Three-dimensional, self-similar, light in unstable canonical optical resonators

TL;DR

This paper demonstrates that unstable canonical optical resonators produce three-dimensional self-similar fractal structures in their eigenmodes, extending previous two-dimensional findings by showing the combined effects of imaging and diffraction in all three spatial dimensions.

Contribution

It introduces the concept of three-dimensional self-similar fractal eigenmodes in unstable optical resonators, revealing the simultaneous imaging and diffraction effects in longitudinal and transverse directions.

Findings

Eigenmodes exhibit 3D fractal structures

Self-similarity occurs in all three spatial dimensions

Imaging and diffraction effects are combined longitudinally and transversally

Abstract

The eigenmodes of unstable canonical optical resonators possess fractal structure in their transverse intensity cross-sections [Karman et al., Nature 402, 138 (1999)]. In one particular plane, the magnified self-conjugate plane, this structure can be explained in terms of a combination of imaging and diffraction [Courtial and Padgett, PRL 85, 5320 (2000)]. Here we show that this combination of imaging and diffraction simultaneously occurs in the longitudinal direction, resulting in three-dimensional self-similar fractal structure around the centre of the magnified self-conjugate plane.