Taking topology to new heights—with light

Boubacar Kanté had been struggling to solve a problem that has plagued laser physics since the devices were invented more than 60 years ago—how to get the maximum amount of laser power out without any loss. In theory, enlarging the size of the laser cavity would increase the energy of the beam, but making the cavity bigger raises the number of modes at which the light waves can exist, limiting the power that goes into the lasing mode.

Now, though, Kanté—an associate professor of electrical engineering and computer science at the University of California, Berkeley—has created a compact, surface-emitting laser that produces just a single mode of light with no limit on beam power. It works thanks to topological photonics, a concept from mathematics that is growing in popularity in optical science. He calls the device a Berkeley surface-emitting laser, or BerkSEL.

Topological photonics grows out of a mathematical principle that has been applied with some success to materials science and, in recent years, has penetrated the world of optics. It deals with properties of an object that remain intact even when that object is stretched or reshaped, but not when it is torn. Moreover, it describes phenomena that change abruptly in distinct steps, rather than a continuous flow, more like an on/off light switch than a dimmer. Researchers are working to understand how to create topological systems in photonics and figure out just what they’ll be good for.

Five years ago, Kanté exploited these properties to create the world’s first topological laser. Using so-called topological photonics meant that he could shape the laser cavity however he wanted, as well as switch the direction of emission using a magnetic field. Now the approach, with its inherent ability to protect certain electrical and optical states, is being explored as a pathway to more compact lasers, chips for optical computers, and components of quantum computing.

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Topology is the mathematics of properties that remain undisturbed, even while the materials that contain those properties are deformed. In an ordinary laser, a material defect or a change in temperature might alter the quality of the light it emits. But in a topological laser, those differences don’t matter. Researchers are excited about topological photonics because it could let them create devices that do previously impossible things, like Kanté’s single-mode cavity. The challenges facing scientists are, first, to figure out how to create these topological states in photonics devices, and then to find practical applications for them.

Some optical scientists’ work is inspired by achievements in materials science. For instance, one common device in electronics based on the theory is a topological insulator. Electrical current runs in one direction along the surface of a topological insulator, but it won’t pass through the bulk of the material. Because topology protects the device’s electrical properties, the current still flows in the same way, even if there’s a difference in the material, such as a missing or misplaced atom or two, or if the material is bent or strained. In a traditional conductor, one without topological protection, a defect or strain could change how current flows, or stop it altogether.

Even extreme changes in temperature won’t alter the properties of a topological material. For example, an alloy of bismuth, rhodium, and iodine remains a topological insulator until it melts. In photonics, such robustness could be used to prevent hurdles like backscattering, so that light propagates in one direction only and despite material defects.

Similarly, the device wouldn’t lose power even if there were defects in the crystal lattice. “If by chance you have an array of lasers and one of the elements really is in trouble, then another element takes over in a seamless way, and the array still operates single mode with high efficiency without really getting impaired,” says Demetri Christodoulides, a professor of optics at CREOL, the College of Optics and Photonics at the University of Central Florida. Christodoulides is one of many researchers developing a photonic version of a topological insulator.

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Figuring out how to make an optical device topological can be a challenge. In materials science, topological properties often can be achieved via uncommon heavy-metal alloys that have unusual electronic bandgap structures. Topology works much the same way in photonics, except that it relies on photonic bandgaps. “That photonic bandgap can be what we call trivial, which means that it doesn’t have topological properties, or it can be topological,” says Andrea Blanco-Redondo, who heads the Silicon Photonics department at Nokia Bell Labs.

To create a topological photonic bandgap, researchers create modified versions of photonic crystals, which use a periodic arrangement of structures about the same size as the wavelengths of interest to control the flow of light. Most photonic crystals are not topological. “To make it topological, you need to play with the symmetries of the system,” Blanco-Redondo says. “There’s only specific symmetries that you can exploit to get these special topologies.”

Hexagonal lattice photonic crystal. Photos courtesy of Nature

The easiest symmetry to envision, she says, is chiral symmetry. Every left-right pair is one unit, and a chain of these units can create a symmetry. That’s not to say that every periodic structure is topological, Blanco-Redondo says. To achieve a topological bandgap, the symmetries must be broken. For instance, you might start stretching the crystal, so that the distance between units increases the further you get from the center. There are even more complex designs that lead to topological bandgaps, and they’re not easy to picture, she says. “As you go, these things become harder to explain and you just have to resort to mathematical models. But you can relate these mathematical models to specific geometries in certain platforms.”

