Geometric Phase Associated with Mode Transformations of Optical Beams Bearing Orbital Angular Momentum

Abstract

We present direct measurements of a new geometric phase acquired by optical beams carrying orbital angular momentum. This phase arises when the transverse mode of a beam is transformed following a closed path in the space of modes. The measurements were done via the interference of two copropagating optical beams that pass through the same interferometer parts but acquire different geometric phases. The method is insensitive to dynamical phases. The magnitude and sign of the measured phases are in excellent agreement with theoretical predictions.

Topological phase structure of entangled qudits

“…[3,4] and experimentally demonstrated in Ref. [5] where a Poincaré sphere representation was used for first order paraxial modes. This representation was also used to discuss the geometric phase conjugation in an optical parametric oscillator [6].…”

Geometric phase in optics and angular momentum of light

“…A Poincare-sphere equivalent for OAM states was proposed by Padgett and Courtial [11], and rotational frequency shift in a rotating mode converter for OAM bearing beams was interpreted in terms of this GP. In a recent paper, Galvez et al [12] claim to have made first direct measurement of GP in the mode space. The meaning of angular momentum exchange remains obscure in the cited works though we clearly related it with the angular momentum holonomy in [5], and gave a plausibility argument for the gauge theoretic approach for the Pancharatnam phase in [13].…”

“…In the examples that differ on the existence of GP according to our analysis and that of [9], the experiments of the kind carried out by Galvez et al [12] offer a feasible experimental test.…”

“…Note that angular momentum flux is incorporated in this formulation. Since Galvez et al [12] do not measure this holonomy their claim regarding angular momentum exchange is unfounded [32].…”

“…vertical linear polarization used in [12], it would be interesting to measure the GP of polarized Gaussian beam undergoing both polarization and k-space (or relevant mode space) cycles. This kind of experiment may give useful information on the physical nature of angular momentum tensor as well as on geometric phase.…”