Near-field electromagnetic devices having an opaque metallic screen with a fractal iterate aperture are provided. More specifically, the aperture is obtained by application of a self-similar replacement rule to an initial shape two or more times. Alternatively, the aperture can be obtained by application of a self-similar replacement rule one or more times to an initial C-shape. Such apertures tend to have multiple transmission resonances due to their multiple length scales. Fractal iterate apertures can provide enhanced transmission and improved spatial resolution simultaneously. Enormous improvement in transmission efficiency is possible. In one example, a checkerboard fractal iterate aperture provides 1011 more intensity gain than a square aperture having the same spatial resolution. Efficient transmission for fractal iterate apertures having spatial resolution of λ/20 is also shown. The effect of screen thickness and composition can be included in detailed designs, but do not alter the basic advantages of improved transmission and spatial resolution provided by the invention.