Spontaneous spatial fractal light patterns in simple nonlinear cavities

Nature furnishes us with a wide variety of patterns that, fundamentally, tend to fall into one of two categories: simple (characterized by a dominant scale-length or “size”) or fractal (containing comparable levels of detail spanning decimal orders of scale). The physical mechanism that drives the emergence of simple patterns in reaction-diffusion models was originally identified by Alan Turing in his seminal work from over 60 years ago [Phil. Trans. R. Soc. Lond. B vol. 237, pp. 37 (1952)]. More recently, our Group proposed that a generalization of that mechanism – multi-Turing instability – could give rise to spontaneous fractal patterns in generic wave-based nonlinear systems [Huang & McDonald, Phys. Rev. Lett. vol. 95, art. no. 174101 (2005)]. In this presentation, we will provide an overview of our latest research into the fractal-generating properties of two simple nonlinear optical systems: the ring cavity and the Fabry-Perot cavity. Laser light is fired into a cavity (constructed from a sequence of mirrors), whereupon it interacts with a thin slice of nonlinear material. After completing a transit, the light partially recombines with the pump light and is fed back into the cavity ad infinitum (an optical feedback loop). We have also taken the first steps toward understanding spontaneous fractal patterns in systems with a finite light-material interaction length, where the slice is replaced by a bulk medium. This conceptual leap, which requires one to take a more complete account of small-scale (nonparaxial) spatial structure in the circulating light, has not previously been addressed in the literature.