Orbitalization ellipse of a light beam

A scalar, harmonic beam-like field possessing an arbitrary number of orbital angular momentum (OAM) components is shown to trace an ellipse, termed here the orbitalization ellipse, at a given transverse cross section and radius, in the space spanned by the spiral OAM basis. The plane and the structure of the ellipse can be readily found by constructing its conjugate semi-diameter vectors from the OAM components.