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In this paper, a synthesis procedure to design thin broad-band fragmented aperture array elements is described. The arrays are assumed to be infinite periodic and the elements consist of a conducting pattern etched on a dielectric backed by a groundplane. A genetic algorithm (GA) is used to design the conducting pattern, relative permittivity, and thickness of the dielectric substrate with respect to array scan and bandwidth performance. The fitness function in the GA is evaluated using a finite-difference time-domain code with periodic boundary conditions. For a substrate thicker than about 0.1 λL (λL= wavelength at the lowest frequency in the frequency band investigated), it was found that a bandwidth of at least one octave can be obtained for arrays scanned within 45° from broadside.