Fractal Light from Lasers

Several patterns of fractal light, created by a laser in the Wits Structured Light Laboratory. (Source: Wits Univ.)

The geome­trically shaped patterns of a shell of a tortoise or the frost pattern on the windshield of a car after standing outside in winter. These patterns are all examples of fractals, the geometry of nature. They have the distinc­tive feature of a repeating geometry with structure at multiple scales and are found every­where. For the past two decades, scientists have predicted that you could create fractal light from a laser. With its highly polished spherical mirrors, a laser is almost the precise opposite of nature, and so it came as a surprise when, in 1998, light beams emitted from a class of lasers were predicted to be fractals. Now a team from South Africa and Scotland have demon­strated that fractal light can be created from a laser, verifying the prediction of two decades. The team provides the first experi­mental evidence for fractal light from simple lasers and add a new pre­diction, that the fractal light should exist in 3D and not just 2D as previously thought.

Fractals are complex objects with a pattern within a pattern so that the structure appears to repeat as you zoom in or out of it. Nature creates such patterns within patterns by many recursions of a simple rule, for example, to produce a snowflake. Computer programmes have also been used to do so by looping through the rule over and over, famously producing the abstract Mandel­brot Set. The light inside lasers also does this: it cycles back and forth, bouncing between the mirrors on each pass, which can be set to image the light into itself on each round trip. This looks just like a recursive loop, repeating a simple rule over and over. The imaging means that each time the light returns to the image plane it is a smaller or bigger version of what it was: a pattern within a pattern within a pattern.

Fractals have found appli­cations in imaging, networks, antennas and even medicine. The team expects that the discovery of fractal forms of light that can be engineered directly from a laser should open new appli­cations and tech­nologies based on these exotic states of structured light. “Fractals is a truly fasci­nating phenomenon, and is linked to what is known as Chaos,” says Andrew Forbes, from the University of the Witwaters­rand, who led the project together with Johannes Courtial of the University of Glasgow. “In the popular science world, Chaos is called the butter­fly effect, where a small change in one place makes a big change somewhere else, for example, a butterfly beating its wings in Asia causes a hurricane in the USA. This has been proven to be true.”

In explaining the fractal light disco­very, Forbes explains that his team realised the impor­tance of where to look for fractals in a laser: “Look at the wrong place inside the laser and you see just a smeared-out blob of light. Look in the right place, where the imaging happens, and you see fractals.” The project combined theo­retical expertise from the Glasgow team with experi­mental vali­dation in South Africa by Wits and CSIR (Council for Scien­tific and Industrial Research) researchers. The initial version of the experiment was built by Darryl Naidoo (of the CSIR and Wits) and completed by Hend Sroor (Wits) as part of her PhD. “What is amazing is that, as predicted, the only require­ment to demon­strate the effect is a simple laser with two polished spherical mirrors. It was there all the time, just hard to see if you were not looking at the right place,” says Courtial. (Source: Univ. Witwaters­rand)

Reference: H. Sroor et al.: Fractal light from lasers, Phys. Rev. A 99, 013848 (2019); DOI: 10.1103/PhysRevA.99.013848

Link: School of Physics, University of the Witwatersrand, Johannesburg, South Africa

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