Supergrowth in speckle patterns

Supergrowth occurs when the local amplitude growth rate of a wave is greater than that predicted by the band limit. While generating supergrowth on demand requires precise source modulation, we demonstrate that supergrowth occurs naturally in a sum of random plane waves. We measure the supergrowing fractional area of transverse, monochromatic, fully developed speckle patterns. For speckle with a disk spectrum, we find that the average fractional supergrowing area approaches 20%. We compare the supergrowing and superoscillating fractional areas and find great similarity in behavior. Our results inform on the ubiquity of superphenomena in speckle patterns and are relevant to imaging and estimation.