Unstable canonical resonators can possess eigenmodes with a fractal intensity structure [Karman et al., Nature 402, 138(1999)]. In one particular transverse plane, the intensity is not merely statistically fractal, but self-similar [Courtial and Padgett, PRL 85, 5320 (2000)]. This can be explained using a combination of diffraction and imaging with magnification greater than one.
Here we show that the same mechanism also shapes the intensity cross-section in the longitudinal direction into a self-similar fractal, but with a different magnification. This results in three-dimensional, self-similar, fractal intensity structure in the eigenmodes.