Focusing Properties of Bicylindrical Acoustic Lenses

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This theoretical report concerns the focusing of a plane progressive acoustic wave by a bicylindrically-curved lens. It was assumed that the lens was made of polymethylmethacrylate (PMMA) and was submerged in water. The analytical approach that is based on full-wave theory began with expanding an incident plane wave into cylindrical waves to satisfy appropriate boundary conditions at an interface between the water and the lens. The continuity conditions of displacement and stress at the interface may determine the generation of longitudinal and shear waves in the lens. Lens-aperture effects on focused field performance were taken into account by confining the incident wave to the region within the aperture. The Rayleigh integral associated with the particle velocity on the exit interface of the lens enabled us to evaluate the entire sound field behind the lens. Numerical examples demonstrated no significant influence on the fields near the focus, even when the shear wave generation was included in the theory. Wave diffraction due to a finite lens aperture, however, became a major effective factor in beam focusing.

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