Inverse, Mie Scattering Techniques Advance 3D Metamaterial Design

Using an inverse design approach, a team led by researchers at the University of Washington designed and tested a 3D-printed metamaterial that can manipulate light with nanoscale precision. Though the researchers chose a spiral helix pattern for their optical element, they said their approach could be used to design elements that focus light in other patterns.

The element created by the team, whose members include researchers from the Air Force Research Laboratory and the University of Dayton Research Institute, is essentially a surface covered with thousands of tiny spheres of different sizes, arranged in a periodic square lattice. The team used a commercially available 3D printer to fabricate two prototypes. The larger of the two has sides just 0.02 cm long. The prototype elements were 3D-printed out of an ultraviolet epoxy on glass surfaces. One element was designed to focus light at 1550 nm and the other at 3000 nm.

A scanning electron micrograph image of the surface of the optical element. Courtesy of James Whitehead/University of Washington.

To simplify the design and simulation process, the researchers used Mie scattering theory. This allowed them to make precise calculations about what the properties of light would be when light interacted with the optical element.

“Our implementation of Mie scattering theory is specific to certain shapes — spheres — which meant we had to incorporate those shapes into the design of the optical element,” researcher Alan Zhan said.

To test whether the optical elements performed as designed, the researchers visualized the elements under a microscope, focusing light of either 1550 nm or 3000 nm at eight specific points along a 3D helical pattern. Under the microscope, most focused points of light were at the positions predicted by the team’s theoretical simulations. For example, for the 1550-nm wavelength device, six of eight focal points were in the predicted position. The remaining two showed only minor deviations.

These images show the performance of the 1550-nm optical element. The images are light-intensity profiles of the optical field as it appears approximately 185 μm above the surface of the optical element. To the left is a simulated light-intensity profile that predicts how the optical element should perform. Note the focal point of light near the center of the image. To the right, an actual light-intensity profile of the optical element, showing that the device produces a focal point of light at the predicted location. The researchers designed the element to focus light at eight such points at different distances above the element’s surface. Scale bar is 10 μm. Courtesy of Alan Zhan/University of Washington.

Based on the prototypes’ performance, the team would like to improve the design process to reduce background levels of light and improve the accuracy of the placement of the focal points, and incorporate other design elements compatible with Mie scattering theory.

“Now that we’ve shown the basic design principles work, there are lots of directions we can go with this level of precision in fabrication,” professor Arka Majumdar said. One promising direction is to progress beyond a single surface to create a true-volume, 3D metamaterial. “3D-printing allows us to create a stack of these surfaces, which was not possible before,” Majumdar said.

The team’s design principles and experimental findings demonstrate that it is possible to model and construct metamaterial devices that can precisely manipulate optical fields with high spatial resolution in three dimensions. Devices with this level of control over light could be used to miniaturize optical elements such as lenses or retroreflectors and to realize new types of elements. In addition, designing optical fields in 3D could enable creation of ultracompact depth sensors for autonomous transportation, as well as optical elements for displays and sensors in virtual- or augmented-reality headsets.

The research was published in Science Advances (https://doi.org/10.1126/sciadv.aax4769).