In the case of Kanté’s laser, he designed what he calls an open Dirac cavity. The cavity is built from a photonic crystal made of indium phosphide perforated with an array of hexagonal holes. He chose indium phosphide because it emits light at around 1.5 µm, a common telecommunications wavelength, but the concept would work with any semiconductor, he says. To make a cavity, he places perpendicular structures on the plane, forming a hexagon. The edges of that structure give rise to the topological bandgap.

The result is that light coming out of one location on the laser has the same phase of light as that coming out of any other location. No matter how big the cavity gets, the light remains at the same phase, and no new modes form, so the larger it grows, the more power it puts out.

To figure out how to build a photonic topological insulator, researchers have tried twisting a waveguide around its axis to create periodic modulation in the light, thus creating topological states. That approach doesn’t work very well because moving the waveguide in space means the separation between different elements in the system can change over time, thus changing the relationships between them that are necessary to create the topological states, says Georgios Pyrialakos, a research scientist at CREOL.

To solve that dislocation problem, Pyrialakos and his colleagues in Christodoulides’ research group came up with a new design. They used laser pulses to create chains of varied refractive indexes in a honeycomb pattern in fused silica. That in turn gave rise to multiple topological states within the material. Such a design might be used to build a photonic circuit that would transport information along the boundaries between two different photonic materials, Pyrialakos says, eventually leading to low-power optical computing.

The Berkeley surface emitting laser, showing the pump beam in blue and the lasing beam in red.

Many of the photonic topological insulators built to date don’t actually prevent backscattering, says Andrea Alù, professor of physics and director of the Photonics Initiative at City University of New York’s Advanced Science Research Center. Alù created a version of the device that he says does stop backscattering by using rapid switching to control the temporal period of the signal, and then using that temporal periodic structure to create the topological states. He accomplished this not by working at optical wavelengths but at radio frequencies in the gigahertz range. The electronic switches allow him to modulate the gigahertz fast enough to be useful. There’s no equivalent switch to allow rapid enough modulation at the higher frequencies of visible or infrared light without also sacrificing the bandwidth of the signal, so his device is not really photonic, but he says it could pave the way to a photonic version. “We are working on translating these to optics,” Alù says. One method to achieve fast enough switching optically might be to use nonlinear effects in a laser.

One of the difficulties with topological photonics has been the reliance on photonic crystals. Such crystals have to have structures roughly the same size as the wavelengths they’re dealing with, and those structures have to be repeated tens or hundreds of times, making any such device relatively large. If there’s a lot of space to work with, Alù says, there might be easier ways to achieve the same goals without coming up with a complicated topological design. “The selling point has been that these topological features are inherently robust. If I am given hundreds of wavelengths of footprint, I can make it very robust in other ways. It’s not that difficult to get a robust response without necessarily getting topological features.” His fast-switching gigahertz device, on the other hand, is relatively tiny, only a fraction of a wavelength in size. Of course, at 10 mm², it seems large compared to photonic crystals. But that’s only because radio wavelengths are so much larger than optical ones, he says. Scaling the device to optical frequencies would make a device much smaller than photonic crystals with topological protection built in.

Because of the space photonic crystals and waveguides take up, trying to use topological photonics to pack a lot of lasers onto a chip, for instance, may not be the most interesting application of the theory. What’s really interesting is using it to provide robust protection in quantum applications, says Blanco-Redondo.

She is building topological lattices to carry pairs of entangled photons. The idea is to protect this quantum state of light for applications like quantum computing. While she can protect the photons from losing their entanglement, she’s not yet sure how to prevent backscattering.

The main challenge still facing topological photonics, she says, is figuring out how to move it from an area that’s scientifically interesting to a way of creating practical applications. “This is undoubtedly a very cool field, but what can we truly do with this that is useful?” she says. “As it stands right now, it is not truly solving the issues of large-scale optical integration or of quantum computing. But we’re taking baby steps towards that.”

Topological photonics has the potential to spark new ideas no one has come up with yet. So far, much of the work has involved translating discoveries in topological materials from electronics to photonics. But because photons behave so differently from electrons, Alù says, photonics could push the field in new directions. “Photonics provides a lot more knobs to build materials with the right properties, with the right symmetries,” he says. So, photonics may be able to discover new classes of topological systems that could never be achieved in electronics.

Christodoulides says he’s eager to see where applying the principles of topology could lead. “The introduction of these concepts in photonics is relatively new. And of course, the exploitation of these ideas as something more tangible is also new,” he says. “The best ideas always come from unexpected places. Hopefully, topology will be another avenue from [which] we can benefit.”

Neil Savage writes about science and technology in Lowell, Massachusetts.