in which signals can be transmitted and received at the same time without interference, and it can prevent contamination by the reflection of signals you send out. Nonreciprocity for Light can protect sensitive laser beam sources from unwanted reflections, and it provides the same benefit in radar or lidar technologies.
Magnetic phenomena are a proven way to break this fundamentalsymmetry. Magnetic phenomena are a way to break this fundamental symmetry. When ferrite, a nonmetallic material with magnetic characteristics, is subjected to a constant magnetic fields, its molecules sustain tiny circulating curents that rotate with a handedness that is determined by the magnetic field orientation. These microscopic currents in turn induce Zeeman splitting. Light waves with right-handed circular Polarization (an electric field that rotates counterclockwise) interact with these molecules. They have a different energy level than the left-handed (counterclockwise). The applied magnetic field is the factor that determines the energy difference. The overall effect of a linearly polarized wave traveling through a magnetized ferrit is to rotate its polarization. This is similar to the metamaterials mentioned earlier. The fundamental difference is that the external magnetic bias determines the handedness of the rotation of the polarization, and not the broken symmetry in metamaterial constituents. These magnetized materials have light’s polarization rotate in the same direction when it travels in one direction and in the opposite direction when it moves in the other direction. This violates reciprocity. Time-reversalsymmetry is now broken.
We can use this phenomenon to create devices that allow waves only to propagate in one direction. Unfortunately, few natural materials have the magnetic properties necessary to achieve this effect. It can also be difficult for silicon-based technologies to incorporate these materials into modern devices. The metamaterials community has worked hard over the last few years to find more efficient ways to break wave mutuality without magnetic materials.
My group has demonstrated that we can replace tiny circulating currents within a magnetized ferrit with mechanically rotating elements of a metamaterial. This effect was achieved in a compact acoustic device using small computer fans spinning air inside an aluminum cavity. It is a first-of its-kind non-reciprocal device for sound. The frequency at which the cavity resonates is different for counterrotating sound wave frequencies. This is similar to Zeeman splitting changing the energy of light’s interactions within a ferrite. This rotating cavity has a different interaction for sound waves depending on how they travel inside it. We can then route sound waves nonreciprocally–one-way only–through the device. This technology is quite simple to develop because the airflow speed required to create this effect can be hundreds of times slower that the speed of sound waves. These non-reciprocal, compact devices can be used to create a metamaterial by connecting them in a lattice. These engineered crystal lattices transport sounds in nonreciprocal ways that are similar to how electrons travel in topological insulators.
Can we use a similar trick to light? In 2018 Tal Carmon’s group at Tel Aviv University demonstrated an analogous effect by spinning the read-head of a hard-disk drive coupled to an optical fiber at kilohertz frequencies, demonstrating nonreciprocal transmission of light through it. Researchers demonstrated that light can be forced to travel in one direction by using mechanically rotating elements. Metamaterials are made up of time-varying constituents and can be switched on and off in specific patterns that mimic rotation. This is arguably more practical. My group has developed several technologies that can be used as non-reciprocal devices based on these principles. Because they are small, we can easily integrate them into larger electronic networks.
We have also extended these techniques for thermal emission, which is the radiation of heat-driven light. All hot bodies emit light. Kirchhoff’s law on thermal radiation, which is a universal principle, states that all materials in equilibrium must absorb and radiate thermal radiation at the same speed. This symmetry has several limitations for device designs, such as those for thermal energy management or energy-harvesting devices like solar cells. We can imagine systems that don’t follow the symmetry of absorption and emission by using design principles similar to those described above to break light reciprocity. Metamaterials can be designed to absorb heat efficiently and not need to reemit any of it toward the source. This increases the energy we can harvest. Analogous principles can also be applied to static mechanics. This allows us to create a 3-D-printed object which asymmetrically transmits a static mechanical force. It is a type of one-way glove that can apply pressure to the back without feeling it.
Many Other Wonders
Metamaterials and broken symmetries offer many opportunities to manipulate and control waves. Scientists are constantly discovering new ways to manipulate light and sound. For example, they combine broken geometric symmetries with temporal symmetries to create novel effects. To control and route electromagnetic waves, metamaterials can be placed on the windows and walls of smart buildings. Nanostructured metasurfaces can shrink bulky optical systems into devices thinner that a human hair. This enhances imaging, sensing, and energy-harvesting technology. Both mechanical and acoustic metamaterials can route and control sound with unprecedented precision. We anticipate many more marvels given the immense opportunities that modern nanofabrication techniques offer, our improved understanding light-matter interactions and sophisticated materials science & engineering.