An acoustic resonator includes a substrate, a first electrode, a layer of piezoelectric material, a second electrode, and a recessed region. The substrate has a first surface. The first electrode is adjacent the first surface of the substrate. The layer of piezoelectric material is adjacent the first electrode. The second electrode is adjacent the layer of piezoelectric material. The second electrode has a second electrode perimeter that is shaped as a polygon. The recessed region is adjacent the second electrode. The recessed region has a shape defining a recessed region perimeter. The recessed region perimeter is recessed relative to the second electrode perimeter.