Metamaterial device makes 16 polarization measurements at once

When you’re walking on the beach on a sunny day, polarized sunglasses come in handy: The glare off the water, even though it’s a reflection of unpolarized sunlight, is horizontally polarized, so it’s blocked by the vertically polarized lenses. The phenomenon is the result of how light reflects off a dielectric, so glare off metal surfaces is different. If you had full polarization vision, you could readily tell whether a shiny object in the distance is a pool of water or a sheet of steel.

What would “full polarization vision” entail? To completely describe light’s polarization state—whether linear, circular, elliptical, or partially or completely unpolarized—it takes four numbers, often represented as the four-component Stokes vector, named after George Gabriel Stokes, who worked out the idea in the 1850s. To get a fully polarized view of a scene, therefore, you’d need in effect to image it four times.

But that fourfold Stokes imaging doesn’t capture all the polarization-changing properties of the objects you’re looking at. It describes the polarization of the light coming out of the scene, but it says nothing about the light going in. A quarter-wave plate, for example, looks like an ordinary clear material under unpolarized light, but it transforms circularly polarized light into linearly polarized light and vice versa. To account for the possibility that any polarization state might be transformed into any other, you’d need a 4 × 4 matrix of images, or 16 in total.

You might think that imaging an object 16 times—a so-called Mueller matrix of images, after Hans Mueller’s work in the 1940s—would require an intricate system of polarizers and wave plates to be carefully aligned and realigned. And until recently, you’d be right. But now Aun Zaidi (a recent graduate of Harvard University), his PhD adviser Federico Capasso, and colleagues have developed an imaging system that can do the job in a single optical shot. ¹

Instead of conventional optical components, the Harvard researchers used optical metamaterials—intricate arrays of tiny dielectric pillars—to control and analyze complex polarization states of light. The metamaterials are so compact, at just a few millimeters in diameter, that the whole imaging system can be packaged into a device that can go almost anywhere. It can even fit into an endoscope, where it would be ideally suited for one of polarization imaging’s most powerful applications: cancer screening.

Constructive interference

Ordinary materials get their properties—optical index of refraction, thermal conductivity, mechanical stiffness, and so on—from the interactions of atoms and molecules on the subnanometer scale. For metamaterials, in contrast, the salient features are orders of magnitude larger, but still small. The metasurface optics that the Capasso group uses are made of titanium dioxide pillars a few hundred nanometers wide, just smaller than the wavelength of visible light. Each one acts like a tiny waveguide that briefly slows down the light that passes through it. By controlling the pillar sizes and shapes, researchers can create interference patterns that both mimic and extend the effects of conventional optics.

The principle is easy enough to state, but the implementation is much more complicated. “If you want to create a metalens, that can be done beautifully,” says Capasso. “You just arrange the pillars so all the light rays interfere constructively at the focus.” (See, for example, Physics Today, October 2022, page 19 .) For anything more complicated than that, researchers quickly find themselves at the mercy of numerical methods: starting with a best guess, then iteratively refining it until the optical output is as close as it needs to be to the desired goal.

“It’s hard to get an intuitive feeling for what the result means,” says Capasso. “It’s very frustrating, because as physicists we want to understand what we’ve done. But the algorithm is very powerful, and it spits out the solution.”

In 2019 Capasso and colleagues, led by then-student Noah Rubin, presented a new mathematical formalism that allowed them to design metamaterials that controlled not just the light’s intensity but also its polarization. ² They then designed a polarization analyzer, shown schematically in figure 1a, that splits incoming light into four independent polarization components. The decomposition is different from the one Stokes used, but it’s mathematically equivalent to imaging the Stokes vector.

Figure 1.

Metasurface-based Stokes imaging may already be on its way to practical commercial use. The technology for fabricating optical metasurfaces is similar to what’s already used to make semiconductor chips, so it’s straightforward to integrate metasurfaces into phones, tablets, and other consumer electronics. And Capasso’s startup company, Metalenz, is pursuing an application in enhancing the security of facial authentication.

Current facial-recognition tools are not foolproof: A thief could unlock a stolen phone by showing it a photo of the rightful owner. But photographs don’t carry polarization information—and light reflected off skin is slightly polarized for much the same reason glare off the ocean is. Including a polarization analyzer in a phone’s facial recognition camera can help ensure that it’s unlocked only by the owner’s actual face.

