Acoustic Flux Density for Ray Propagation in Discrete Index Media and in Gradient Index Media

Abstract

General formulas are derived for the energy per unit area per unit time (flux density) over an arbitrary receiver surface for acoustic ray propagation in discrete index media and in gradient index media. The equation of the deflected ray coupled with the equation for the deflecting surface and the equation for the receiver surface provide a transformation which maps an element of deflecting area onto the receiver surface, thereby enabling one to calculate the flux density over the receiving surface. A formula for the flux density along a ray path is obtained as a special case. An equation for the caustic surface is obtained from the latter. As an example, flux density contours are calculated over a planar surface for plane-wave acoustic radiation reflected from a sphere embedded in a gradient index medium.