Fractal patterns are common in nature, including geometric tortoise samples, shell shell structures, succulent plant leaves that repeat to produce a complex pattern, and a frosty pattern on the windscreen of a car in the winter.
The fractals have a characteristic feature of repeating geometry with a structure in varying scales and are found everywhere, ranging from Broccoli Romanesco to ferns, and even on larger scales such as salt flats, mountains, coasts and clouds. Forms of trees and mountains are also similar, so the branch looks like a small tree and a rocky outcrop like a small mountain.
Over the last two decades, scientists have predicted that fractal light can be created using a laser. Thanks to its highly polished spherical mirrors, the laser is almost exactly the opposite of nature, so it was a surprise when in 1998 scientists predicted fractal light rays emitted from the lasers. Now a team from South Africa and Scotland has demonstrated that fractal light can be made from a laser and verify the two decade's prediction.
Report this month in 2009 Physical Overview A, the team provides the first experimental evidence for fractal light from simple lasers and adds a new prediction: that a fractal formula should exist in 3-D and not just in two-d, as previously thought.
Nature creates such "patterns within patterns" by many recursions of a simple rule, such as creating snowflakes. Computer programs also make fractals by repeatedly repeating a rule that makes a great set of abstract Mandelbrots.
The lights inside the lasers also cycle back and forth, jumping between the mirrors on each passage, which can be set to show the light to each other on each turn of the road. It looks exactly like a recursive loop, a repeating simple rule over and over again. Displaying means that each time the light returns to the image plane, it is a smaller (or larger) version of what it was: a pattern inside the pattern inside the pattern.
Fractals have applications in imaging, networking, antennas and even drugs. The team expects that the discovery of fractal light forms that can be created directly from the laser should open new applications and technologies based on these exotic states of structured light.
"Fractals are a truly fascinating phenomenon associated with what is called chaos," says Professor Andrew Forbes of Witwatersrand University, who led the project together with Professor Johannes Courtiale of the University of Glasgow. "In the popular scientific world, chaos is known as the Butterfly Effect, where a small change in one place leads somewhere else to a big change-a butterfly that blows wings in Asia causing a hurricane in the US has been proven to be true."
In explaining the discovery of fractal light, Forbes explains that his team has realized the importance of looking for fractals in the laser. "Look at the wrong place inside the laser and you will see only the blurred light spot. Look at the right spot where imaging is going and you see fractals."
The project combined the theoretical knowledge of the Glasgow team with experimental verification in South Africa by researchers Wits and CSIR (Council for Scientific and Industrial Research). The initial version of the experiment was built by Dr. Darryl Naidoo (CSIR and Wits) and complemented by Hend Sroor (Wits) as part of his Ph.D.
"It's amazing that according to predictions, the only requirement is to prove the effect of a simple laser with two polished spherical mirrors. It was there all the time, it was hard to see that you had not seen the right place," says Courcil.
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Beautiful mathematical fractals
Hend Sroor et al., Fractal Light from Lasers, Physical Overview A (2019). DOI: 10.1103 / PhysRevA.99.013848