Topological Solitons Power a Chip-Scale Frequency Comb Source

Caltech scientists have developed a new way to produce optical frequency combs—important tools in devices that keep time and measure distances very precisely—at the chip scale, an advance that should make it easier to incorporate such combs in optical devices and more practical to use them outside the laboratory. To generate the combs, the new research demonstrates the utility of a robust class of light pulses, called topological solitons, that had been previously predicted but largely unexplored until now.

The scientists, led by Caltech's Alireza Marandi, professor of electrical engineering and applied physics, describe their findings in a paper that was published online on March 25 in the journal Nature.

Frequency combs are light sources that emit a precise ruler-like "comb" of many evenly spaced frequencies. Over the last three decades, they have become important tools in spectroscopy, in telecommunications, and even in astronomical research. Currently, most frequency comb sources rely on bulky tabletop laser sources. The new work shows that an electrically pumped laser diode integrated with a photonic chip with strong nonlinearity can serve as a frequency comb source.

"Our new approach allows us to explore a completely different path," Marandi says. "It promises that many of the challenges we have faced with other on-chip methods for generating frequency combs may be avoided."

The power of quadratic nonlinearity

In typical linear optics, a material or device—say, the lenses in a pair of eyeglasses—responds proportionally to the electric field of incoming light. In other words, the frequencies that enter the device are the same as those coming out. In contrast, when nonlinearity is involved, the response of the material is not proportional. To understand the concept, consider another case of nonlinear response: audio distortion. A guitar amplifier turned up slightly continues to produce a pure tone, but if turned up too high, a listener begins to hear harmonics and overtones—in other words, distortions—that were not in the original sound.

Similarly, in nonlinear optical materials, when light reaches high-enough intensities, the way the material's electrons shift in response to the light's electric field increases not just proportionally to the field strength but also by the square or cube of it. These effects are central to making frequency combs and correspond to what physicists call quadratic and cubic nonlinearities. In many chip-scale systems, frequency combs rely on cubic nonlinearity. Although this effect exists in all optical materials, it is typically weaker than quadratic nonlinearity. As a result, extremely high-quality resonators are needed; these resonators trap light, which then circulates within the resonator long enough to build up sufficient nonlinear response and generate combs. Stringent fabrication constraints are required to make such high-quality resonators. Additionally, there are strict limitations imposed by the material properties on the wavelength ranges in which these combs can be generated.

A new Caltech device called a degenerate optical parametric oscillator (DOPO) instead exploits the much stronger quadratic nonlinearity in a material called lithium niobate, which relaxes many of these constraints. Such a strong quadratic nonlinearity is absent in many materials typically used in integrated photonics, such as silica, silicon, and silicon nitride. Because of this strong nonlinearity, the resonator does not need to trap light for as long a time to achieve the nonlinear response, meaning a lower quality resonator that is easier to fabricate is sufficient to produce the nonlinear effects.

A topological twist in the light field

DOPOs enable optical frequency conversion: Starting from input light at a given frequency, they generate signal light at half that frequency. Specifically, the outgoing signal light can emerge with only two possible phases, or states, within the electric field's oscillation—either 0 or π, also written as +1 or -1. The signal field wants to be either a continuous wave with a "+1" or "-1" amplitude. "It looks like taking a square root," Marandi says. "If you take the square root of one, you can get both plus one and minus one. That is a fundamental feature of DOPOs, which has been observed in many different contexts."

What has not been observed but has been predicted, Marandi says, is that you can actually operate a DOPO such that both "+1" and "−1" states can co-exist in the DOPO. When this happens, the two states connect at a transition region (at zero), forming a dark pulse, a sharp dip in the otherwise continuous field. This connection, or boundary, carries a topological charge, meaning it is locked in place. Physicists call such a structure a topological soliton, which is a robust structure that persists even in the presence of small disturbances.

Spatial versions of topological solitons, where the two states of opposite phases exist side by side in the output beam, were observed by scientists in the 1990s. However, the current work marks the first experimental demonstration that such solitons can be achieved in the time domain where the field in the DOPO is in the "+1" state for part of each round trip and the "-1" state for another part. The Caltech scientists confirmed the formation of these dark pulses that lasted approximately 60 femtoseconds (a femtosecond is a quadrillionth of a second), which corresponds to a broad frequency comb.

"Thanks to the DOPO, this topological frequency comb forms at half the frequency of the input light," says Nicolas Englebert, a postdoctoral scholar at Caltech and one of the lead authors of the study along with Robert M. Gray (PhD '25), now of ETH Zurich. "This is particularly exciting since it allows for generating combs in the hard-to-access mid-infrared spectral region, starting from readily available integrated near-infrared lasers," Englebert adds.

The team also demonstrated a proof-of-concept, fully integrated frequency comb source by coupling an electrically driven laser diode directly to a DOPO chip. The result was both a two-soliton comb state and a "soliton crystal state, "meaning that it features multiple solitons (here, 16 evenly spaced dark pulses).

"There is still a lot to understand about how these topological soliton states form and evolve inside the DOPO," Marandi says. "Our next step is to further characterize their behaviors and explore potential applications beyond frequency comb sources."

The paper is titled "Topological Soliton Frequency Comb in Nanophotonic Lithium Niobate."Authors Luis Ledezma (PhD '23) and Ryoto Sekine (PhD '25) worked on the project at Caltech. Additional authors are Caltech graduate students Thomas Zacharias (MS '25), Rithvik Ramesh, and Benjamin K. Gutierrez (MS '23); and Pedro Parra-Rivas of the University of Almeria in Spain. The DOPO was fabricated at the Kavli Nanoscience Institute at Caltech. The work was supported by funding from the Defense Advanced Research Projects Agency, the National Science Foundation, the Army Research Office, the Air Force Office of Scientific Research, Caltech's Center for Sensing to Intelligence, the Alfred P. Sloan Foundation, the Jet Propulsion Laboratory, which Caltech manages for NASA, the Belgian American Educational Foundation, and the European Union's Horizon Europe research and innovation program.