The Eikonal ray equations in optical fibers

The traditional methods for the characterization of ray trajectories in nonhomogeneous media are based on the Eikonal equation valid in the region of geometrical optics. To apply Eikonal theory to fiber optics requires a fairly extensive use of vector calculus and geometry. Alternatively, through a simple correspondence rule, and a few intuitive guidelines for relating rays to waves, an equivalent set of trajectory equations can be obtained. This approach results in the Eikonal equations for the space evolution of optical fiber rays which are expressed in terms of the mode analysis invariants, azimuthal mode number, and optical waveguide propagation phase constant.