  Supergrowth refers to the local amplitude growth rate of a signal being
faster than its fastest Fourier mode. In contrast, superoscillation pertains to
the variation of the phase. Compared to the latter, supergrowth can have
exponentially higher intensities and promises improvement over
superoscillation-based superresolution imaging. Here, we demonstrate the
experimental synthesis of controlled supergrowing fields with a maximum growth
rate of ~19.1 times the system-bandlimit. Our work is an essential step toward
realizing supergrowth-based far-field superresolution imaging.
