Perfect focusing of scalar wave fields in three dimensions.

A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analysed.