  Luneburg lens is a symmetric gradient-index lens with a refractive index that
increases from the outer surface to the center in a radial manner. It has the
ability to focus and collimate waves, which makes it useful for energy
harvesting, waveguiding and as a component in transducers. An ideal Luneburg
lens should be easy to fabricate, has broadband and omnidirectional
characteristics, as well as a focal length that can be easily tuned. However,
existing structural Luneburg lenses based on phononic crystals can hardly
achieve these requirements. Here, we propose an alternative structural Luneburg
lens which has a refractive index that varies smoothly with its radial distance
as a result of a changing thickness. Theoretical calculations, numerical
simulations and experimental measurements of flexural wave propagation through
the lens showed that flexural wave focusing can be obtained inside, at the edge
and outside of the variable thickness lens for different frequencies and
propagation directions. Flexural wave collimation was also demonstrated when a
point source was placed at the respective focal points for each lens.
Furthermore, it was shown that flexural waves that were focused onto a
piezoelectric energy harvester by the Luneburg lens can lead to a significant
increase in the harvested voltage compared to that obtained without focusing.
