An energy-depleted optical or particle beam is generated, transformed into a beam of converging annular cross section, and directed along the same axis as a primary beam. The energy-depleted beam intersects with the primary beam in a tapered annular region in which the two beams destructively interfere, because their wave intensities are adjusted to be equal and their phases are adjusted to be opposite (180 degrees apart). The region of destructive interference effectively compresses and focuses the primary beam to produce a spot size substantially smaller than any spot size attainable using conventional, diffractively limited, optics.