Abstract
Guided by the aim to construct light fields with spin-like orbital angular momentum (OAM), that is light fields with a uniform and intrinsic OAM density, we investigate the OAM of arrays of optical vortices with rectangular symmetry. We find that the OAM per unit cell depends on the choice of unit cell and can even change sign when the unit cell is translated. This is the case even if the OAM in each unit cell is intrinsic, that is independent of the choice of measurement axis. We show that spin-like OAM can be found only if the OAM per unit cell vanishes. Our results are applicable to the z component of the angular momentum of any x- and y-periodic momentum distribution in the xy plane, and can also be applied other periodic light beams, arrays of rotating massive objects and periodic motion of liquids.
Highlights
At the heart of angular momentum lies rotation: angular momentum is conserved due to the isotropy of space; the conjugate variable in the quantummechanical uncertainty pair to angular momentum is rotation angle; and, rotating objects have angular momentum
In other light beams the phase structure rotates uniformly about the beam axis, which is marked by a phase singularity; these correspond to orbital angular momentum (OAM) states [2]
From the results presented in this paper we conclude that this is not possible with strictly rectangularly periodic light beams
Summary
At the heart of angular momentum lies rotation: angular momentum is conserved due to the isotropy of space (i.e. invariance under rotations); the conjugate variable in the quantummechanical uncertainty pair to angular momentum is rotation angle; and, rotating objects have angular momentum. In other light beams the phase structure rotates uniformly about the beam axis, which is marked by a phase singularity (optical vortex line); these correspond to orbital angular momentum (OAM) states [2]. A light beam in which both the phase structure and the electric field vectors at every point rotate uniformly corresponds to a total angular momentum state; we do not consider such states here. This rotation of the light itself is reflected in the mechanical effects the light’s spin and OAM.
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