Abstract
The wave theory for an underwater Luneburg lens is discussed in terms of a generalized wave equation, which differs from the ordinary wave equation in that it contains a term involving the gradient of the material density of the lens. We then consider the special case where, to a first approximation, the density of the lens has a constant value equal to that of water. This case is of some importance since it corresponds to the compliant tubing lens built and tested by W. J. Toulis [J. Acoust. Soc. Am. 35, 286 (1963)]. For this special case, we determine the analytic solution of the wave equation when the lens is being irradiated by plane waves, and then present the results of a numerical evaluation of that solution. In particular, we calculate the acoustic pressure field along the axis of the lens and the pressure receiving patterns. These results give us the gain and beamwidths for the range 1 ⩽ k0a ⩽ 30 (k0 the wavenumber in water, a the radius of the lens).
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