Four by four

As powerful as Stokes imaging is, it’s just one step on the path to full 16-fold Mueller-matrix imaging. To measure an object’s Mueller matrix, you’d need to probe its response to four different polarization states of light. You could do that sequentially in time, but that would require moving parts to physically swap out one metasurface element for another. Instead, Zaidi decided to try using structured light, whose polarization varies in space, as shown schematically in figure 1b.

The idea was to bounce structured light off an object and then image it with a Stokes camera. Each pixel in the resulting Stokes images comes from light with a slightly different polarization; from the known structure of the incoming light, the researchers could calculate the object’s Mueller matrix.

The structured-light approach has the slight disadvantage of sacrificing spatial resolution: If the object’s Mueller matrix varies on a finer spatial scale than the structured light, those details are lost. But to the extent that the resolution loss is a problem, it can be solved by better engineering. “Fundamentally, our only limit is the diffraction limit,” says Zaidi. “Everything else is fabrication: the size of the nanopillars, the size of the metasurface, and so on. There are lots of degrees of freedom when it comes to the design.”

For one of their proof-of-concept experiments, the researchers imaged the chiral beetle—which, as the name suggests, has an unusual asymmetric effect on light. Figure 2a shows the four raw Stokes images. (The fifth image, in the center, is the zero-order, undiffracted light, which carries no additional polarization information.) Although too small to see, tiny fluctuations in the images encode the effects of all the polarizations of the structured light. From those, the researchers computed the Mueller matrix, shown in figure 2b.

Figure 2.

The chiral beetle’s shell is a uniform circular polarizer, so its Mueller matrix is nearly the same everywhere. The researchers expected—and found—the whole beetle to be visible in all the matrix’s nonzero components. Furthermore, because it’s a circular polarizer, they expected the only nonzero components to be in the corners: M₀₀, M₀₃, M₃₀, and M₃₃. The zeroth row and column carry information about the light’s total intensity, and the third row and column encode its degree of circular polarization. The matrix elements in the middle, which encode the degree and direction of linear polarization, should be zero. That’s more or less what the researchers found.

Wealth of data

“Mueller-matrix imaging existed already,” says Zaidi, “but this work makes it more accessible. You no longer need bulky optical components at specific orientations that you need to control precisely. People in other fields, without experience in optics, might have shied away from that.”

The potential applications abound in the biomedical and biochemical sciences. Nearly all biomolecules are mirror asymmetric, so they nearly all have some effect on circularly polarized light. Polarization measurements are a quick way of probing aspects of the composition—such as the sugar content—of a clear solution. It’s even possible to noninvasively check diabetic patients’ glucose levels by making polarization measurements on the clear parts of their eyes. ³

And then there’s cancer. Malignant tissues grow wildly and erratically, and their collagen fibers and other structures are jumbled up. So tumors have a different polarizing effect on light than do healthy tissues, whose collagen fibers are straight. Skin cancer is known to be detectible by Mueller-matrix imaging, but clinical implementation has struggled because of the complexity of the instrumentation. ⁴

Skin cancer is already the easiest cancer to screen for by visual inspection. Most cancers grow in far less accessible areas, where neither doctors’ eyes nor conventional optical instruments can go. But metasurface optics are small enough that they can reach parts of the body that are hard to access otherwise.

“We had a collaboration with a team at Massachusetts General Hospital to develop a metalens to put in an endoscope,” says Capasso. “And for the first time, we could image the very beginning of a bronchial tumor, when its features were of wavelength size.” That work didn’t involve polarization measurements. ⁵ But the Mueller-matrix metasurfaces are no less compatible with endoscopic imaging.

Other applications may still be discovered. Mueller-matrix data are currently sparse, but as more images come in, researchers will learn more about how they can or can’t use the data to classify materials, structures, and biological tissues. As Zaidi points out, the task is well suited to machine-learning algorithms. “Machine learning would find correlations that we’re not aware of yet,” he says. “It’s easier for us to think physically in terms of polarizers and wave plates, but there may be other elements to the data that machine learning can pick up. I think there’s a huge opportunity here.”