Parabolic propagation-invariant optical beams

We present in this work the propagation-invariant optical fields (PIOFs) which are exact solutions of the Helmholtz equation. These solutions are given in parabolic coordinates and have an inherent parabolic geometry. Our new approach allowed to obtain the proper solutions that describe the whole family of parabolic PIOFs in a straightaway manner. Based on the McCutchen theorem we have also identified the corresponding angular spectrum, which common to all PIOFs, lies on a ring. Another interesting features of these beams is that their order is not quantised as occurs for the Bessel and Mathieu beams and that they have a definite parity.