The relationship between rays and modes in a waveguide with large‐scale inhomogeneities

Abstract

The well‐known results of Tindle and Guthrie, Felsen, and other authors on studying the relationship between rays and normal modes in a range‐independent waveguide are generalized for a waveguide with large‐scale inhomogeneities of refractive index. It is shown that in complete analogy with the range‐independent case, the raylike behavior of a cluster of normal modes takes place. The notion of Fresnel zones for normal modes is introduced, which is analogous to the usual Fresnel zones introduced for rays. Using Fresnel zones for modes one can simplify the analysis of mode scattering at large‐scale inhomogeneities (such as an opaque screen or an inhomogeneity of refractive index) in a waveguide. Simple and statistical averaging‐suited formulas are deduced to calculate mode amplitude variations under scattering at inhomogeneities of refractive index, which are ‘‘mode analogues’’ of the formulas of geometrical optics and those of the Rytov method.