Characterization of vector diffraction-free beams

It is observed that a constant unit vector denoted by $\mathbf{I}$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $\mathbf{I}$-dependence of the longitudinal component of diffraction-free beams is also discussed.