Path-integral derivation and analysis of approximate directed wave propagators

In this paper we derive an approximate high-frequency Green´s function (propagator) for directed waves propagating in an inhomogeneous medium. The analysis is based on a path integral formalism incorporating the ray concept into a full-wave description of the diffraction effects. Although a 2D version of the propagator was obtained earlier by using another method, the procedure based on the path integral technique is conceptually much more simple, and also clarifies the physical nature of the approximations performed in the derivation of final result.