Fractal modes of unstable lasers with polygonal and circular mirrors

The lowest-loss modes of unstable lasers are fractals, emerging asymptotically in the limit of high Fresnel number. The fractality depends on the shape of the feedback mirror. An explicit asymptotic theory can be constructed for the lowest-loss mode, in terms of a superposition of successively magnified edge waves. For polygonal mirrors, the superposition is anisotropic, and gives rise to a mode \u(x,y)\ whose graph is a surface with fractal dimension 3, consistent with previous analysis for strip (one-dimensional) mirrors. For circular mirrors, the lowest-loss mode is dominated by focusing of edge waves at the centre of the mirror; the resulting superposition of circular waves gives rise to a mode \u(r)\ whose graph is a curve with fractal dimension 3/2. (C) 2001 Elsevier Science B.V. All rights reserved.