Analytic Solution of Ray Equations in Cylindrically Inhomogeneous Guiding Media 1: Meridional Rays

Abstract

Analytic methods are employed to solve the meridional ray equations for propagation in inhomogeneous cylindrical systems such as gas lenses and GRIN rods, which focus rays by virtue of a gradual radial decrease in refractive index. Digital computer programs are used to carry out the necessary algebraic manipulations, and the results apply for arbitrary index variations and initial conditions. Comparisons are made with known exact solutions.