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 by urn:x-wiley:00486604:media:rds618:rds618-math-0001 where c(y, z) is the wave velocity, C0 and ϵ0 are constants, ϵ2(z) is an arbitrary function of z, and ϵ corresponds to the dielectric constant for electromagnetic waves. It has been shown that the intensity A02 of the wave is in general given by urn:x-wiley:00486604:media:rds618:rds618-math-0002 where E0 is a constant, yo is a constant, F is an arbitrary function of [y/yoƒ(z)L], and ƒ(z) is a dimensionless beam‐width parameter given by urn:x-wiley:00486604:media:rds618:rds618-math-0003 in the geometrical optics approximation. The nature of the variations of ƒ with z has been discussed for some simple profiles of ϵz(z) in the geometrical optics approximation; diffraction has also been taken into account when the beam (F) is Gaussian.