Wave beam with minimum divergence in a smoothly inhomogeneous medium

We consider acoustic wave beams propagating in a smoothly inhomogeneous medium along a given reference ray. It is shown that in the aberration-free approximation, a Gaussian beam diverges with distance (on the average) less than any other beam with the same initial width. This result has been obtained by solving a variational problem that is similar to the well-known quantum-mechanical problem of seeking the quantum state with minimum uncertainty (coherent state). An example of the beam with minimum divergence in the realistic model of a deep-ocean acoustic waveguide is considered. An approximate analytical estimate for the amplitudes of normal modes forming the beam is obtained.