Fractal patterns are common in nature, including the geometric patterns of the tortoise shell, the structure of the snail shell, the leaves of a succulent plant, which repeat to form an intricate pattern, and a frost pattern on the windshield of a car in winter.
Fractals have a distinctive feature of repetitive geometry with structure on several scales and are found everywhere, from Romanesco broccoli to ferns, and even on larger scales such as salt marshes, mountains, coastlines and clouds. The shapes of the trees and mountains are also self-similar, so the branch looks like a small tree, and the rocky cliff looks like a small mountain.
Over the past two decades, scientists have predicted that fractal light can be created with a laser. Possessing highly polished spherical mirrors, laser is almost the exact opposite of nature, and therefore came as a surprise when in 1998 researchers predicted fractal light rays emitted from a class of lasers. Now, a team from South Africa and Scotland has demonstrated that fractal light can be created from a laser, confirming the prediction of two decades.
Reporting this month at Physical Overview AThe team provides the first experimental evidence of fractal light from simple lasers and adds a new prediction: a fractal model must exist in 3-D, and not only in 2-D, as previously thought.
Nature creates such “patterns within patterns” by many simple recursion rules, for example, to create a snowflake. Computer programs also create fractals, repeatedly repeating the rule, creating a cool Mandelbrot set.
The light inside the lasers also moves back and forth cyclically, being reflected between the mirrors on each aisle, which can be adjusted to display light in itself during each roundabout. It looks like a recursive loop, repeating a simple rule over and over again. The display means that each time the light returns to the image plane, it represents a smaller (or larger) version of what it was: the pattern inside the pattern in the pattern.
Fractals are used in visualization, networks, antennas and even medicine. The team expects that the discovery of the fractal forms of light that can be projected directly from the laser should open up new applications and technologies based on these exotic states of structured light.
“Fractals are a truly fascinating phenomenon associated with what is known as chaos,” says Professor Andrew Forbes from the University of Witwatersrand, who led the project together with Professor Johannes Curtil from the University of Glasgow. “In the world of science, chaos is known as the“ butterfly effect, ”where a small change in one place leads to a big change somewhere else, for example, if you beat a butterfly in Asia, it causes a hurricane in the United States. it was proven to be true. "
Explaining the discovery of fractal light, Forbes explains that his team realized the importance of where to look for fractals in a laser. “Look at the wrong place inside the laser and you will only see a blurred ball of light. Look in the right place where the image takes place, and you see fractals. ”
The project combined the theoretical expertise of the Glasgow team with experimental testing in South Africa by Wits and CSIR researchers (Council for Scientific and Industrial Research). The original version of the experiment was built by Dr. Darryl Naidu (from CSIR and Wits) and completed by Hand Sror (Wits) as part of her PhD thesis.
“What is surprising is that, as expected, the only requirement for demonstrating the effect is a simple laser with two polished spherical mirrors. He was there all the time, it's just hard to see if you looked at the right place, ”he says. Courtial.
Beautiful math fractals
Hand Sroor et al., Fractal light from lasers, Physical Overview A (2019). DOI: 10.1103 / PhysRevA.99.013848