Virtual Source of a Swallowtail Beam

Abstract

By applying a virtual source method, the exact and the paraxial solutions of the Swallowtail beams (SBs) that are governed by the inhomogeneous Helmholtz equation are introduced. The paraxial SBs generated experimentally possess both self-accelerating and self-focusing features. The parameters controlling the field distributions are discussed in theory. From the spectral representation of the Swallowtail wave, in the appropriate limit, the first four terms of the nonparaxial correction series for the (1+2)-dimensional Swallowtail waves that simplify to the SBs are obtained.