Generalization of Brittingham’s localized solutions to the wave equation

Abstract. A family of localized solutions of Brittingham’s type is constructed for different cylindric co-ordinates. We use method of incomplete separation of variables with zero separation constant and, then, the Bateman transformation, which enables us to obtain solutions in the form of relatively undistorted progressing waves containing two arbitrary functions, each of which depends on a specific phase function. PACS. 43.20.Bi Mathematical theory of wave propagation – 41.20.Jb Electromagnetic wave propagation; radiowave propagation The purpose of this Rapid Note is generalization of the family of Brittingham’s localized solutions to the wave equation known as the focus wave modes. In fact, they are presently represented by three specic solutions: Gauss [1], Hermite-Gauss [2], and Bessel-Gauss [3] modes. Most of reported Brittingham’s type solutions [4{6] reduces to Ψ (; ’; z; ) = meimϕ (z − )m+1 v z +