We reveal the geometric structure existing on segregation of a pair of orbital angular momentum (OAM) states from the total random light beam and introduce new quantities, to the best of our knowledge, for its characterization. In particular, the degree and the ellipse of orbitalization are introduced in analogy with those in the polarization theory. Free-space propagation of these quantities is illustrated by numerical examples. The limiting case of a deterministic light beam is also separately discussed.
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