Magic Window uses liquid crystals to project images

Made in China and then Japan at least 2000 years ago, magic mirrors look like simple flat bronze mirrors with intricate patterns on the back. But shine a light directly on the front of one of them, and the back design will be projected in the reflection.

By the early 20th century, after many years of puzzling over the optical properties of mirrors, scientists had discovered that mirror surfaces are not as perfectly flat as they appear. The front has height variations on the order of hundreds of nanometers that match the pattern on the back. Depending on where it hits the relief of the surface, incident light is reflected in different directions, and the resulting pattern of brightness creates the desired design in the reflected image.

The last piece of the mathematical puzzle was completed in 2005 by Michael Berry of the University of Bristol. He realized that the intensity of the light in each part of the design was related to the surface height variations. So he described the height of the mirror as a function of the position on the reflecting surface. The intensity is directly related to the Laplacian of this height function, which contains the curvature. Therefore, the brightness of the light at any given part of the design is determined by the curvature between adjacent protrusions on the mirror surface.

Still intrigued by the subject, in 2017 Berry theorized a magic window that, rather than reflecting light, would refract light into the desired design. The glass of the window would have a different thickness creating an effect identical to that caused by the surface variations of the mirror. As with the magic mirror, the intensity of the light in the design is described by the Laplace operator.

With Berry’s math and some advanced gear, you have all the tools to create a magic mirror or window with any image you want. Now a team from the University of Ottawa in Canada and MIT, led by Ebrahim Karimi, has created a magical window that is completely flat. Instead of using different thicknesses of glass to refract the light, the researchers’ magic window uses liquid crystals to create optical phase shifts.

“It’s a really versatile approach because it gives us complete control,” says Felix Hufnagel, a member of Karimi’s team and lead author of a paper published in optics in May. “It leaves a lot of freedom to do different types of projects.”

Liquid crystals can refract light in different directions depending on how they are oriented, so by rotating the crystals the researchers were able to shift the phase of the incident polarized light. The interaction of liquid crystals with light also depends on the polarization of the light: different polarizations lead to different phases of the emitted light. And due to the fluidity of the crystals, different parts may have different orientations. The variation in orientations simulates the variations in height in the original magic mirrors and windows.

The Ottawa team used Berry’s technique to determine the orientation each pixel’s crystals would need to produce the desired image. Then the liquid crystals in the magic window were aligned to their desired alignment using a digital micromirror device in combination with a UV alignment laser. This device is a 600×600 array of mirrors, each acting as a single pixel of the image. The mirrors can then be turned on or off individually, aligning the pixel’s crystals. Using many small mirrors allowed the researchers to vary phases in a small area of ​​the magic window and project more complex images.

The researchers were able to use Berry’s Laplacian to realize their designs because the combination of the polarization of the incident light and the phases of the crystal mimics the height function in magic mirrors and windows. And since the polarization is either right-handed or left-handed, the magic windows have two states showing the image. When hit by light of opposite polarization to which the phases have been matched, the light parts of the image become dark and the dark parts become light.

Hufnagel and his Ottawa colleagues tested their new technology by projecting the logos of the university, the school’s sports teams, and the lab. The magic windows featured in the publication are wavelength and polarization dependent, but Hufnagel says that by using certain filters one could create a window that projects a design when sunlight shines on it.

Magic liquid crystal windows are useful for other things than creating fun designs. The images produced by the windows are stable over long distances, a very desirable quality for three-dimensional displays. Much like sci-fi holograms, such screens are currently limited by the focal lengths of the images. Because the image of a flat magic window can be seen from many distances, a person could view the image from multiple locations.

The Ottawa team was drawn to the project in part by Berry’s academic interest in magical windows. Best known for his description of the Berry phase, Berry is such an influential figure that researchers are listening to what he thinks is important, says Hufnagel. The researchers were also enthusiastic about the creative possibilities. “The antique magic mirrors motivated me a lot,” says Hufnagel. “It was demonstrating this beautiful effect and seeing what we can create with these liquid crystal devices and math.”