Directivity is essentially a measure of a sonar array's beamwidth that can be obtained in a spherically isotropic ambient noise field; narrow array mainbeam widths are more directive than broader mainbeam widths. For common sonar systems, the directivity factor (or directivity index) is directly proportional to the ratio of an incident acoustic trace wavelength to the sonar array's physical length (which is always constrained). Increasing this ratio, by creating additional trace wavelengths for a fixed array length, will increase array directivity. Embedding periodic structures within an array generates Bragg scattering of the incident acoustic plane wave along the array's surface. The Bragg scattered propagating waves are shifted in a precise manner and create shorter wavelength replicas of the original acoustic trace wavelength. These replicated trace wavelengths (which contain identical signal arrival information) increase an array's wavelength to length ratio and thus directivity. Therefore, a smaller array, in theory, can have the equivalent directivity of a much larger array. Measurements completed in January 2015 at the Naval Undersea Warfare Center's Acoustic Test Facility, in Newport, RI, verified, near perfectly, these replicated, shorter, trace wavelengths.