Confinement of electromagnetic radiation in cylindrical symmetry systems

We considered a cylindrical symmetry system where the refractive index (n(ρ, ν)) varies with the distance from the cylinder axis (ρ). We apply the Fermat's extremal principle in the framework of the geometrical optics to show that radiation traveling through the system could be confined in it. For a given n(ρ, ν), a confinement region can be obtained in the ρ0α plane, ρ0 and α   being two parameters characterizing a given ray. Our simple criterion given by the expression ρ2n2(ρ)=[n2(ρ0)sin2α]ρ2+[ρ02n2(ρ0)cos2α] may be used to improve the design of optical devices.