Manipulating Light by Checkerboard

From Vans shoes to Pinterest cakes and the 2020 Olympic Games logo, checkerboard patterns draw us in. Their contrasting colors have symbolized duality, co-existence, and harmony throughout history. They cover floors, flags, and furniture. In work that puts a 21st century spin on checkerboards, a team of Japanese researchers recently demonstrated that a special kind of checkerboard can be used to create state-of-the-art optical tools.

Marble and Granite Checkerboard floor of the Old Royal Palace (Prague, Czech Republic).
Image Credit: Chris Walts (CC BY 2.0).

Yosuke Nakata, an engineer at Shinshu University, is the lead author of an upcoming article in the journal Physical Review Applied that describes this work. He traces his fascination with checkerboards back to Paris, 2012. Not to a game of chess or a runway fashion statement, but to an international science meeting. In between talks, Professor Masanori Hangyo from Osaka University captured Nakata’s attention by introducing him to the “eccentric properties of checkerboards,” recalls Nakata.

In a checkerboard, the colors of the squares can be switched but the pattern remains the same. If you remove the connection points between different colors, you get a kind of disconnected checkerboard, as shown below. In image (a), the white squares are all connected, but the gray are not. In (b), the gray squares are connected but the white ones are not. Note that the white part of the disconnected checkerboard is identical to the gray part of the connected checkerboard. The two patterns are complements of each another. Applying this pattern to create a special kind of surface, called a metasurface, results in unique abilities to control light.

A disconnected checkerboard (a) and its complement (b).
Image Credit: Nakata, et al.

Metamaterials are materials made up of tiny structures that are individually smaller than the wavelength of light. The design, size, and arrangements of these structures affect the way light interacts with the material. In other words, we can build materials out of these structures that interact with light in ways that materials in nature can’t. Among other applications, metamaterials open the door to seemingly impossible devices like invisibility cloaks and super lenses.

An extremely thin metamaterial is called a metasurface. Like metamaterials, metasurfaces interact with light in unique, controllable ways. With careful design, you can do things like change the brightness of light passing through, alter its path in strange ways, and make holograms.

Imagine a checkerboard-patterned metasurface in which the gray squares are metal. When they are all connected, current can travel through them as in a circuit. Referring to the image above, (a) would be in “off” state and (b) would be “on” state. A metasurface with a checkerboard pattern controls the brightness of light passing through.

If you modify the checkerboard by replacing the connection points with a material whose resistance you can control, shown in green below, you can switch between the on and off states by varying the resistance. In other words, changing the resistance of the interconnection points changes the checkerboard from one state into its complement—from (a) to (b) or vice versa.

In this modified checkerboard design, the gray squares are metallic and the green interconnections are made out a material whose resistance you can control.
Image Credit: Nakata, et al.

Previous experiments have shown that the light transmitted by a checkerboard metasurface in one state is reflected by its complement. Therefore, by flipping the switch you can alternate between transmitting and reflecting the same wavelength of light.

In this new work, the researchers demonstrate how to control the polarization of light with a checkerboard metasurface. Why is this important? Light contains all kinds of information. Similar to the way that looking at your surroundings in infrared light gives you information that you can’t see with your eyes, looking at light polarized in different directions gives you more information about an object. Ideally, researchers should be able to change their viewing mode quickly without disturbing their setup.

A metasurface with a simple checkerboard pattern only affects the brightness of light at a specific wavelength, not polarization. However, the team realized that when you break the symmetry of the design, the metasurface becomes sensitive to polarization. The act of switching the surface on and off now lets you alternate between transmitting and reflecting different components of a light wave.

After exploring a few designs theoretically, they landed on one that gave the metasurface the functionality they were looking for—the ability to alternate between transmitting and reflecting the perpendicular components of a light wave. The key to the team’s success was keeping the symmetry of the checkerboard pattern, but adding in a feature offset by 90-degrees between the black and white squares. The concept is illustrated below, although the actual design isn’t quite as smiley!

An illustration highlighting the symmetry-breaking concept behind the new design.
Image Credit: Mayuko Tanaka.

To test its effectiveness, the researchers created a metasurface with this design optimized for light in the terahertz range. Tests of the experimental device matched their simulated data well, and indicate that this design could work not only for terahertz applications, but for light in other frequency ranges as well. The next steps include optimizing the fabrication process, testing this in other frequency ranges, and then putting this tool to work.

Just two years after the Paris meeting, Professor Hangyo passed away unexpectedly. “I will never forget the importance of my impromptu meeting in Paris with Professor Hangyo, and I hope my work will honor his memory,” says Nakata.

Kendra Redmond

You may also read these articles