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Focusing Ultrasonic Waves Using a Biconcave Lens: Normal Incidence on the Lens

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In this paper, we theoretically and experimentally investigated the focusing of plane progressive waves and directive beams using a spherically curved biconcave lens at normal incidence. The lens is made of acrylic resin or polymethylmethacrylate (PMMA) and is submerged in water. Our analytical approach is based on a classical theory that expands an incident wave into spherical waves to satisfy boundary conditions conveniently at the spherical interface between the water and the lens. The continuity conditions of displacement and stress at the interface determine the generation of longitudinal and shear waves in the lens. Additionally, sound absorption in the lens is considered. The Rayleigh integral associated with the particle velocity on the exit interface enables us to evaluate all sound fields behind the lens. Numerical examples demonstrate that no significant effect appears in the fields near the focus rather than in the pre-focal and post-focal regions even when the shear wave generation is included in the theory. To verify the usefulness of the present theory, we conducted experiments in water using a directive beam emitted from a 1-MHz circular-aperture transducer. It has been demonstrated that the agreement between the theory and the experiment is generally excellent.

Document Type: Research Article


Publication date: January 1, 2008


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