On Fresnel optics problems with fractal boundaries: apertures, screens, and unstable resonators James Christian (Salford) The diffraction of scalar plane waves by complex apertures is a well-known configuration in optics, with the overwhelming majority of experiments and analyses performed in the Fraunhofer (far field) limit. Here, we will show how the two-dimensional Fresnel integral can be deployed to solve a wide class of propagation problem involving irregular (or `rough') hard-edged boundaries comprising hierarchies of straight-line segments. By transforming the area integral into a circulation, exact expressions can be obtained for near-field diffraction patterns from fractal-type apertures and, by exploiting Babinet's principle, for their complementary screens. These patterns are formulated mathematically using a generalization of Young's edge waves. The single-aperture Fresnel patterns provide essential basis functions for modelling geometrically-unstable optical resonators (linear systems with inherent magnification and periodic aperturing that naturally possess scale-free eigenmodes). We will conclude with a survey of recent results from virtual-source computations for cavities whose small feedback mirror has a boundary corresponding to increasing iterations of some classic self-similar curves (e.g. snowflakes, pentaflakes, Gosper islands, and Cesaro fractals).