An ultra-wide bandwidth acoustic transducer may include multiple layers, including an inner piezoelectric layer, a polymer coupling layer and an outer piezoelectric layer. The polymer layer may be located between, and may be bonded to, the inner and outer piezoelectric layers. The transducer may have multiple eigenfrequencies of vibration. These eigenfrequencies may include primary resonant frequencies of the inner and outer piezoelectric layers respectively and may also include resonant frequencies that arise due to coupling between the layers. An acoustic backscatter system may employ such a transducer in backscatter nodes as well as in a transmitter. The multiple eigenfrequencies may enable the system to perform spread-spectrum communication at a high throughput. These multiple eigenfrequencies may also enable each backscatter node to shift frequency of an uplink signal, which in turn may enable the system to mitigate self-interference and to decode concurrent signals from multiple backscatter nodes.