Fractal Light From Lasers

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 [G. P. Karman et al., Nature (London) 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 three-dimensional self-similar fractal structure around the center of the magnified self-conjugate plane and 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.