Sonic crystal lenses that obey Lensmaker's formula

This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed using the standard multiple scattering theory, and the band structures are computed by the plane-wave expansion method. It is shown that properly arranged arrays not only can behave as acoustic lenses, but also the focusing effect can be well described by Lensmaker's formula. Possible applications are also discussed.