Fractal light from lasers

TL;DR

This paper demonstrates the experimental generation of fractal light within laser cavities, confirming theoretical predictions and revealing self-similar 3D structures in laser eigenmodes, thus advancing understanding of fractal patterns in optical systems.

Contribution

It provides the first experimental observation of fractal eigenmodes in lasers and extends the theory to include 3D self-similar structures around the magnified self-conjugate plane.

Findings

Fractal shapes observed in transverse intensity cross-sections of laser modes.

Intensity cross-sections are most self-similar in the magnified self-conjugate plane.

Experimental verification of fractal laser modes predicted in 1999.

Abstract

Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of Nature, and so it came as a surprise when, in 1998, transverse intensity cross-sections of the eigenmodes of unstable canonical resonators were predicted to be fractals [Karman et al., Nature 402, 138 (1999)]. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity cross-sections through the lowest-loss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. We also advance the existing theory of fractal laser modes, first by predicting 3D self-similar fractal structure around the centre of the magnified self-conjugate plane, second by showing, quantitatively, that intensity cross-sections are most self-similar in the magnified self-conjugate plane. Our work offers a significant advance in the understanding of a fundamental symmetry of Nature as found in lasers.