Credit: Felix Hufnagel, University of Ottawa
MAGIC WINDOW COM WINDOWS
Liquid crystals enable the creation of magic windows that produce hidden images. The variation in orientations simulates the height variations in the original magic mirrors and windows. And because of the crystals’ fluidity, different parts can have different orientations. Liquid crystals’ interaction with light also depends on the light’s polarization: Different polarizations result in different phases in the outgoing light. Liquid crystals can refract light in different directions depending on their orientation, so by turning the crystals, the researchers could shift the phase of the incoming polarized light. “It allows for a lot of freedom to do different kinds of projects.” “It’s a really versatile approach because it allows us complete control,” says Felix Hufnagel, a member of Karimi’s team and the lead author of a paper published in Optica in May. Instead of using varying thicknesses of glass to refract the light, the researchers’ magic window uses liquid crystals to impart optical phase shifts. Now a team from the University of Ottawa in Canada and MIT led by Ebrahim Karimi has created a magic window that is completely flat. Using Berry’s math and some advanced equipment, one has all the tools to make a magic mirror or window with any image. The intensity of the light in the design is described by the Laplacian, just as for the magic mirror. The window’s glass would have a varying thickness that creates an effect identical to the one caused by the mirror’s surface variations. Still intrigued by the subject, Berry in 2017 theorized a magic window, which instead of reflecting would refract the light into the desired design. Therefore, the brightness of the light at any given part of the design is determined by the curvature between adjacent protrusions on the mirror’s surface. The intensity is directly related to the Laplacian of that height function, which includes the curvature. So he described the height of the mirror as a function of position on the reflecting surface. He realized that the intensity of the light in each part of the design is related to the surface-height variations. The last piece of the mathematical puzzle was completed by Michael Berry of the University of Bristol in 2005. Credit: Rob Deslongchamps/Cincinnati Art Museum A Buddhist bronze “magic mirror” that was created in China or Japan in the 15th or 16th century is on display at the Cincinnati Art Museum. Incoming light is reflected in different directions depending on where it strikes the relief on the surface, and the resulting brightness pattern produces the desired design in the reflected image. The front surface has height variations on the scale of hundreds of nanometers that match the pattern on the back. But shine a light directly at the front of one of them, and the back’s design is projected in the reflection.Īfter many years of puzzling over the mirrors’ optical properties, scientists had determined by the early 20th century that the mirror surfaces are not as perfectly flat as they appear. Created in China at least 2000 years ago and then in Japan, magic mirrors look like simple flat bronze mirrors with ornate designs on the back.
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