Research Team Has Demonstrated First Laser to Generate Laser Beams with Fractal Pattern

A research team at Illinois has demonstrated the first laser to generate laser beams having a fractal pattern. The team includes members Jose A. Rivera, Thomas C. Galvin, Austin W. Steinforth, and J. Gary Eden, an MNTL researcher and Professor in Electrical & Computer Engineering at Illinois. The research group’s paper, “Fractal Modes and Multi-beam Generation from Hybrid Microlaser Resonators” was published in early July by Nature Communications.

A fractal is a geometric image based on a particular basic pattern or design that is repeated throughout, but is progressively reduced in size as the image is constructed. Fractals often occur in nature. Examples include snowflakes, neurons, and even a particular type of broccoli known as Romaneso broccoli. The Sierpinski Triangle (or Sierpinski Sieve) and the Menger Sponge are well-known examples in mathematics.

Conventional lasers produce Gaussian beams having cross-sectional shapes determined primarily by the separation between the two laser mirrors and their radii of curvature. In contrast, laser fractal modes were discovered by placing arrays of microspheres in the laser resonator, which led to fractal laser modes being produced in the gaps (interstices) between the spheres. If the spheres were “close-packed”, forming a hexagonal pattern, the fractal laser modes consisted of triangles of differing sizes. When a gap was carefully opened in the microsphere, the resulting fractal patterns comprised the superposition of rectangles or squares.

Eden commented on the relevance and impact of this discovery: “One significant aspect of this work is that laser beam cross-sectional patterns are no longer confined to the specific parameters of the laser resonator but can now be designed to match a mathematical expression. This, in turn, suggests that fractal laser modes will be of continuing interest in their own right, but also for optical information processing and imaging.”      

Eden is the Director of the Laboratory for Optical Physics and Engineering in Electrical & Computer Engineering, and the Principal Investigator for the Air Force Office of Scientific Research (AFOSR) grant that supported this work. Eden also acted as the Ph.D. advisor for Rivera and Galvin, and is currently Steinforth's advisor.