Diffractive origin of fractal resonator modes

The modes of unstable optical resonators possess fractal character. In this paper, the fundamental question of how and why fractals originate in one of the simplest linear optical systems is addressed. The answer is related to the fact that unstable resonator modes consist of a superposition of Fresnel diffraction patterns with effectively random phases. A connection is established between the mode eigenvalues and their fractal dimensions, and the consequent prediction that higher-order modes should exhibit lower fractal dimension is confirmed by numerical demonstration