Numerical Solution of Full‐Wave Equation With Mode Coupling

Abstract

A new method for the numerical solution of the wave equation governing the propagation of electromagnetic waves in a horizontally stratified, inhomogeneous, anisotropic medium is described. The wave equation is a homogeneous set of four linear differential equations of the first order. Four linearly independent solutions are derived. The medium is divided into a number of thin horizontal subslabs. Within a subslab, the propagation coefficient matrix is assumed to vary linearly with respect to height. Under this assumption, the modification of solutions from one height to another is expressed in power‐series form, and the inhomogeneity effect in a subs lab is examined. This, together with the extraction of the phase memory integral from the solution, allows an increase in the integration step size by a factor of 10 over that traditionally used. During an ordinary integration for an inhomogeneous medium a degradation occurs in the degree of linear independence among special solutions. This cause is analyzed. To obtain a complete set of special solutions with good linear independence, a technique is developed suitable for general application. This method has been programmed for computer calculation. The resultant wave fields and wave polarizations for the independent modes are shown for a model ionosphere. The resultant wave is described as a “scrambling” of four characteristic waves. The “scrambling” state is illustrated at each height.