Orbitalization structure of random light beams

Abstract It is demonstrated that at a given cross-section and radius, a scalar, wide-sense stationary, beam-like optical field carrying orbital angular momentum (OAM) in L states can be uniquely characterized by the degree of orbitalization and the orbitalization ellipse pertaining to a plane in the L -dimensional functional space spanned by basis <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:msup> <mml:mtext>e</mml:mtext> <mml:mrow> <mml:mtext>i</mml:mtext> <mml:mi>l</mml:mi> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:msup> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> </mml:math> , with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> </mml:math> and φ being the OAM index and the polar angle, respectively. This characterization bears similarities with that in polarization optics.