  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.
