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 o f the simplest linear optical systems is addressed. The answer is related t o the fact that unstable resonator modes consist of a superposition of Fres nel diffraction patterns with effectively random phases. A connection is es tablished between the mode eigenvalues and their fractal dimensions, and th e consequent prediction that higher-order modes should exhibit lower fracta l dimension is confirmed by numerical demonstration. (C) 2001 Elsevier Scie nce B.V. All rights reserved.