Variational Principle for Optical Phase

Abstract

{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in the far field. Variational principle provides the necessary and sufficient conditions for at least the $local$ $maximum$ of the $beam$ $propagation$ $functional$. The wavefront shape is obtained as an exact solution of nonlinear integral equation. }