10 - Ray tracing in a loss-free stratified medium

Summary

Introduction

The term ‘ray’ was used in § 5.3 when discussing the field of a radio wave that travels out from a source of small dimensions at the origin of coordinates ξ, η, ζ in a homogeneous medium. The field was expressed as an integral (5.29) representing an angular spectrum of plane waves. The main contribution to the integral was from ‘predominant’ values of the components n_ξ, n_η of the refractive index vector n such that the phase of the integrand was stationary for small variations δn_ζ, δn_η For any point ξ, η, ζ there were one or more predominant values of the refractive index vector n, such that the line from the origin to ξ, η, ζ was normal to the refractive index surface. Each predominant n defines a progressive plane wave that travels through the whole of the homogeneous medium.

Instead of selecting a point ξ, η, ζ and finding the predominant ns, let ns choose a fixed n and find the locus of points ξ, η, ζ for which this n is predominant. For a homogeneous medium this locus is called the ‘ray’. The arguments leading to (5.31) still apply and show that it is the straight line through the origin, in a direction normal to the refractive index surface at the point given by the chosen n.