Focusing of Waves in Ducts

This paper presents an investigation of the propagation of cylindrical waves (the field being independent of x) along the z direction inducts described bywhere c(y, z) is the wave velocity, C 0 and ϵ 0 are constants, ϵ 2 (z) is an arbitrary function of z, and ϵ corresponds to the dielectric constant for electromagnetic waves. It has been shown that the intensity A 0 2 of the wave is in general given bywhere E 0 is a constant, y o is a constant, F is an arbitrary function of [y/y o ƒ(z)L], and ƒ(z) is a dimensionless beam‐width parameter given byin the geometrical optics approximation. The nature of the variations of ƒ with z has been discussed for some simple profiles of ϵ z (z) in the geometrical optics approximation; diffraction has also been taken into account when the beam ( F ) is Gaussian.